Hi everyone, Joe for jazzy's casebreaks.com coming at you with 2019 Panini contenders football six-box half-case random team a break number one No vet common ship all 32 teams are in obviously. We're chasing Kyler's this is last year's draft class class Drew Locke DK Metcalf Josh Jacobs and a ton of other players that we can chase as well It's a random team break big. Thanks all of these folks for getting into the action You have a little rooftop next to your name. I mean you won that spot in that filler break We did one of those Donner's football packs There's all 32 teams. Let's roll it. Let's randomize it four and a four eight the hard way one two three four five six seven and Eighth and final time After eight we've got Jigar Darjee down to Oliver Soria in the spot that he won Let's put all those names in here four to four hard eight for the teams one two three four five six seven and Eighth and final time after eight. We got the New York football Giants down to the Seattle Seahawks Now remember to trade at your own risk the trading is allowed while I Actually take a look at this case and see which half I'm gonna do All right, so Darjee you got the Giants Adam with the Ravens Jake with the Cowboys EA with the Cardinals Sean with Washington Denver and Atlanta Nicholas with the Patriots Matthew with the Packers Karen with the Chiefs have been with the Browns Cory with Jags EA with the Raiders nice Josh Jacobs hunting Adam with the Bengals Mike with the Panthers Jake with the Texans of any with the Titans Ryan With the Bears and Vikings Adam with the Bills and Lions Clay with the Buccaneers Ben with the Steelers David with the Eagles Sean with the Rams Bill with the Colts Sean with the Niners Mike with the Saints Adam gets his Jets Alex with the Charters Matthew with the Dolphins and Oliver with the Seattle Seahawks All right, so let's get all that on one page and sort by column B If that is a little might be a little too small if you're watching on a phone or something But if you need to see your teams again, let me know now while you're considering trades Let's consider which half we're gonna do right here So 2019 contenders football. Yeah, there it is. It's a pretty desirable set as most of you know in contenders is it's got to be right up there with with prism and select maybe now mosaic, but You want like the key rookies along with NT of course, but if you're looking for People's rookie cards. They're like, hey that means a lot of times are talking about this the contenders rookie. All right, so Six on the left left side six on the right side right here. Let's select a die Let's select that one And we'll go one two three for the left side and four five six for the right side And it's gonna be one so we're gonna go left side right here. So this side Right over here Will be for break two which is on the website right now RT to random team to That all that we can run this back tonight, too We just have to fill up the straight-up spots and one filler pack and that is that all right any trades Bears up for trade Keep the video running just for a little bit while the trade window is going on Adam Copperman's reporting that the Jets released levy on Bell. He wishes that Adam Gase would go along with him Where's levy on where's levy on Bell gonna go? He's healthy now, right? The Chargers maybe could use levy on Bell No, so strong Chesapeake Austin Eckler's out for four to six weeks Doesn't care. All right Who could use a levy on Bell? He needs a little just change of scenery. All right. It looks like no offers for the bear. So let's close it up TWC means trade window close. Let's print and rip got Tennessee up 2810 on the Buffalo bills There's six packs a six cards were packed 18 packs brought looking at five autographs including one on card Cracked ice is what we're looking for among others Lions. Yeah, that's what Sean Jaspy just said lions could be interesting Who fills that roster spot Adam? Is there like a rookie being elevated into that spot? Oh Michael P. Rhine getting those touches, but he's already on the roster, right? doesn't Wouldn't there be an extra spot available? Yeah, P. Rhine's already on Adam Adams. I guess I'm sure someone awesome Maybe mims coming off the IR and then he fills that slot so We'll see what happens Can I play wide receiver? No For a second, I thought I might and then I realized no I was like I could be like a like an Edelman type my best chance would maybe be would maybe be I Guess a linebacker Where maybe I wouldn't have to cover anybody, but I would just kind of run towards the offensive line And try to climb over linemen and try to get to the quarter every the only thing I'd be able to do Just kind of be a waste of space out there But as long as I'm just not in the way and I'll just continue to to blitz the quarterback at all times Realistically, that's all I would do was just would just kind of Crawl towards just try to You know, I'm a small guy. Maybe weave in through in between a In between a lineman, maybe maybe they won't see me like I'm a small mouse underneath the feet of elephants Just scamper around their their tree trunk legs All right, there's a Josh Oliver and Quincy Williams both on the same team right there 57 out of 75 That'll be for the Jags Corey. I Can do it says J-Dog just don't go across the middle. I just don't think I have the I don't think I could catch like a I don't know. I'm sure flacco and Sam Darnold throw They throw pretty hard Yeah, I might hurt my breaking hands my case breaking hands I'd have like a crook. I'd have a that an index finger pointing the other way Those passes might be too hot for me to handle. No kicker kicker punter. No, I can't kick the ball long snapper. Oh, okay, I Might be able to long snap That might be the only NFL job like if they just how's your long snapper at him? How's the Jets long snapping situation their first autograph? Deontay Harris Saints that'll be for Mike G and There's Jaguars Josh Allen nice Good pass rusher here speaking of rushing the quarterback that goes to Corey and the Jaguars GT is thinking Levy on bell to the bills no, no issues on the punting side because Adams pointing out that they do punt often so they've gotten a lot of practice. Here's Tony Pollard on Card autograph for the Cowboys. Oh Can I don't want to talk about it, but I don't think we've talked about it today poor Dak Prescott That with that injury was brutal That goes to the Cowboys Jake Stacy with that I haven't seen an injury like that In a long time usually it's like obscured by another player or you can't really get a clean look at it But he was in the open field. It was It made my stomach turn a little bit rookie ticket Autograph Kailin Saunders going to Karen and the Chiefs and then me being me I had to look up on YouTube What exactly happened? Like like like like like a doctor on YouTube there's Drew sample and there was like a video I forget who it was sorry for not crediting this but there's a doctor on YouTube. There's Drew sample for the Bengals Adam Cupperman He the doctor showed what happened it wasn't it it looks like it's it hurt a lot And I guess the scary thing is is the is the the blood vessels. I think is really where the scary part is What's that No, they're not gonna They're not gonna do it. I will I will cry. I will cry if if they actually come back Sure, sure, I mean with that bullpen though Raise bullpen pretty good see Dak Prescott's ankle I'll show you guys what it what it looks like Your your tibia bone and your I looked at Your tibia and your fibula lock around your ankle, right? There's like a little bone that connect on your ankle. It's like a tie fighter, but Connects to your ankle, right? Like and your foot sticks out this way, right? Let's let's say your foot sticks out this way All right, so these are your toes right here this part snapped and that part came out That's what it is And that part flopped out so there's like these bones that connect there that part snapped that part snapped This part slipped slips out your ankle sort of joint there slips out Yeah, who's this kind of the same thing to those that connect there and there's ligaments there and blood vessels there Well Yeah It's not the same right But you know, you know cowboys friends when Carson got targeted in the playoffs was yeah, yeah No, it's it's Like the kind I mean allegedly the the Cowboys front office I think Jerry Jones's son was like oh that's gonna be a big part of our plans You know they didn't pay him No, Zach or Dak was kind of holding out for a bigger deal too, but I don't know I think There's some negotiations on both sides there. So it's just all in all Kind of a terrible situation We'll see how all that shakes out and now this guy Zeke. Hello. I have to carry the load here Here's John Brown to 175 Points sorry We'll randomize those point that usually takes the place of an auto But we'll randomize those points to one person in the break. There's more than one point There's multiple points cards. We'll just collect them as to into one lot and there's Trayvon Mullin jr. It was actually one of the bright spots of that Raiders defense and that win I don't know if defensive back Rookie cards are gonna be skyrocketing anytime soon, but he looked pretty good EA and the Raiders Rex you let me know if he does that one more time Baltimore Ravens Antoine Wesley Ravens Adam Cuperman won that spot. We've got Jacobi Myers Rookie ticket autograph for the Pats that'll go to Nick Stone and a Darius Layton On-card autograph for the New York football Giants That's gonna go to Jigar Gargi with that and the points right there Buckle Bills with a touchdown another five autographs to go got still got three boxes left and the second half of this is In the store if you want to get that going Jasper's case breaks calm Wow dust off your TJ Yelden rookie autographs. He's alone with the touchdown and the two point Throws it away. I actually don't know this rule you guys can a two-point conversion Be Could it be turned over for points? Let's send it to Sean Jaspy with the answer. You think so is it two? For a point because I think you can actually Catch a missed field goal, right if it stays in the field and run it back for three points a missed field goals At touchdown Wow, that's a touchdown if you run it back the other way, right, right, right? Yes, Adam's confirming. Yes, two points at the other team returns it all the way. Gosh You can return a blocked extra point for two. Wow. Those are the wild things in the NFL that Like we almost never see I Think I seen the field goal thing once It was like a 55 yard field goal and it was way short and someone was back there to actually Catch it and bring it back Was it happen? Did happen recently something. Yeah, it was something crazy like that There's Levy on Bell. He just got a he just got released. Who's gonna pick him up? 50 out of 99 this goes to Adam and his jets because he doesn't want this card It'll go into his into his remember when box of cards There's will Harris Rookie ticket Rookie ticket auto for the Lions Adam Kaeperman with this one GT saying was Cramarty that maybe There's Dylan Mitchell for the Vikings. That's gonna go to Ryan Kasin and the Purple people eating team and another pro. Oh, that's Ola BC Johnson Right there. I think did I did he have a touchdown last week? I Thought he was gonna be an MVP contender Adam There's Levy on Bella MVP content. I thought it was I thought it was a great pickup by the Jets There's Ryan burns for Carolina Mike Krasinski with that. I was just like well Darno is a running game now. He's Get a decent receiver and slinging around a little bit Brian burns from Mike once again in Carolina There's another Tony Pollard Rookie ticket autograph another one for the Dallas Cowboys Jake Stacy with that one Three more boxes to go Yeah, they sure did Tyler Jets led that's what Adam was reporting Adam Kaeperman and his jets. That's his team Just let Bell just released him. I guess he was just that bad or either I don't know or just didn't fit with the team And that's enough to get you released on a football team everyone's got to work in concert That's just bad luck all around Adam said when they first opened the sports books in New Jersey He put five dollars on Bell to win the MVP when he was with the Steelers. That was a cease and he sat out Oh, but you also ended up with the Mahomes MVP. That's good. Hiring up a little bit 80 to one on what was what was Levy on massage? Probably better than 80 to one right or shorter than 80 to one I want to say Nick also Was it Lamar Jackson or was it Mahomes? I feel Nick. I feel like Nick also put Put put a little bit on on Mahomes to win the MVP that year Yeah, Bell was probably shorter 20 to one or something like that that makes sense. I mean feel bad for running backs, but It's kind of why like you don't really Unless you get like an Adrian Peterson type Just don't really pay those running backs for that long or for that much because You see so many you see DeMarco Murray just kill it With the Cowboys get signed to Tennessee and then just drops off You see Levy on Bell Kind of sit out for more money this and that and then he gets released by the Jets No Adrian peers is not doing much now in Detroit, but that guy's carved out like a 12-13 year career that's not common for Running backs You know like you just don't see that kind of longevity. He was productive last year Not as a lead back or anything like that, but he was putting in work. He was grinding out Yards when you needed it does he have why does he have to oh is he does he have financial issues? I see Christian McCaffrey to 99 He'll be back soon Christian McCaffrey Mike with that one We got Charles Omaneyu Rookie ticket kind of die cut into that into a like a ticket stop 83 out of 94 that's a cool looking design Texans with that one Jake Stacy Texans looking good in the first game without Bill O'Brien You know that here's Melvin Gordon. I mean he kind of held out a little bit And then was ultimately replaceable and the charge can get a lot of value out of Austin Enkler There's Travis Homer Rookie ticket autograph for Oliver and the Seahawks Yeah, it's looking like Derek Kenra. That's a good point Tyler Brenner looks looking like Derek Henry could be like an Adrian Peterson type like he can You know he can last for a long time. There's Antoine Wesley Another purple bird autograph for Adam and the Ravens and we've got for the Green Bay Packers 11 out of 49 championship ticket autograph Tim Boyle and Rookie of the Year contenders Dwayne Haskins on-card autograph 23 out of 25 Sean Maddock with the Washington football team Dwayne not in a good spot right now, but I don't know still he's still very young Still could use a little marinating still could be a future for him Maybe with Washington probably not but maybe elsewhere if he needs to change a scenery with someone Who wants to maybe Design some place for him see what he can do Yeah, I don't think he can turn in I think so too. I mean I keep getting reminded that That he didn't play too much in college. I don't follow college too closely But I think he only played like a season in college Sounded like he didn't play a lot of games and then made Decide to make the leap to the NFL Maybe the Redskins probably took him a little earlier than they should have but I feel like I don't know Maybe maybe won't work with Juan Rivera. I think he wants his own guy in there, you know eventually Cliff Kingsbury moved Josh Rosen to get his guy. I think most new coaches probably want that opportunity Dwayne Haskins just need to light and this needs to be a backup somewhere to somebody For a couple years or so And then maybe just marinate and turn into What team could use that? Ben Rossburg is not getting any younger. You think the Steelers? Steelers give Dwayne Haskins a shot? Maybe probably not Maybe a lot of weapons on that team chase Claypool went off All right, there's for the blue horseshoes Rock Yasin That'll go to build and the blue horseshoes John what's going on? How are you? And we got Jelani to buy. He's got some nice penmanship there Jelani to buy 46 out of 99 He could be a guest speaker at Jaspie's autograph camp That goes to Adam and the Detroit Lions and Cat team mojo There's Jarrett stittum on card autograph. That's pretty solid Nicholas Stone with the Patriots Still could be the future of that of that team who July's have eyes a local guy That I did not realize And we got Trayvon Wesko for the New York Jets for Adam and His jets and we got Zach Allen for the Cardinals EA with the red birds. All right, so this Raiders card is gonna represent the The randomizer that I'm gonna have to do I know these are the same team, but I think there's a few cards with different teams on them We'll go we'll go left right on that and This will have to do a randomizer for separately because it's numbered 66 out of 75 So that'll be between the Titans That's actually a pretty cool card between AJ Brown the Titans and DK Metcalf Seahawks so that'll be between Vinny and the Titans and And then Oliver and the Seahawks will do that same dice roll As the points right here final five autographs remember we got the second half of this in the store jasky's case breaks calm about 20 some odd spots and One just one filler break. That's it to give away some spots There's Derek Henry with a nine-yard touchdown. I think I actually bench Derek Henry. I just thought this game wasn't gonna happen And then all my guys played on Sunday, so Couldn't put him back in Another difficulty This is just trying to figure out now and there's all sorts of schedule changes now for teams impacted by the teams that had COVID Unexpected by week schedules being pushed around games being postponed to later in the season. It's got another challenge of The pandemic just got to figure out These these starts starts and starts and non-starts Starts and sits All right final box final five autographs good luck everybody Once again second half in the store jasky's case breaks calm if you're watching live Nice Tyler. We're making progress. I love that. I love it That's what I like to hear man. Thank you so much for that look at this Tyler Brenner Looking at the schedule proactively and Realizing that Jason Jaspie is indeed going early tomorrow ladies and gentlemen with gold label baseball Thanks Tyler That's the way it's done ladies and gentlemen. Hopefully everyone can learn from that example 11 no check that 17 out of 75 Tom Brady Patriots edition Nicholas Stone One's just gonna do another 24 hours of raking Although now that we have Sean Jaspie on board might be a little bit easier to do a 24-hour stream next time Actually, technically we're all you know Rex We actually Sean Sean's right if you heard him in the background. There's Julian Love for the Giants There's some nights where we're doing almost 24-hour breaks regularly because Jason will go live like At like 10 a.m. Sometimes for a major new release and then usually on a major new release a Sean's doing lay I'll do my eight-hour primetime shift there's Rodney Anderson and then You know Sean could do it like another seven or eight hours and get out That that maybe the 20-hour mark so We're kind of doing it already on the regular Adam with the bangles and a redemption coming up get with the redemptions were There's oh, that was another card on the jade Jake dola gala For the bangles Adam. I'll fumble and a pickup by Tennessee Dunzo's and there's Taysum Hill on card autograph for the Saints. That'll be for Mike Graczynski That's a veteran ticket autograph Debo is Tyler's guess. I guess I don't know when then I probably a bowman product a Bowman product would probably be the next like scheduled 24-hour break Where we like promoted and make a think make a big deal out of it and all that sort of thing Rex is like, you know, it's funny. He thinks that Sean Jaspie isn't even a real person Thinks he's AI Maybe a cyborg might be a cyborg. Well, and how many days will you come in the next day? No, you You'd go six to six and then come in for the next shift Wow, I will have to test that some someday. All right, the final autograph of the break before I do those randomizers is DK Metcalf nice rookie ticket variation RPS DK Metcalf for the Seattle Seahawks Oliver with that one. He won that spot in The lone filler break and he's having a great season this year There you go. All right now some randomizing to do All right, do I have a couple blank? I need a few blank lists here. There's one two and three So let's go back to the list here Everyone's got a shot at the 250 points from EA down to Sean Maddock and the Washington football team Let's get all your names in there. So name on top. We'll get it We'll use one dice roll for all the lists for the generic round numbers cards the ones without numbers Just the base versions. We'll just do a left-right randomizer going by the back of the card and Then the one that was number got to do separately that was Tennessee AJ Brown on the left side and DK Metcalf Seattle on the right side Let's roll it. Let's randomize it six and a two eight times for all three lists one two three four five six Seven and eighth and final time after eight looks like it's Jake Stacy. There you go Jake I'm not sure if I don't know. You got a couple Tony Pollard. You got next to twenty two hundred and fifty points as Well six into two eight times for the left right one two and eighth and final time That'll be for left side. So I know these are the same teams right here But all the left side teams will get the non numbered round numbers card So that other one was numbered. So let's go six into two eight times Tennessee That's Vinny and Seattle. That's Oliver. Good luck to both of you one happy person one sad person one two Seven good luck and eighth and final time flips to Seattle the DK Metcalf at the end for Oliver and now the round numbers round two numbers card 66 at a 75 Also for Oliver a little bit of cardboard dust on there, but there you have it I'm Joe for jazby's case breaks.com. Thanks everyone for joining in on 2019 Panini contenders football six-box random team at number one Second one in the store jazby's case breaks.com. Check it out. I'm Joe and I'll break that with you next time. Bye. Bye


Hello everyone, welcome to the next lecture on the topic remote sensing image acquisition and characteristics of the data. In the last class, we discussed the concepts such as temporal resolution, radiometric resolution and also we started discussing about the characteristics of data collected by WISP room scanner. In this lecture also, we are going to continue looking at the characteristics of WISP room and push room scanners. In the last lecture, I told you that the data collected by WISP room scanner will undergo increase in JFOV as the scanner moves away from the nadir and increase in GSI, ground resolution cell size variation as the sensor again moves away from the nadir point. I will tell you with one example of how this is happening in sensor called AVHRR. AVHRR is one sensor which is works under the principle of WISP room scanner, okay. So now the sensor has a spatial resolution of 1.1 kilometer at nadir. So this is example of the data. So this collects 2048 pixels, 2048 samples say if this is the along track direction, this will be the across track direction and hence then this sensor will collect 2048 samples that is 2048 pixels will be there in the across track direction, okay. So this is cross track pixel number and since this is from nadir, this will be 1024 on the left side 1024 on the right side or east west we can see. So this is just one half of it. So it starts from pixel number 1024 goes up to pixel number 2048. At nadir everything is fine. The sensor has a circular JFOV and it collects data with radius of like 1.1 kilometer, like the JFOV is 1.1 kilometer, GSI is 1.1 kilometer that is fine. Now as the sensor or as the scanner moves away from nadir, now this is across track away from the nadir point, just see what happens. This is the number of pixels or the number of samples collected. Here the sample number is 1024, here the sample number is 2280. So the difference is 256 samples. So 256 samples got collected in 200 kilometer distance. The next 256 samples from here to here 256 samples got collected, now this is the ground distance on the top. So now the difference between them is 230 kilometers, 256 samples got collected in ground distance of 230 kilometers. The next 256 samples on ground now got collected with the distance of 320 kilometers and so on. So here what are we seeing? The number of pixels or the number of samples collected is the same. Here we are seeing examples of the increment of 256 samples for simplicity sake. But you can see as the scanner moves away from the nadir in the across track direction, same number of samples is getting collected, but the ground distance covered by the scanner increases. It was just 200 kilometers for the first 256 samples closer to nadir. The next second set of 256 samples was collected over a ground distance of 230 kilometers then it became 320 kilometers and so on. So if you look at the GSI or the ground distance covered per sample, the ground distance per sample increases that is the GSI or the Ground Projected Sampling Interval or GSD also we can call Ground Projected Sampled Distance increases as the sensor or as a scanner moves away from the nadir. The GIFOV that is the projection of detector element on the ground that also will elongate will increase in size that is also depicted clearly here. Here it was like a perfect circle no distortion in shape as the scanner moves away from the nadir it becomes an ellipse rather than being a circle and it starts to overlap because there is an increase in GIFOV size both in the across track and along track direction. In both the directions GIFOV will increase and distort. So this is because of the geometry with which the data is collected. You know like if a circle is projected at an angle it will became an ellipse we know that same thing is happening here same thing was happening with respect to GSI also. What is the effect of it? What is the implication of this? I already we told you that whatever is the energy coming out from a single GIFOV will be kind of average and stored as one single value within the system. As the scanner moves away from the nadir the GIFOV becomes pretty large in case of AVHRR sometimes it may even be more than 3 kilometers. It should be 1.1 kilometer but it goes all the way up to say like 3 kilometers sometimes at very end of the scan line. So what will happen? Instead of collecting data over a area of 1 square kilometer it is now collecting image over an area of like 3 square 3 kilometers by 3 kilometer square if you assume a square what to say square projection definitely more than 1 square kilometer. So whatever be the feature present there all the radiances will be averaged together and stored within one single pixel of size 1.1 kilometer. So essentially we are averaging energy over a very large area and storing that particular energy in a pixel assuming pixel of size 1.1 kilometers. So what essentially we are assuming in mind we are assuming that the radiance recorded in that 1.1 square 1.1 kilometer pixel essentially came out from a ground area of 1.1 kilometer by 1.1 kilometer that is not the case. If that pixel was at the end of the scan line then the radiance recorded in that particular pixel actually came from a ground area of somewhat 3 to 5 square kilometers a much larger ground area. So this is what is happening in visbrum scanners. We are collecting energy over a larger footprint of the ground averaging them a single radiance value everything is now stored in a pixel of 1 square kilometer in case of AVHR. So normally in sensors with very large scan angles such as modals AVHR and all if some pixel falls at the end of the scan line then naturally the ground area covered for that particular pixel will be much larger than the pixel size itself. So if the pixel size is say 1 kilometer the energy collected by that particular pixel will not be 1 kilometer by 1 kilometer it may be 3 kilometers or 2 kilometers definitely larger than it as it moves away from the nadir. Only at nadir the GAFOV will be 1 kilometer by 1 kilometer that will be preserved. This we should always keep in mind when we work with data from scanners with very high scan angle. So we should not always think that okay the pixel size is 1 kilometer the data got collected from a ground area of 1 kilometer that is not the case we should always look at the scan angle of the scanner at which the data got collected. In this particular figure like it is like little bit clearly explained how the GAFOV will vary. So this is the variation of GAFOV here GAFOV element is like a circle for the system the beta is the IFOV the angle. The angle is fixed for a system it is not going to change but as the scanner moves away from the nadir now it has moved at a triangle theta away from the nadir the GAFOV has now become has now increased by a term of 1 by cos square theta in the across track direction and 1 by cos theta term in the along track direction. So the distortion of GAFOV is not uniform in both along track and across track it varies but essentially it varies in terms of like 1 by cos square theta in the across track 1 by cos theta in the along track. This is for the variation in GAFOV. Similarly, GSI also will vary GSI at an angle theta away from the nadir is equal to GSI at nadir divided by cos theta square that is GSI at certain angle theta is equal to GSI at nadir divided by cos theta square. So the GSI also that is the ground sample distance also will be keep on increasing in addition to GAFOV. You should always remember the GAFOV will increase the GSI will increase GSI or GSD will increase. So here again coming back to this AVHR example this ellipse denotes the GAFOV this lines represents the points at which the samples were collected that is essentially the GSI. So this we should always keep in mind that the data collected by a vis-broom scanner always has enlarged GAFOV problem and enlarged GSA problem as the scan angle goes away and away from nadir. Actually this is the main drawback of not all sensors having a very wide swap angle. We can make all the we can just increase the scan angle of all the sensors and start collecting data over large areas of the globe possible. But as the scan angle increases the distortions also will increase and hence not all systems has this large scan angle only certain systems which has the need to cover the globe really quickly such as motors or we are a sensor and all they are equipped or they are provided with a large scan angle because they are sent with an application they should cover the globe regularly at a much larger temporal frequency that is why they have been provided with such a large scan angles. But they will have their own distortions which we should always keep in mind when we work with such data sets. Now just we will see like one example of geometrical distortion that will happen in vis-broom scanner that is what is known as a tangential scale distortion. So, what exactly is like a tangential scale distortion a very good example is given here in this particular slide. Here you can see an image of a area taken as it is. So, the scale is lateral in both along track and across track direction. Now this is the along track direction this is the across track direction. Now I have told you that as the sensor scans as the scanner moves away from the nadir the GAFO will keep on increasing. It will became like ellipse or it will became like a rectangle. So, what will happen let us say there are like two buildings like this is like one building exactly covering the size of GAFOV of the pixel. Let us say this is like 500 meter by 500 meter some feature it is there. Now this is at nadir and let us say the GAFOV of the system is also 500 meters. This will be covered as one single feature. So, it will be represented as it is. Now let us come to the end of the scan line. Let us say there are like two adjacent buildings each of size 500 meters by 500 meters. If these two buildings were at nadir they would have been imaged as two separate points and two separate pixels. But now let us say this is at end of the scan line this is across track direction. Now the GAFOV has become let us assume 1.1 kilometer. Let us say the GAFOV has increased at the end of scan line. So, now the GAFOV will be something like this covering both the buildings together. So, initially at nadir the GAFOV was just 500 meters building size was also 500 meters it was imaged perfectly. Now at the end the GAFOV has increased it is now covering two buildings together. So, what will happen because of this both the buildings will appear little squeezed because same one pixel this will be stored as just one pixel data. But instead of showing one building per pixel both the buildings will be located let us say this is the pixel at nadir this is the pixel at the end of the scan line. Here you will see the image of only one building at nadir. At the end of scan line because both these two buildings were covered by the same GAFOV element this pixel will have both the buildings covered in one pixel. So, when we see those pixels what we will feel those two buildings actually have a smaller size than what actually it is. So, as the scan angle increases objects will appear squeezed together in the across track direction that is depicted here in this example also here it is like a perfect circle actually. But because of this scan angle distortion it is now squeezed and appearing as an ellipse. Similarly this diamond this diamond is now squeezed in the across track direction. So, this kind of squeezing of elements two buildings in our example were squeezed together to form part of one single pixel right. So, these two are squeezed and they will appear little shorter in size especially in the across track they will be squeezed only in the across track rather than along track. So, this distortion is much larger in the across track objects will appear squeezed in the across track direction when compared with the along track direction. So, a circle present at the end of the scan line may appear like as an ellipse rather than appearing as a circle it will be squeezed in the across track direction. This is what is known as tangential scale distortion objects will be squeezed will appear like distorted or squeezed as the scan angle moves away from the nadir continuously. So, till now we discussed the characteristics of visc-broom scanner we saw few examples of how the GSI changes how JFAV changes and all. So, these are some of the important limitations of visc-broom scanning. So, that is why now most of the systems are moving to push-broom scanning. Push-broom scanning avoids these sort of geometrical distortions to a large extent because you know like as the if the scanning introduces more distortions then finally, the geometric accuracy will be affected. Geometrical accuracy means a ground point having a coordinate of x comma y. If we calculate the coordinate from the image we should get the same coordinate x comma y. Let us say there is a building standing at point 100 comma 100 coordinate on the ground. From the image also the building should have a same ground coordinate 100 comma 100. But just imagine in visc-broom scanning if everything appears squeezed together in one pixel we may wrongly calculate the coordinate of that building if we do not correct for geometric distortions. So, visc-broom scanners come with their own geometric distortions which affects the geometric accuracy of the image. There is always a need to do correction of these images. That is major limitation of visc-broom scanner. In push-broom scanner all these sort of distortions are reduced to a large extent because in push-broom scanner if you assume like a flat earth then the GSI will not change because in push-broom scanner what is going to happen? In push-broom scanner like we are having like lot many detector elements each detector element will cover simultaneously the different parts of the area in the ground whatever energy comes in will be saved. So, the sampling interval is actually set because I told you in the earlier classes the GSI for push-broom scanner is determined by the spacing between two adjacent detector elements that is fixed when the system is launched that is not going to change. So, GSI is not going to change for push-broom scanner, but the IFOV will change because the pixel at the center will have like a full conical angular coverage, but a detector at the end may not have that particular coverage. So, the IFOV will change that is given in this particular slide and the IFOV varies in the across track direction due to the viewing angle. IFOV will vary with this particular relation, but the distortion in general in push-broom scanner is not as serious or not as troublesome as the distortions occurring in this room scanner. So, naturally push-broom scanners because of their fixed detector pattern which is not going to change and since there are no scanning involved that particular image will have higher geometric fidelity or higher reliability in comparison to images acquired from this room scanners. This is a major advantage of using a push-broom scanner over this room. So, already we saw one advantage that push-broom scanner provides a very high dwell time in comparison with this room that is a major advantage, but one more advantage is the geometric fidelity of the images acquired by push-broom scanner is much higher than the geometric characteristics of data collected by this room scanner. Now some distortions we have seen that can come because of scanning geometry or data collection geometry and so on, but as the sensor is moving or as the satellite is moving there can be change in attitude of the satellite which can cause geometric distortions. So, what is attitude of a satellite? We will just take an example of an aircraft. So, let us say like an aircraft is moving like this. So, this is the flight direction. This is from my right hand side to my left hand side moving like this. Let us take this as x-axis the direction in which the flight is moving. This is x-axis and y-axis is towards the screen like this and z-axis is the vertical. We will take 3-axis. Now the flight is moving like this. If I hold the x-axis like x-axis along the flight direction, if I hold it and let us imagine I am rotating the flight, what will happen? The flight will rotate like this. So, if I project like this in this direction, flight is coming towards you now. If I hold the x-axis and rotate, the flight will rotate like this. This is known as roll. Okay. So, the platform which is moving like here in example aircraft is undergoing some roll. Then pitch, I told you where is y-axis. This is flight direction, y-axis is like this. I hold the y-axis, I rotate it now. So, what happens? The plane nose moves up or down. This is known as pitch. Okay. So, rotation along x-axis is known as roll, rotation along y-axis is known as pitch. Similarly, I now hold the z-axis, I rotate. This is known as yaw. So, pitch is this like the nose of the airplane going up and down. Roll is this, plane itself is like kind of like rotating and yaw is this, moving along the z-axis. That is what we call attitude or distortions in attitude of a platform. In aeroplane, we can feel this if we are like traveled in like for long distances. It is very easy for us to feel. Flight will undergo a roll, especially when the captain banks the aircraft, it will suddenly have a roll and it will move like this. It can have a pitch during landing, they will increase the pitch, they will make the nose up, they will land. We can feel that. Similar attitude distortions like these three pitch roll and yaw, together we call it as the attitude of the platform. Okay. Similar to aircraft, a satellite also can undergo minor variation with this. A satellite is planned to move in one particular direction without any movement. Sometimes some unwanted things can happen, solar storm, atmospheric drag, change in gravity on the earth surface, all these things may change the position of the satellite, may cause some distortions in the attitude pitch roll yaw, which will cause distortions in the image. So, when finally the data comes down from the satellite, the satellite along with the image data will also give information about its position and attitude, at which position it was when the image was collected and what was the attitude, the pitch roll and yaw of the sensor, everything will be sent together. So, the people sitting here in the ground will process the data and correct the image for this variation in satellite attitude. So, that is what is given in this particular slide. Here I have just shown you how pitch roll and yaw is defined and the change in pitch roll yaw may happen due to change in gravity, atmospheric drag or some effect of solar winds, etc., etc. And these things normally they will be corrected like any distortion in the pitch roll yaw, like a satellite. If it has to move like this, it has to move like this while collecting data, suddenly let us say it has undergone a roll, slight roll, what will happen? Instead of collecting ground point here, the sensor would be looking somewhere away from it. So, the geometry of the image or the geometric accuracy of the image is lost, instead of collecting here, it is now looking somewhere else. So, that attitude information will be passed on to the ground and they will correct it. Now, the satellite is not looking at the ground point x comma y, it is now looking at some other ground point x, x1 comma y1. Hence, we should correct it. So, these sort of corrections will happen even before the data reaches us. Though we do not worry about it most of the time, it is always good to know. So, here I will complete the sentence, they will be corrected by the data providing agency who manages the satellite. So, till now we have seen some distortions in the images due to scanning characteristics, attitude characteristics and so on. There are other ways also in which the image or the data we get from satellite may get distorted. Some of them are, first thing is a multi-band core registration error. Let us say the satellite is collecting images in 4 bands, like this is 1 pixel, coordinate xy, band 1, coordinate ground coordinate x2, x comma y, band 2, band 3, band 4. This is 4 bands, it is collecting image over some ground point x comma y. Let us say this is pixel number 1 comma 1, like it is a 2D image, this is pixel number 1 comma 1. In all the 4 band images, pixel number 1 comma 1, like 1 comma 1 means first row first column, like this I meant 1 comma 1. So, pixel number 1 comma 1 should correspond to same xy. Then only we will say all the multiple bands within the image has same geometric accuracy. But you know what will happen is the sensor layout or the band layout means like all band 4 data may be collected by sensor here. This may be data for band 3 and so on. So, this may be band 3, this may be band 2 and so on. So, what essentially happens? All the 4 band sensors are actually located slightly away from each other and the ground points or there are very high chances that same pixel in each band, pixel number 1 comma 1 may have information about different points on the ground. Instead of like 4 multiple bands, let us say 4 bands are there in one particular sensor. All the 4 bands, same pixel number in the 4 band image should correspond to same ground point. There are high chances that those 4 band images or the pixels same exact number of pixel may look at different different parts of the ground. It is possible there can be slight mismatch in the ground data collected by 4 different bands or n number of different bands whatever be the number of bands. This is we call multi band co-registration error. Same pixel number 1 comma 1 in all the bands has different different ground points image drawn it. They must be corrected because we normally want to do we stack all the image data one over the other and then we visualize or then we process. That sort of image processing will suffer. So, all the bands all the pixels should have same corresponding coordinates with its adjacent bands. This sort of errors is quite natural it can happen in satellites. They will also be nowadays mostly corrected by the data providers. The next error that may come is topographic effects, sudden scale change.  What will happen and let us say this plateau is like quite tall let us say in case of like Tibet pretty high region. What will happen suddenly the orbital height of the satellite will be reduced from the surface over like see it may be like 700 kilometers. Let us say this is some let us say this is some 10 kilometers like 10,000 meters pretty high surface may not it is extreme example I am telling but just for explanation sake. So, when it comes over this there is a drastic change of drastic change in the height of the satellite above the terrain from this point to this point. So, there will be like a change in scale because of this these points may appear little closer and zoomed in. That is what we call sudden scale change in image due to presence of large topography. So, these two are some examples of image distortions. But how these image distortions have to be corrected we told you like there will be lot of distortions will come in the picture which will affect the geometric accuracy how to correct it. Nowadays mostly we need not worry about the geometric accuracy of the data the geometric standards are pretty high for nowadays images they are almost like corrected for distortions to the extent possible and it is being supplied to us. That is if it is a ground point x y on the ground from the image also you will be able to identify it pretty closely the accuracy is pretty high now. But how to generally do it say if we got one image which has some geometric distortion in ground a ground point is having a coordinate of 100 comma 100 but in satellite if I calculate the coordinate is 75 comma 80 there is a change how to correct it. Then we need to do a process of what is known as image to map registration that is we should have a proper map of the area let us say we have it. In map we assume all the coordinates are perfect and correct. So, what we do we take an image and we say okay this pixel in the image should have a ground coordinate of this like this we will identify some 5 to 10 points in the image get that actual ground coordinate from a map or from like a GPS survey we have done on the ground we will feed it into image we will reorient it or create a new image after correcting for job area distortion. This is known as image to map registration. Similarly, some scanners can look at some angles away from the nadir we can also correct to some extent and make sure and the image appears as if the scanner is looking from nadir that is say I am looking like this means from a top angle a building may appear like a square. But if I look at a building from an at an angle instead of being like a square or seeing the top I will see the side of the building right that sort of distortions will be there we can correct for such distortions we call it as ortho rectification we make sure that all the points on the image will appear as if we are looking from the top. So, these are some of the examples in which we will correct the image actually these sort of corrections the in detailed principles will naturally form a part of like a digital image processing course. So, we will not cover these topics in this particular course, but just for your information I am telling all this. So, whatever we have covered in the series of lectures the last few series of lectures is we discussed in detail about the four important characteristics of a remote sensing system spatial, spectral, radiometric and temporal characteristics. After which we also discussed what are the different ways in which images can be distorted or the characteristics of the data how it will be and we should always keep this in mind. The change in JFO we element and element in wisdom scanner and all actually cannot be corrected even though we can do some sort of geometric correction, but once the JFO is enlarged and data is collected over it we cannot change it practically speaking. So, that sort of characters above the data we should always keep in mind and we should remember them while we work with remote sensing images. With this we end this lecture. Thank you very much.


George Lucas was born in the year 1944 in Modesto, California. At a year old, he and his parents attended Disneyland the first week it was opened. George fell in love with the pack ever since and desired to visit often. His interest in animation, television programs, comics and science fictions were a priority until he later developed a passion for car racing. During his high school years, George was usually found racing at fairgrounds and hanging out at garages. His love for auto racing was inextinguishable so his parents never bothered themselves trying to dissuade him from it. In 1962, a few days before his high school graduation, George was driving when another driver collided with him, flipping his car several times before it finally crashed into a tree. George's lungs were severely bruised and he was in hemorrhage until an emergency medical treatment was administered. After recovering from the accident, he abandoned his interest in racing and pursued other passions. George's father operated a stationary store and wanted his son to work for him but George wasn't interested. Later on, he was admitted at Modesto Junior College where he studied literature, sociology and anthropology. He developed an immense love for capturing events with a camera which led him into the filming industry. George attended the School of Cinematic Arts at the University of Southern California where he graduated with a Bachelor's of Fine Arts in film. After his graduation, George was ready to venture into filmmaking. He came up with a unique story that was produced into a full-length movie. However, this production failed completely and resulted in a loss of money. George wasn't discouraged or deterred by this even though many of his acquaintances advised him not to waste money and time on something that wouldn't yield profit. He came up with another project, American Graffiti, a movie he directed all by himself. This movie became a success and led to a breakthrough that announced a judge to Hollywood. However, this courageous man wanted something bigger. He proposed another movie project to two large film manufacturing companies in America but was reportedly turned by both companies and the movie was rejected because of its bizarre story. George kept showing his scripts to other studios who declined until 20th Century Fox accepted the story and produced it. The movie was titled Star Wars and it became one of the highest-grossing films of all time. This made George incredibly famous within the movie industry. To this day, he's one of the world's best filmmakers worldwide with an estimated net worth of $5 billion. So many people would have accomplished their goals and become great if only they had rebuffed to the discouragements they got from people. Discouragement is the persuasion not to take a particular decision that will lead to happiness due to the difficult circumstances surrounding that decision. Guy finally said, Discouragement is a negative emotion with more than one trick up its dark sleeve. It tricks you into emotionally or mentally dwelling in the very place you want to leave. Nobody wants to dwell on challenges. However, many people are still entrapped in their problems because they've allowed themselves to be discouraged by taking the necessary steps to becoming free from such problems. When you succumb to discouragement, you will always remain in a particular sport without progressing. Joel Austin said, Stone of judgment, discouragement or doubt may be thrown at you. You can't stop them, but you can make a choice to keep your words up and not let them affect you. Whenever you're striving to achieve a goal, certain people will definitely discourage or judge you. You can't seal the amount from speaking, but you can seal your ears from listening to them. Cajun Positire said, Do not be discouraged if your plans do not succeed the first time. No one learns to work by taking one step. No one has ever achieved success after a single attempt. It took a series of repeated efforts before success was actualized. Just because you feel that something doesn't mean you can't try again and succeed at it. People tend to discourage you from doing a particular thing because it's not working, but it's your sole duty to simply ignore them and keep trying until it works out. As you wake up this morning, make a promise to yourself never to look back. Make a promise to yourself never to be discouraged by life's obstacles. Make a promise to yourself never to listen to those who want you to take the easy way out.


In this lecture, we are going to look at an introduction to cyber society, cyber culture and cyber space, which are three very closely knit topics. The topics that we are going to cover in this lecture include the objectives, a brief a crisp introduction to cyber society, culture, components of culture, the culture of computing, the concept of cyberspace, cyberspace communities, as well as the effect of cyber culture on the society. The main objectives of this lecture include that we are going to see that you know how by looking into these concepts, a positive online environment of internet users and a healthy cyber culture from the internet community, why it is important, how it can be created. The second objective of this lecture is a recognition of the power of the internet to benefit ourselves as well as the community at large. And the third objective is that we want to reflect on how to become a responsible user of social networking sites and we want to you know manifest a commitment towards building a healthy cyber culture. Let's look at what a cyber society is.  A society which is formed by us humans consists of the interconnections between humans, their surrounding, their environment, our connection with one another, our living style, our culture. Now with the advent of internet, nothing I believe has you know transformed humans the way this advent of internet has. No other technology has possibly brought about a global change the way internet did. And now with the birth of internet, it brought about you know a virtual society which is you know a virtual manifestation of the society that we have otherwise. And that is called a cyber society. A cyber society most specifically is defined as the construction, maintenance and facilitation of community in electronic networks and computer mediated communication. Now what is a cyber society that just how in a real life we as individuals, as humans have connections one another in site and in order to live our day to day life, we carry out businesses, we interact with others, we have certain sources of entertainment. Similarly, in a virtual way in a cyber society, we carry out businesses, we interact with others, we have sources of entertainment and so on.   As ordinary societies are marked by a certain culture, which of which we are living in boredom and similarly a cyber society, which is a virtual society also is defined by its own unique culture. Now what is a cyber culture? Well, cyber culture is that just how in a regular society there is a certain language we use, there is a certain way in which we interact with each other, there is a certain etiquette we follow, there is a certain decorum we follow, there is a certain code of conduct of business. Similarly, the cyberspace, it has its own etiquette, it has its own language, it has its own means of carrying out business and this overall constitutes the cyber culture. As I said earlier, you know, like every culture in real life, the cyber culture has its own language and it is, you know, and what that language is that it actually converts our human written language or our human spoken language into machine language, which is understandable by computers in general. Furthermore, especially, you know, the cyber culture in contrast to the actual societal culture, it allows for, you know, a written text communication, it allows for oral communication, which can be done through a number of means, a number of means and medium. Let's now look at the various components of cyber culture, which define the cyber society. Those components include internet, it includes various websites which we browse, it includes email, it includes blog, it includes online chatting, it includes e-commerce and it includes various social networks such as Facebook, Twitter, Instagram and so on. Now we'll briefly look at what these components are. Internet we all know is a network formed by the cooperative interconnection of a large number of computer networks. Nobody really owns the internet, there is no central administration to the internet. Main goal of the internet is to connect several computers together for the exchange of messages and for sharing information. And internet, as I told you earlier, which has revolutionised the human race is a community of basically all people and it is a collection of all resources. The second component of cyber culture, which comes under the umbrella of internet is having a website. A website technically defined is a location connected to the internet that maintains one or more web pages, web pages are the building blocks of the website. We can access the website and access the web pages and access any information, any content whether that may be technical content, entertainment content is provided on the website and the enclosed web pages. The third component which we're all at some level or the other familiar with is an email, electronic email which allows people sitting at the two opposite ends of the word to reliably communicate with each other. The fourth component what we can say is a blog. A blog is a discussion or an informational site published on the web and it consists of discrete entries. Then the next component which each one of us are now on our daily base using is the online chatting. You know whether it is done through social networks, whether it is done through text messaging, online chatting is a very, very essential feature of the cyber culture which is defining the cyber society. Then further more moving on how in a regular society, societies are marked and defined by the businesses that we carry out. Similarly, a very important component of cyber culture is e-commerce where you know we're doing online shopping where we have online marketplaces, we have a business to business buying and selling, we may even have business to consumer buying and selling. Then you know they can be online newsletters for marketing perspectives. Lastly, but I would say most importantly the cyber culture these days is characterized by social networks which most of us are at you know one or the other. We are making use of one or the other social network whether that is for staying connected with our loved ones through you know sharing messages, sharing our daily activities, sharing our photos, videos or whether it is for professional purposes such as a use of website like LinkedIn whether it is you know so it's use of these social networks an example which could be Instagram, Facebook, Twitter, LinkedIn. This is you know a very, very important aspect or component of the cyber culture. The third very closely connected component of cyber culture and cyber society is the cyberspace. A cyberspace is a space that is created through the union of electronic communication networks such as the internet which enables computer facilitated communication between any number of people who may be geographically dispersed around the globe. Cyberspace is a public space where individuals can meet, exchange, ideate, share information, provide support social support and carry out business. Now if I contrast cyberspace with an actual physical space before the advent of internet it is how let's say in a corner gathering or in a meeting where several individuals could meet, share ideas, carry out discussions so a cyberspace is actually a virtual version of that physical space of those physical meetings that people would have. You know they can include political discussions, they can include various forms of entertainment, they could include you know at times these gathering of families and very close ones, a reunion of sort. Carrying on with you know the essence or the concept of cyberspace we know that human interaction does not require physical connection to communicate but it is rather characterised by the interconnection of millions of people throughout the world to chat rooms, emails, Facebook. Here we see the various mediums which help us in creating that cyberspace. Facebook for instance, Twitter for instance, Skype for instance, Google for instance are just some of the mediums through which you know cyberspace exists and people are making use of it. Moving on to cyberspace communities we see that due to worldwide use of computer networks people are now able to get together and form cyber communities that can exchange messages easily through the cyberspace. Physical meeting has been reduced to the introduction of cyber culture and cyber meetings. Moving on to the effects of the cyber culture on our society.  In education the style of teaching and learning has changed. Student-teacher interaction has specially changed. This came, became even more prominent during the times of COVID-19 when even regular universities, regular schools, regular colleges shifted to the cyberspace, had to adopt the cyber culture in order to teach and impart. Further you know as as far as due to this introduction of cyber culture a lot of business such as you know carrying out meetings, carrying out conferences has now very easily moved into the cyberspace and that is bringing about an advantage of reducing time of saving resources of all kinds. Moving on to other effects and impacts of cyber culture. We see that cyber culture has reduced the gap between groups and individuals which may be separated from one another for various reasons. For instance if a certain individual is carrying out higher education in a far off country that particular individual is very easily able to stay connected to family at home whether that person wants to stay connected to their parents or to their peers and so on. Further however like like all inventions when there are positives and good sides there is also a downside. The downside of this prevalence of cyber culture is that face to face communication human to human bond, human to human interaction has greatly suffered. It is not a scene that we do not see on our daily lives that we have individuals sitting in the same room or family members living in the same house however you know instead of communicating with one another at a personal level they are making use of cyberspace they are making use of social networks to communicate with each other. Nevertheless as I said with all inventions while there are advantages there are disadvantages while these disadvantages exist the advantages are humongous not just the fact that this cyber culture has reduced distances this cyber culture has made business very easy has made education very easy has made staying connected with a large number of people very very easy.


.In the previous lecture, we have seen how can we remove euler symbols or say unit productions to simplify a grammar. In this lecture today, we will first see how can we remove unit productions. The procedure is almost similar to that of your removal of epsilon productions. So, we have said that unit productions in the form a goes to b where a and b are non terminals. Now, what we can do is that we say that for any Cfg say g which is n sigma p s we can say that d r is an equivalent Cfg say g s which has no unit production. We will prove this using similar approach that we did for removal of epsilon production. So, first we will construct a Cfg say g hat. So, from g we construct a Cfg say it is g hat which is n sigma p hat and s that means, we are going to include some more productions. We say that p hat contains all the productions of p and it is closed under the following rules. So, the rule is that if a goes to b and b goes to beta r in p hat then we include a goes to beta as well in p hat. Obviously, p hat will be finite because there are finite numbers of productions in p hat.   So, it is quite clear. Now, we can also show that l of g hat is a subset of l of g. We can show that g and g hat are equivalent. Now, this is a case because every new rule that added to p hat is because of the above rules and that rule can be simulated using two steps because we have said that if a goes to b and b goes to beta is in p or p hat say since everything is there in p will also be in p hat. So, if these two rules are there in p then a goes to beta is in p hat. So, these are rule we used. So, therefore, if in the original grammar g if we use these two rules then or if we use this rule in grammar g hat in some derivation then that can be simulated by using these two steps using these two productions in grammar g. That means, say alpha 1 a alpha 2 suppose in g hat in one steps in one step suppose we derive alpha 1 beta alpha 2 then this step can be simulated in g as like this say alpha 1 a alpha 2 in one step in g will be alpha 1 b alpha 2 and in one more step in g alpha 1 beta alpha 2. So, it needs only one more step. So, therefore, these two grammar are equivalent g and g hat are equivalent. Now, what we can do that using a similar reasoning that we gave in case of say removal of unit productions we can say that a minimal length derivation in g hat really do not use any unit productions and hence we can throw out all the unit productions from a grammar g hat and to have a new grammar say g dash and which will be equivalent to original grammar g. That means, from g hat we remove all unit productions to get a new g dash and eventually g and g dash will be equivalent. Now, what we want to show that a minimal length derivation in g hat do not use any unit production in that case only we can throw out all unit productions from g hat to get the equivalent grammar g dash suppose that a string w is derived under g hat where w is a string of terminals only. Now, say this is a minimal length derivation in g hat and assume for contraction that that minimal length derivation in g hat for w uses some unit production that is this derivation will be like this. So, as derives under g hat say in 0 or more steps it goes to alpha 1 a alpha 2 this form then one step this a is replaced by b unit using the unit production alpha 1 b alpha 2 and then in 0 or more steps under g hat we derived w. So, what we have said that at this point in this step we use the production a goes to this unit production is used and we have said that this is a minimal length derivation. Now, we will arrive at a contraction the point is that the occurrence of this non terminal b eventually must be removed this post of using some production of the form say b goes to beta the production of the form must be used at some point to dispose of this non terminal b. So, therefore, this product derivation look like this. So, s from s in say m steps in g hat where m is greater than or equal to 0. So, it is alpha 1 a alpha 2 say it takes m steps then in one step under g hat it is replaced by b using the unit production. Then in another suppose n steps in under n steps say this alpha 1 alpha 2 are converted to some other string of terminal say gamma b delta and eventually in another one step in g hat this b is replaced by beta using this rule and eventually in another suppose k steps under g hat we get the string of terminals say it is w. So, it total requires m plus n plus k plus 2 steps in grammar g hat and we have said that this is the minimal length derivation. But according to our rule that we have followed that if a goes to beta a goes to b and b goes to beta is there in p hat then a goes to beta must also be there in p hat. Now, what we can do is that we can use this steps starting with s in say m steps under g hat we will get alpha 1 a alpha 2. Then in another one step instead of replacing a by b we can replace a by beta using this rule since this rule is also there. So, alpha 1 beta alpha 2 then in under n steps in the same steps that we use earlier that will be gamma beta delta and in another k steps under g hat we will have w.  So, this takes m plus n plus k plus 1 step. So, it takes 1 step less compared to the previous derivation. So, our assumption that this previous derivation is of minimal length is false. So, therefore, we can easily throw out all the unit productions and can still have an equivalent grammar. By this way following this rule from g we can have g dash which will be equivalent to the original grammar g and will not have any unit production. Now, we will come to the discussion of normal form. We define in normal form by imposing some restrictions on the form of productions allowed in the grammar. For many applications it is often helpful to assume that CFGs are in one or another special restricted form or normal form. We will consider two of the most useful normal forms. One is Somskin Normal Form simply CNF and another is Greibach Normal Form simply GNF. We will first discuss this Homskin Normal Form and we will come to Greibach Normal Form at a later point. We say that first let us define this Homskin Normal Form. We say that SCFGs and sigma PS is in Somskin Normal Form or CNF if all productions are the form say A goes to BC or A goes to A where A B C are non terminals and small A is a terminal symbol. Please note that we do not use productions of the form A goes to epsilon and therefore, a grammar in CNF cannot generate the string epsilon that means empty string cannot be generated since we do not allow productions of this form. Now what we say is that in the form of a theorem say for any CFGs and sigma PS there is a CFG say G dash which is ANDS sigma P dash and say S in CNF in CNF form or in CNF such that L of G is equivalent to or identical to L of G dash that means G and GR equivalent that means for every CFG G we can find in CFG G dash which is in CNF and which is equivalent to G. Let us see how to get that CFG G dash which is equivalent to G and which is in Homskin Normal Form that means the proof of the theorem. So, without loss of generality what we can assume that the given grammar G does not have any is less symbol does not have any unit production or epsilon productions even if it has we can remove all those productions using the methods that we have already discussed. Now we use the following procedure to construct to construct G dash from G the first step is that for each terminal for each terminal symbol a belonging to sigma we introduce a new non terminal say it is a subscript a for every small a terminal symbol we introduce a new non terminal which is not there in the grammar G and we introduce a production and a production AA goes to in P dash. So, in P dash will include AA goes to a where a is the new non terminal and replace all occurrences of a in the right hand side of all productions. Whenever small a appears in the right hand side of any production and that occurrence will be replaced by that that occurrence will be replaced by and replace all occurrences of a in the right hand side of all production by AA. Of course, except for the production except for productions of the form B goes to a suppose if B goes to a is there we do not touch the right hand side, but if otherwise suppose we have a productions of like this A goes to say A B then this will be replaced by A goes to AA B and already we have included AA goes to A in the grammar. So, for this type of production we do not replace this A by A that is what we have said. So, after this step all productions will be of the form A goes to A where capital A is a non terminal and small a is a terminal symbol or it will be of the form A goes to some B1 B2 up to say Bk for some k greater than or equal to 2. So, every production will be either of this form or this form. So, it is quite clear from this construction and we have seen that by using this or by this construction we are not changing the language of the grammar that means g and g s are equivalent because in the new grammar whatever is generated in the old grammar any string in the new grammar it will take one more step and whatever we can generate in this new grammar can also be generated in the old grammar. Now, for all productions of the form A goes to say B1 B2 up to say Bk say if we have a production of this form. So, what we do we replace it by this production we replace by A goes to B1 C where C is a new non terminal that we have introduced in the grammar which was not there in the previous grammar and C goes to B2 B3 up to say Bk that means the remainder of the string. So, this part in this case also we are not changing the language of the grammar. So, we have for us this production we have introduced two new productions. So, whatever is generated in this previous grammar can also be generated in this new grammar, but it will take only one more step. Similarly, everything that can be generated in this new grammar can also be generated in the old grammar. So, this way we have reduced the length of the origin side here by one non terminal by one symbol. We continue this process that means again we introduce a new non terminal and from for this production again introduce a new non terminal and we write it as say C goes to B2 D and D goes to B3 up to Bk where D is a new non terminal and it is not going to sense the language of the grammar. So, this way we keep on introducing new non terminal and until the length of the origin side of each production becomes equal to 2. That means in the origin side we will have only two non terminal. So, eventually every production will be of the form A goes to Bc eventually because eventually it has a terminal. Since the length of the origin side is always finite it will be of the form A goes to Bc or it will be of the form A goes to A. So, we will get only this kind of productions in the grammar and at that point it will be in Homskin normal form. Just for example, we introduce or construct a grammar in Homskin for a given language. Say the set of G is given like this S goes to A as B epsilon. This generates a language A triple n B triple n n greater than equal to 0. So, this is a language generated by this grammar. So, L of G so it is a set of strings numbers of S flowed by same numbers of B's. Now, since this contains an epsilon productions. So, you can remove this epsilon production by introducing is A as B or as goes to A B. So, you introduce a new production as goes to A B to remove this epsilon production that we have already discussed. Now, this is not in CNF because both the productions as goes to A as B or as goes to A B is not in a form that to be in CNF. So, what we do introduce non-terminal say it should have been small B since we are talking about B only. Now, introduce two non-terminals say A and B for each of the terminals over here. So, A goes to A we introduce in the grammar and B goes to B we introduce in the grammar. That means the new grammar will have the following rules as goes to A as B A B A goes to A and B goes to B. Now, every occurrence of this A and B A and B in the right hand side of the production will be replaced by this non-terminals. So, from this now we get as goes to A as B as goes to A B A goes to A and B goes to B. Now, last three productions are in the form in the form of CNF, but this production is not in the form CNF. So, correspond to this we introduce a new non-terminal say C and we write it like this A as goes to A C then C goes to S B where C is a new non-terminal and we retain all the earlier productions A goes to A B goes to B. Now, we see that in this every production obeys the rule that we have given for productions of CNF and this is equivalent to the original one, but of course this cannot generate the string epsilon other than that every string will be identical or same string can be generated that can be generated in G as well. So, therefore, this is the grammar which is in CNF for the given language A to power n B to power n. Now, let us consider the other normal form which is called Greibach normal form. First let us define Greibach normal form GNF we say that a C L G G is in GNF if all productions in the grammar is at the form A goes to A B 1 B 2 up to B k for some k greater than equal to 0 where A B 1 B 2 up to say B k all these symbols are non-terminals and symbol A is a terminal symbol that means every production should be of this form where the first symbol that appears in the right hand side is a terminal symbol and the remaining all symbols it may be 0 or more symbols there all the symbols should be non-terminals. So, every production should be of this form. So, here you see that k may be 0 since k may be 0 therefore, productions of the form A goes to A is also allowed only thing we do not allow is that the epsilon production similar to your GNF. We will now show that every C F G C F G can be transformed to an equivalent C F G G dash. So, now to do that what we do we first introduce two lemmas that means given any these two lemmas will be helpful in constructing a C F G in GNF for any C F G G. So, given any C F G G which contains some left recursive productions we can always construct an equivalent C F G G dash. So, removing those left recursive productions by right recursive productions for any grammar G if it contains some left recursive productions we can replace those by right recursive productions and that new grammar will be equivalent to the original grammar. We will first prove this we call it say lemma 1 let G equal to n sigma PS B SCF G and let A goes to A alpha 1 A alpha 2 like this we have k numbers of left recursive productions. So, these are the beta set of all left recursive productions this is called left recursive because this terminal non-terminal A appears in the left side. So, which is there in the left side of the right hand side is called left recursive. We have set of all left recursive productions and let of course these are left recursive A productions where A is the left hand side there may be some other left recursive productions where it may be B productions or C productions and like that and let A goes to beta 1 beta 2 up to say beta n B the remaining A productions. So, there may be two kinds of A productions this is the left recursive type and this is the remaining type. So, assume that these are the remaining A productions that we have in the grammar then there is a C F G G dash. So, it is n dash sigma P dash S where n dash is n union B we introduce a new non-terminal B which is not there in the previous set of non-terminals. That means, B does not belong to n and P dash contains all productions in P except the left recursive productions. We will remove all left recursive productions left recursive A productions we remove the left recursive A productions and also contains the following additional productions by removing left recursive A productions we include the following additional productions A goes to beta 1 B beta 2 B up to say beta n B B goes to alpha 1 alpha 2 up to alpha k this is n B goes to alpha 1 B alpha 2 B alpha k B such that L of G dash is equal to L of G that means, G and G dash are equivalent. So, we have removed all left recursive A productions and introduced a new non-terminal B and these new productions have been introduced in the grammar. Now, we can show that these two grammars are equivalent we first show that L of G is a subset of L of G dash. Now, what again you can see is that A goes to A alpha 1 A alpha 2 A alpha k these productions were there in the grammar G which are not there in G dash, but if in the derivation in G if we use at any point this kind of productions which are not there in G dash that can be simulated by a step of by few steps in G dash. So, whenever we use this kind of productions eventually this A goes to A alpha 1 A alpha 2 or in general if A goes to A alpha i is used. So, this A has to be eventually disposed of by using a productions of this form some A goes to beta j. So, therefore, the derivation will be like this say S goes to in G some gamma A delta in 0 more steps. Then in one step in G we replace A by A alpha i 1 suppose A alpha i 1 delta then in another one step in G we replace this A by again say A alpha i 2 gamma A alpha i 2. So, alpha i 1 is there in the previous step delta. So, continuing this eventually every time in one step we are using an A productions we will get it like this gamma some alpha we will go up to alpha i 1 alpha i 2 up to say alpha i p and eventually this A left side A has to be replaced by some beta j.  So, this is how we need to proceed now this same thing can be derived in G dash as well like this say S goes to gamma A delta. Now, instead of using A goes to A alpha i because this kind of production we do not have in gamma G at G dash. So, we use in G dash. So, in one step in G dash we use A goes to beta j instead we use A goes to beta j. So, gamma beta j delta now in the next step we can use the production that we have already added A goes to we have the kind of production A goes to beta j A goes to beta 1 B beta 1 B beta 2 B and beta j B. So, we will have beta j B. So, in next step it will be we can use the production on the form where B goes to alpha 1 alpha 2 up to alpha k we can use B goes to alpha B goes to say alpha P we have B goes to alpha 1 B alpha 2 B like that. So, we can use gamma beta j this B goes to say alpha P B delta. Then next step again we can use B goes to alpha P minus 1 B and continue this like this beta j.  Then in one step we can replace this B by sorry. So, we go up to say alpha i 2 and one step we can replace it by B goes to alpha 1 to dispose of this B. So, it is gamma beta j alpha i P up to say alpha i 1 and then delta. So, the same external form we have arrived at in this case also only thing is that the length of the derivation in this case is more. Similarly, derivation in G is also a derivation in G dash because there is a subset of G is a subset of G dash. Now, to show that L G dash is a subset of L G we need to follow just the reverse process that we have already given over here. By using the reverse process of this we can show that L G dash is a subset of L G as well. That I can show that G dash and G are equivalent. So, even though we use this transformation to remove the left recursive production and replace it by right recursive production the two grammars will be equivalent. Then we introduce another lemma which is called lemma 2. So, where suppose there is a C of the G with n sigma P s and say A goes to alpha 1 B alpha 2 is in the production and B goes to beta 1 beta 2 up to say beta k with a set of all B productions which are which are during P. Then we can have construct from G the grammar G dash which is n dash sigma P dash and s such that P dash contains all those productions which are during already in P and then all productions the form A goes to alpha 1 beta 1 alpha 2. That means this B is replaced by this beta 1 or A goes to alpha 1 beta 2 alpha 2 this B is replaced by this B 2 and like that will go up to alpha 1 beta k alpha 2. And then we remove this production that means we subtract from this set this particular production A goes to alpha 1 B alpha 2. That means we remove this production and replace this occurrence of B in the middle by all the right hand side of this B productions. So, we get a new grammar which contains this kind of productions we have to show that L of G dash and L of G are equivalent. So, it is quite easy to see that whatever we can simulate in G can also be simulated in G dash it requires only one more step and whatever we can generate in G dash can also be generated in G. So, we left it to the reader to prove it. So, it is quite simple to show what we do now is that we use these two lemurs to transform any grammar which is not in grammar form to grammar form. So, we say that for any C of G and sigma p s with epsilon not in the grammar there is an equivalent C L G G dash say n dash sigma p dash say as dash which is in G n f. That means all productions are the form A goes to small a B 1 B 2 up to B k for some k greater than equal to 0. So, given any grammar G we can always construct an equivalent grammar G dash which is in G n f. So, we will consider instead of giving the proof of this theorem I will explain how can we construct the equivalent grammar in G n f for the grammar with the help of an example. So, in the construction step what we assume is that first we assume that the grammar G is in C n f if it is not in C n f we can always convert it by in the process that we have already given. So, therefore, all productions will be of the form A goes to B C or A goes to A and in the construction process we first rename all variables or all non-terminals. Suppose that there are m numbers of non-terminals in n in this n numbers of non-terminals is m which are say and those can be renamed to have say A 1 A 2 up to say A m. So, there are m numbers of non-terminals these are set of non-terminals. So, this n this will have this non-terminals. So, we have renamed all those non-terminals without changing the language of the grammar. Then in the second step what we will do we process the productions in P such that they satisfy a property called increasing non-terminals non-terminal property and this increasing non-terminal property is defined like this. We say that all productions are increasing non-terminal property if it is of the form say A i goes to A alpha where it starts with a terminal symbol or A i goes to A j alpha where j is greater than i and where alpha is basically string of non-terminals. To enforce the increasing non-terminals property what we do we start with A 1 production of the form A 1 goes to A and A 1 goes to some A i as because all productions of this form according since it is in CNF. Now, here we can apply this lemma 1 and lemma 2 to bring it to CNF. We will illustrate it with the help of an example. For example, say we consider this grammar A goes to B B, B goes to A C A and C goes to A B, B A and A. Suppose, this is a given grammar we have these productions. So, in step 1 we renamed the non-terminals and suppose A is written as A 1 and B is say A 2. So, we will have it is A 2, A 2 then B is A 2, A 2 goes to A 1, A 3 where C is A 3 and is A and A 3 goes to because C is A 3, A 1, A 2 or A 2, A 1 for this one and this A. So, we have renamed and by renaming we have got all these productions from the original productions. Then in step 2 we consider first this A 1 production.  Now, we process this A 2 production. So, when you process this A 2 productions to enforce this increasing non-linear property, what you do first apply lemma 2 to A 2 goes to A 1, A 3. When you apply lemma 2 over here we get A 2 goes to A 2 and we replace this A 1 by the right hand side of this A 1 production that is it is A 2, A 2 because we know that already A 1 production is in satisfies increasing non-linear property. So, it will be A 2, A 2, A 3 and the other production A 2 production is A 2 goes to A.   So, in this case all these productions satisfied this increasing non-linear property and hence the resulting lemma will be A 1 goes to A 2, A 2 already A 1 production satisfies increasing non-linear property. Now, A 2 productions are also satisfied increasing non-linear property.  So, what is going to be here is 2 greater than minus 2 and we have already A 3 productions under form A 1, A 2 and A 2, A 1 and A. Now, this A 3 productions do not satisfy this increasing non-linear property and hence we consider this A 3 productions now. So, that it can satisfy increasing non-linear property. So, we have A 3 goes to A 2 by applying again lemma 2 to A 3 productions and introducing a non-terminal say A minus 3. Now, in this case we need not apply this lemma 1 because there is no any left recursive productions because A 3 goes to A 1, A 2 and A 3 goes to A 2, A 1. So, we need to simply apply lemma 2 instead of lemma 1. So, that it satisfies increasing non-linear property. So, therefore, we can write it as A 3 goes to A 2, A 2, A 2 since we have A 3 goes to A 1, A 2 this A 1 will be replaced by the right hand side of this A 1 production which is A 2, A 2 and hence we get instead of A 1, A 2, A 2 and already we have this A 2 over here and the other production is it is A 2, A 1 and this is A. Now, again we apply lemma 2 because this is A 2 and this is A 3 this 2 is less than 3 it has to be greater than or equal to 3 according to our increasing non-linear property.  So, this is A 1 in fact.  Now, all A 3 production and A 2 productions are already in G N F because this should have been A 3 goes to because A 3 goes to it starts with a terminal symbol, starts a terminal symbol, starts a terminal symbol, terminal symbol and terminal symbol and remaining string is a string of non-terminals that we introduced already in the grammar and already in the grammar. Similarly, A 2 production also this is already in G N F only means that this A 1 production and A minus 2 productions they are not in G N F because they start with a non-terminal. So, now again we can apply lemma 1, lemma 2 to A minus 2 to convert it to G N F form that means this A 2 can be replaced by the right hand side that means we have the production form A minus 2 goes to A 2, A 3. So, this A 2 can be replaced by the right hand side of this A 2 productions that we have already over here.  So, in such a case these two will be in G N F.   So, this is the resulting grammar by applying lemma 2 to A 1 and A minus 2 productions and we see that all productions are in G N F. So, this is how by applying repeatedly lemma 1 and lemma 2, lemma 1 to remove left recursion and lemma 2 to convert it to G N F. So, that the leftmost symbol of the right hand symbol right hand side is a terminal symbol. So, we can eventually get the grammar to be in G N F form and since at every step we apply either lemma 1 or lemma 2 and when we apply lemma 1 or lemma 2 the resulting language does not sense. Therefore, the resulting language in this equivalent in this grammar which in G N F will not be changed. Therefore, this is an equivalent grammar corresponding to the original grammar. So, that is how we transform any given grammar to G N F form.