A survey of motion-parallax-based 3-D reconstruction algorithms
---
paper_title: When is the Shape of a Scene Unique Given its Light-Field: A Fundamental Theorem of 3D Vision?

paper_content:

The complete set of measurements that could ever be used by a passive 3D vision algorithm is the plenoptic function or light-field. We give a concise characterization of when the light-field of a Lambertian scene uniquely determines its shape and, conversely, when the shape is inherently ambiguous. In particular, we show that stereo computed from the light-field is ambiguous if and only if the scene is radiating light of a constant intensity (and color, etc.) over an extended region.
---
paper_title: A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses

paper_content:

A new technique for three-dimensional (3D) camera calibration for machine vision metrology using off-the-shelf TV cameras and lenses is described. The two-stage technique is aimed at efficient computation of camera external position and orientation relative to object reference coordinate system as well as the effective focal length, radial lens distortion, and image scanning parameters. The two-stage technique has advantage in terms of accuracy, speed, and versatility over existing state of the art. A critical review of the state of the art is given in the beginning. A theoretical framework is established, supported by comprehensive proof in five appendixes, and may pave the way for future research on 3D robotics vision. Test results using real data are described. Both accuracy and speed are reported. The experimental results are analyzed and compared with theoretical prediction. Recent effort indicates that with slight modification, the two-stage calibration can be done in real time.
---
paper_title: The Geometry of Multiple Images

paper_content:

Nitrocyclopropane is prepared by reacting 3-chloro-1-nitropropane with an amine which has a polar center in addition to an amino function in the presence of a polar, aprotic solvent. For example, the reaction of 3-chloro-1-nitropropane with ethylene diamine in the presence of dimethyl sulfoxide produces nitrocyclopropane in high yield.
---
paper_title: Multiple view geometry in computer vision

paper_content:

From the Publisher: ::: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. The book covers the geometric principles and how to represent objects algebraically so they can be computed and applied. The authors provide comprehensive background material and explain how to apply the methods and implement the algorithms directly.
---
paper_title: The Geometry of Multiple Images

paper_content:

Nitrocyclopropane is prepared by reacting 3-chloro-1-nitropropane with an amine which has a polar center in addition to an amino function in the presence of a polar, aprotic solvent. For example, the reaction of 3-chloro-1-nitropropane with ethylene diamine in the presence of dimethyl sulfoxide produces nitrocyclopropane in high yield.
---
paper_title: A flexible new technique for camera calibration

paper_content:

We propose a flexible technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closed-form solution, followed by a nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and real data have been used to test the proposed technique and very good results have been obtained. Compared with classical techniques which use expensive equipment such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one more step from laboratory environments to real world use.
---
paper_title: Multiple view geometry in computer vision

paper_content:

From the Publisher: ::: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. The book covers the geometric principles and how to represent objects algebraically so they can be computed and applied. The authors provide comprehensive background material and explain how to apply the methods and implement the algorithms directly.
---
paper_title: A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses

paper_content:

A new technique for three-dimensional (3D) camera calibration for machine vision metrology using off-the-shelf TV cameras and lenses is described. The two-stage technique is aimed at efficient computation of camera external position and orientation relative to object reference coordinate system as well as the effective focal length, radial lens distortion, and image scanning parameters. The two-stage technique has advantage in terms of accuracy, speed, and versatility over existing state of the art. A critical review of the state of the art is given in the beginning. A theoretical framework is established, supported by comprehensive proof in five appendixes, and may pave the way for future research on 3D robotics vision. Test results using real data are described. Both accuracy and speed are reported. The experimental results are analyzed and compared with theoretical prediction. Recent effort indicates that with slight modification, the two-stage calibration can be done in real time.
---
paper_title: Gauge fixing for accurate 3D estimation

paper_content:

Computer vision techniques can estimate 3D shape from images, but usually only up to a scale factor. The scale factor must be obtained by a physical measurement of the scene or the camera motion. Using gauge theory, we show that how this scale factor is determined can significantly affect the accuracy of the estimated shape. And yet these considerations have been ignored in previous works where 3D shape accuracy is optimized. We investigate how scale fixing influences the accuracy of 3D reconstruction and determine what measurement should be made to maximize the shape accuracy.
---
paper_title: A flexible new technique for camera calibration

paper_content:

We propose a flexible technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closed-form solution, followed by a nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and real data have been used to test the proposed technique and very good results have been obtained. Compared with classical techniques which use expensive equipment such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one more step from laboratory environments to real world use.
---
paper_title: Cooperative computation of stereo disparity

paper_content:

Perhaps one of the most striking differences between a brain and today’s computers is the amount of “wiring.” In a digital computer the ratio of connections to components is about 3, whereas for the mammalian cortex it lies between 10 and 10,000 (1).
---
paper_title: A combined corner and edge detector

paper_content:

The problem we are addressing in Alvey Project MMI149 is that of using computer vision to understand the unconstrained 3D world, in which the viewed scenes will in general contain too wide a diversity of objects for topdown recognition techniques to work. For example, we desire to obtain an understanding of natural scenes, containing roads, buildings, trees, bushes, etc., as typified by the two frames from a sequence illustrated in Figure 1. The solution to this problem that we are pursuing is to use a computer vision system based upon motion analysis of a monocular image sequence from a mobile camera. By extraction and tracking of image features, representations of the 3D analogues of these features can be constructed.
---
paper_title: Performance of optical flow techniques

paper_content:

While different optical flow techniques continue to appear, there has been a lack of quantitative evaluation of existing methods. For a common set of real and synthetic image sequences, we report the results of a number of regularly cited optical flow techniques, including instances of differential, matching, energy-based, and phase-based methods. Our comparisons are primarily empirical, and concentrate on the accuracy, reliability, and density of the velocity measurements; they show that performance can differ significantly among the techniques we implemented.
---
paper_title: Three-dimensional computer vision: a geometric viewpoint

paper_content:

Projective geometry modelling and calibrating cameras edge detection representing geometric primitives and their uncertainty stereo vision determining discrete motion from points and lines tracking tokens over time motion fields of curves interpolating and approximating three-dimensional data recognizing and locating objects and places answers to problems. Appendices: constrained optimization some results from algebraic geometry differential geometry.
---
paper_title: SUSAN—A New Approach to Low Level Image Processing

paper_content:

This paper describes a new approach to low level image processing; in particular, edge and corner detection and structure preserving noise reduction. ::: ::: Non-linear filtering is used to define which parts of the image are closely related to each individual pixel; each pixel has associated with it a local image region which is of similar brightness to that pixel. The new feature detectors are based on the minimization of this local image region, and the noise reduction method uses this region as the smoothing neighbourhood. The resulting methods are accurate, noise resistant and fast. ::: ::: Details of the new feature detectors and of the new noise reduction method are described, along with test results.
---
paper_title: Subspace methods for recovering rigid motion I: Algorithm and implementation

paper_content:

As an observer moves and explores the environment, the visual stimulation in his/her eye is constantly changing. Somehow he/she is able to perceive the spatial layout of the scene, and to discern his/her movement through space. Computational vision researchers have been trying to solve this problem for a number of years with only limited success. It is a difficult problem to solve because the optical flow field is nonlinearly related to the 3D motion and depth parameters.
---
paper_title: Computing visual correspondence with occlusions using graph cuts

paper_content:

Several new algorithms for visual correspondence based on graph cuts have recently been developed. While these methods give very strong results in practice, they do not handle occlusions properly. Specifically, they treat the two input images asymmetrically, and they do not ensure that a pixel corresponds to at most one pixel in the other image. In this paper, we present a new method which properly addresses occlusions, while preserving the advantages of graph cut algorithms. We give experimental results for stereo as well as motion, which demonstrate that our method performs well both at detecting occlusions and computing disparities.
---
paper_title: Optical Flow Based Structure from Motion

paper_content:

Reconstructing the 3D shape of a scene from its 2D images is a problem that has attracted a great deal of research. 3D models are nowadays widely used for scientific visualization, entertainment and engineering tasks. Most of the approaches developed by the computer vision community can be roughly classified as feature based or flow based, according to if the data they use is a set of features matches or an optical flow field. While a dense optical flow field, due to its noisy nature, is not extremely suitable for tracking, finding corresponding features between different views of large baseline is still an open problem. The system we develop in this thesis is of a hybrid type. We track sparse features over sequences acquired at 25Hz from an hand held camera. During the tracking good features can be selected as those laying in high textured areas: this guarantees higher precision in the estimation of features displacements. Such displacements are used to approximate optical flow. We demonstrate that this approximation is a good one for our working conditions. Using this approach we bypass the matching problem of stereo and the complexity and time integration problems of the optical flow based reconstruction. Time integration is obtained by an optimal predict-update procedure that merges measurements by re-weighting by the respective covariance measurements. Most of the research effort of this thesis is focused on the robust estimation of structure and motion from a pair of images and the related optical flow field. We test first a linear solution that has the appealing property of being of closed form but the problem of returning biased estimates. We propose an non-linear refinement to the linear estimator showing convergence properties and improvements in bias and variance. We further extend the non-linear estimator to incorporate the optical flow covariance matrix (maximum-likelihood) and, moreover, we show that, in the case of dense sequences, it is possible to locally time integrate the reconstruction process for increased robustness. We experimentally investigate the possibility of introducing geometrical constraints in the structure and motion estimation. Such constraints are of bilinear type, i.e. planes, lines and incidence of these primitives are used. For this purpose we present a new motion based segmentation algorithm able to automatically detect and reconstruct planar regions. To asses the efficacy of our solution the algorithms were tested on a variety of real and simulated sequences. ISBN 91-7283-308-4 • TRITA-02-11 • ISSN 0348-2952 • ISRN KTH/NA/R 02-11
---
paper_title: Gauge fixing for accurate 3D estimation

paper_content:

Computer vision techniques can estimate 3D shape from images, but usually only up to a scale factor. The scale factor must be obtained by a physical measurement of the scene or the camera motion. Using gauge theory, we show that how this scale factor is determined can significantly affect the accuracy of the estimated shape. And yet these considerations have been ignored in previous works where 3D shape accuracy is optimized. We investigate how scale fixing influences the accuracy of 3D reconstruction and determine what measurement should be made to maximize the shape accuracy.
---
paper_title: Depth from Edge and Intensity Based Stereo

paper_content:

The past few years have seen a growing interest in the application" of three-dimensional image processing. With the increasing demand for 3-D spatial information for tasks of passive navigation [7,12], automatic surveillance [9], aerial cartography [10,13], and inspection in industrial automation, the importance of effective stereo analysis has been made quite clear. A particular challenge is to provide reliable and accurate depth data for input to object or terrain modelling systems (such as [5]. This paper describes an algorithm for such stereo sensing It uses an edge-based line-by-line stereo correlation scheme, and appears to be fast, robust, and parallel implementable. The processing consists of extracting edge descriptions for a stereo pair of images, linking these edges to their nearest neighbors to obtain the edge connectivity structure, correlating the edge descriptions on the basis of local edge properties, then cooperatively removmg those edge correspondences determined to be in error - those which violate the connectivity structure of the two images. A further correlation process, using a technique similar to that used for the edges, is applied to the image intensity values over intervals defined by the previous correlation The result of the processing is a full image array disparity map of the scene viewed.
---
paper_title: A direct method for stereo correspondence based on singular value decomposition

paper_content:

This paper proposes a new algorithm for matching point features across pairs of images. Despite the well-known combinatorial complexity of the problem, this work shows that an acceptably good solution can be obtained directly by singular value decomposition of an appropriate correspondence strength matrix. The approach draws from the method proposed previously but, besides suggesting its usefulness for stereo matching, in this work a correlation-weighted proximity function is used as correspondence strength to specifically cater for real images.
---
paper_title: Robust image corner detection through curvature scale space

paper_content:

This paper describes a novel method for image corner detection based on the curvature scale-space (CSS) representation. The first step is to extract edges from the original image using a Canny detector (1986). The corner points of an image are defined as points where image edges have their maxima of absolute curvature. The corner points are detected at a high scale of the CSS and tracked through multiple lower scales to improve localization. This method is very robust to noise, and we believe that it performs better than the existing corner detectors An improvement to Canny edge detector's response to 45/spl deg/ and 135/spl deg/ edges is also proposed. Furthermore, the CSS detector can provide additional point features (curvature zero-crossings of image edge contours) in addition to the traditional corners.
---
paper_title: A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms

paper_content:

Stereo matching is one of the most active research areas in computer vision. While a large number of algorithms for stereo correspondence have been developed, relatively little work has been done on characterizing their performance. In this paper, we present a taxonomy of dense, two-frame stereo methods designed to assess the different components and design decisions made in individual stereo algorithms. Using this taxonomy, we compare existing stereo methods and present experiments evaluating the performance of many different variants. In order to establish a common software platform and a collection of data sets for easy evaluation, we have designed a stand-alone, flexible C++ implementation that enables the evaluation of individual components and that can be easily extended to include new algorithms. We have also produced several new multiframe stereo data sets with ground truth, and are making both the code and data sets available on the Web.
---
paper_title: What energy functions can be minimized via graph cuts

paper_content:

In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes many previous constructions and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration, and scene reconstruction. We give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a general-purpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible and then follow our construction to create the appropriate graph. A software implementation is freely available.
---
paper_title: Stereo Correspondence Based on Line Matching in Hough Space Using Dynamic Programming

paper_content:

This paper presents a method of using Hough space for solving the correspondence problem in stereo vision. It is shown that the line-matching problem in image space can readily be converted into a point-matching problem in Hough (/spl rho/-/spl theta/) space. Dynamic programming can be used for searching the optimal matching, now in Hough space. The combination of multiple constraints, especially the natural embedding of the constraint of figural continuity, ensures the accuracy of the matching. The time complexity for searching in dynamic programming is O(pmn), where m and n are the numbers of the lines for each /spl theta/ in the pair of stereo images, respectively, and p is the number of all possible line orientations. Since m and n are usually fairly small, the matching process is very efficient. Experimental results from both binocular and trinocular matchings are presented and analyzed. >
---
paper_title: Gray-level corner detection

paper_content:

The usual approach to detecting corners in shapes involves first segmenting the shape, then locating the corners in its boundary. We present several techniques for measuring 'cornerity' values in gray-level images, without prior segmentation, so that corners can be detected by thresholding these values.
---
paper_title: Generalized Voxel Coloring

paper_content:

Image-based reconstruction from randomly scattered views is a challenging problem. We present a new algorithm that extends Seitz and Dyer's Voxel Coloring algorithm. Unlike their algorithm, ours can use images from arbitrary camera locations. The key problem in this class of algorithms is that of identifying the images from which a voxel is visible. Unlike Kutulakos and Seitz's Space Carving technique, our algorithm solves this problem exactly and the resulting reconstructions yield better results in our application, which is synthesizing new views. One variation of our algorithm minimizes color consistency comparisons; another uses less memory and can be accelerated with graphics hardware. We present efficiency measurements and, for comparison, we present images synthesized using our algorithm and Space Carving.
---
paper_title: Rapid octree representation from image sequences

paper_content:

A mercury trap apparatus used in connection with a differential pressure meter comprising a plurality of mercury trap receptacles, each of the mercury trap receptacles having a pipe with a T-shaped nozzle inserted therein, and extending a predetermined distance into the enclosed area of the mercury trap receptacle; each of the mercury trap receptacles are connected to a gas pipeline by a high-pressure conduit and with the trap receptacle pipe being connected to a mercury differential pressure meter by a connector conduit.
---
paper_title: Photorealistic scene reconstruction by voxel coloring

paper_content:

A novel scene reconstruction technique is presented, different from previous approaches in its ability to cope with large changes in visibility and its modeling of intrinsic scene color and texture information. The method avoids image correspondence problems by working in a discretized scene space whose voxels are traversed in a fixed visibility ordering. This strategy takes full account of occlusions and allows the input cameras to be far apart and widely distributed about the environment. The algorithm identifies a special set of invariant voxels which together form a spatial and photometric reconstruction of the scene, fully consistent with the input images. The approach is evaluated with images from both inward- and outward-facing cameras.
---
paper_title: Variational multiframe stereo in the presence of specular reflections

paper_content:

We consider the problem of estimating the surface of an object from a calibrated set of views under the assumption that the reflectance of the object is non-Lambertian. In particular, we consider the case when the object presents sharp specular reflections. We pose the problem within a variational framework and use fast numerical techniques to approach the local minimum of a regularized cost functional.
---
paper_title: Variational principles, surface evolution, PDE's, level set methods and the stereo problem

paper_content:

We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (greater than or equal to 2). It is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images. The Euler-Lagrange equations which are deduced from the variational principle provide a set of PDE's which are used to deform an initial set of surfaces which then move towards the objects to be detected. The level set implementation of these PDE's potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformation, i.e. to deal with multiple objects. Results of a two dimensional implementation of our theory are presented on synthetic and real images.
---
paper_title: Canonic representations for the geometries of multiple projective views

paper_content:

We show how a special decomposition of general projection matrices, called canonic enables us to build geometric descriptions for a system of cameras which are invariant with respect to a given group of transformations. These representations are minimal and capture completely the properties of each level of description considered: Euclidean (in the context of calibration, and in the context of structure from motion, which we distinguish clearly), affine, and projective, that we also relate to each other. In the last case, a new decomposition of the well-known fundamental matrix is obtained. Dependencies, which appear when three or more views are available, are studied in the context of the canonic decomposition, and new composition formulas are established, as well as the link between local (ie for pairs of views) representations and global (ie for a sequence of images) representations.
---
paper_title: A Factorization Based Algorithm for Multi-Image Projective Structure and Motion

paper_content:

We propose a method for the recovery of projective shape and motion from multiple images of a scene by the factorization of a matrix containing the images of all points in all views. This factorization is only possible when the image points are correctly scaled. The major technical contribution of this paper is a practical method for the recovery of these scalings, using only fundamental matrices and epipoles estimated from the image data. The resulting projective reconstruction algorithm runs quickly and provides accurate reconstructions. Results are presented for simulated and real images.
---
paper_title: SUSAN—A New Approach to Low Level Image Processing

paper_content:

This paper describes a new approach to low level image processing; in particular, edge and corner detection and structure preserving noise reduction. ::: ::: Non-linear filtering is used to define which parts of the image are closely related to each individual pixel; each pixel has associated with it a local image region which is of similar brightness to that pixel. The new feature detectors are based on the minimization of this local image region, and the noise reduction method uses this region as the smoothing neighbourhood. The resulting methods are accurate, noise resistant and fast. ::: ::: Details of the new feature detectors and of the new noise reduction method are described, along with test results.
---
paper_title: Shape and motion from im-age streams under orthography: A factorization approach

paper_content:

A weft yarn control device for assuring proper positioning of the weft yarn during the second phase of the weaving cycle in shuttleless looms of the type wherein weft yarn from a stationary source is inserted individually into separate sheds of warp threads in pairs of interconnected picks.
---
paper_title: Using vanishing points for camera calibration

paper_content:

In this article a new method for the calibration of a vision system which consists of two (or more) cameras is presented. The proposed method, which uses simple properties of vanishing points, is divided into two steps. In the first step, the intrinsic parameters of each camera, that is, the focal length and the location of the intersection between the optical axis and the image plane, are recovered from a single image of a cube. In the second step, the extrinsic parameters of a pair of cameras, that is, the rotation matrix and the translation vector which describe the rigid motion between the coordinate systems fixed in the two cameras are estimated from an image stereo pair of a suitable planar pattern. Firstly, by matching the corresponding vanishing points in the two images the rotation matrix can be computed, then the translation vector is estimated by means of a simple triangulation. The robustness of the method against noise is discussed, and the conditions for optimal estimation of the rotation matrix are derived. Extensive experimentation shows that the precision that can be achieved with the proposed method is sufficient to efficiently perform machine vision tasks that require camera calibration, like depth from stereo and motion from image sequence.
---
paper_title: Multiple view geometry in computer vision

paper_content:

From the Publisher: ::: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. The book covers the geometric principles and how to represent objects algebraically so they can be computed and applied. The authors provide comprehensive background material and explain how to apply the methods and implement the algorithms directly.
---
paper_title: Determining vanishing points from perspective images

paper_content:

Abstract This paper describes a computationally inexpensive algorithm for the determination of vanishing points once line segments in an image have been determined. The approach is particularly attractive since it has no computationally degenerate cases and the only operations necessary are vector cross products and arc tangents. The need to know the distance to the focal plane is also eliminated thus avoiding tedious calibration procedures.
---
paper_title: Contribution to the determination of vanishing points using Hough transform

paper_content:

We propose a method to locate three vanishing points on an image, corresponding to three orthogonal directions of the scene. This method is based on two cascaded Hough transforms. We show that, even in the case of synthetic images of high quality, a naive approach may fail, essentially because of the errors due to the limitation of the image size. We take into account these errors as well as errors due to detection inaccuracy of the image segments, and provide a method efficient, even in the case of real complex scenes. >
---
paper_title: Determining perspective structures using hierarchical Hough transform

paper_content:

In this paper, we present an efficient algorithm determining perspective structures such as vanishing points and horizon lines for indoor scenes. The algorithm is implemented as a hierarchical Hough transform on the pyramidal sphere.
---
paper_title: Using vanishing points for camera calibration

paper_content:

In this article a new method for the calibration of a vision system which consists of two (or more) cameras is presented. The proposed method, which uses simple properties of vanishing points, is divided into two steps. In the first step, the intrinsic parameters of each camera, that is, the focal length and the location of the intersection between the optical axis and the image plane, are recovered from a single image of a cube. In the second step, the extrinsic parameters of a pair of cameras, that is, the rotation matrix and the translation vector which describe the rigid motion between the coordinate systems fixed in the two cameras are estimated from an image stereo pair of a suitable planar pattern. Firstly, by matching the corresponding vanishing points in the two images the rotation matrix can be computed, then the translation vector is estimated by means of a simple triangulation. The robustness of the method against noise is discussed, and the conditions for optimal estimation of the rotation matrix are derived. Extensive experimentation shows that the precision that can be achieved with the proposed method is sufficient to efficiently perform machine vision tasks that require camera calibration, like depth from stereo and motion from image sequence.
---
paper_title: Interpreting perspective images

paper_content:

A fundamental problem in computer vision is how to determine the 3-D spatial orientation of curves and surfaces appearing in an image. The problem is generally underconstrained, and is complicated by the fact that metric properties, such as orientation and length, are not invariant under projection. Under perspective projection (the correct model for most real images) the transform is nonlinear, and therefore hard to invert. Two constructive methods are presented. The first finds the orientation of parallel lines and planes by locating vanishing points and vanishing lines. The second determines the orientation of planes by 'backprojection' of two intrinsic properties of contours: angle magnitude and curvature.
---
paper_title: Multiple view geometry in computer vision

paper_content:

From the Publisher: ::: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. The book covers the geometric principles and how to represent objects algebraically so they can be computed and applied. The authors provide comprehensive background material and explain how to apply the methods and implement the algorithms directly.
---
paper_title: Cooperative computation of stereo disparity

paper_content:

Perhaps one of the most striking differences between a brain and today’s computers is the amount of “wiring.” In a digital computer the ratio of connections to components is about 3, whereas for the mammalian cortex it lies between 10 and 10,000 (1).
---
paper_title: Kruppa's equations derived from the fundamental matrix

paper_content:

The purpose of this paper is to give a specific form for Kruppa's equations in terms of the fundamental matrix. Kruppa's equations can be written explicitly in terms of the singular value decomposition (SVD) of the fundamental matrix.
---
paper_title: Three-dimensional computer vision: a geometric viewpoint

paper_content:

Projective geometry modelling and calibrating cameras edge detection representing geometric primitives and their uncertainty stereo vision determining discrete motion from points and lines tracking tokens over time motion fields of curves interpolating and approximating three-dimensional data recognizing and locating objects and places answers to problems. Appendices: constrained optimization some results from algebraic geometry differential geometry.
---
paper_title: Camera Self-Calibration: Theory and Experiments

paper_content:

The problem of finding the internal orientation of a camera (camera calibration) is extremely important for practical applications. In this paper a complete method for calibrating a camera is presented. In contrast with existing methods it does not require a calibration object with a known 3D shape. The new method requires only point matches from image sequences. It is shown, using experiments with noisy data, that it is possible to calibrate a camera just by pointing it at the environment, selecting points of interest and then tracking them in the image as the camera moves. It is not necessary to know the camera motion.
---
paper_title: Subspace methods for recovering rigid motion I: Algorithm and implementation

paper_content:

As an observer moves and explores the environment, the visual stimulation in his/her eye is constantly changing. Somehow he/she is able to perceive the spatial layout of the scene, and to discern his/her movement through space. Computational vision researchers have been trying to solve this problem for a number of years with only limited success. It is a difficult problem to solve because the optical flow field is nonlinearly related to the 3D motion and depth parameters.
---
paper_title: Computing visual correspondence with occlusions using graph cuts

paper_content:

Several new algorithms for visual correspondence based on graph cuts have recently been developed. While these methods give very strong results in practice, they do not handle occlusions properly. Specifically, they treat the two input images asymmetrically, and they do not ensure that a pixel corresponds to at most one pixel in the other image. In this paper, we present a new method which properly addresses occlusions, while preserving the advantages of graph cut algorithms. We give experimental results for stereo as well as motion, which demonstrate that our method performs well both at detecting occlusions and computing disparities.
---
paper_title: Optical Flow Based Structure from Motion

paper_content:

Reconstructing the 3D shape of a scene from its 2D images is a problem that has attracted a great deal of research. 3D models are nowadays widely used for scientific visualization, entertainment and engineering tasks. Most of the approaches developed by the computer vision community can be roughly classified as feature based or flow based, according to if the data they use is a set of features matches or an optical flow field. While a dense optical flow field, due to its noisy nature, is not extremely suitable for tracking, finding corresponding features between different views of large baseline is still an open problem. The system we develop in this thesis is of a hybrid type. We track sparse features over sequences acquired at 25Hz from an hand held camera. During the tracking good features can be selected as those laying in high textured areas: this guarantees higher precision in the estimation of features displacements. Such displacements are used to approximate optical flow. We demonstrate that this approximation is a good one for our working conditions. Using this approach we bypass the matching problem of stereo and the complexity and time integration problems of the optical flow based reconstruction. Time integration is obtained by an optimal predict-update procedure that merges measurements by re-weighting by the respective covariance measurements. Most of the research effort of this thesis is focused on the robust estimation of structure and motion from a pair of images and the related optical flow field. We test first a linear solution that has the appealing property of being of closed form but the problem of returning biased estimates. We propose an non-linear refinement to the linear estimator showing convergence properties and improvements in bias and variance. We further extend the non-linear estimator to incorporate the optical flow covariance matrix (maximum-likelihood) and, moreover, we show that, in the case of dense sequences, it is possible to locally time integrate the reconstruction process for increased robustness. We experimentally investigate the possibility of introducing geometrical constraints in the structure and motion estimation. Such constraints are of bilinear type, i.e. planes, lines and incidence of these primitives are used. For this purpose we present a new motion based segmentation algorithm able to automatically detect and reconstruct planar regions. To asses the efficacy of our solution the algorithms were tested on a variety of real and simulated sequences. ISBN 91-7283-308-4 • TRITA-02-11 • ISSN 0348-2952 • ISRN KTH/NA/R 02-11
---
paper_title: Depth from Edge and Intensity Based Stereo

paper_content:

The past few years have seen a growing interest in the application" of three-dimensional image processing. With the increasing demand for 3-D spatial information for tasks of passive navigation [7,12], automatic surveillance [9], aerial cartography [10,13], and inspection in industrial automation, the importance of effective stereo analysis has been made quite clear. A particular challenge is to provide reliable and accurate depth data for input to object or terrain modelling systems (such as [5]. This paper describes an algorithm for such stereo sensing It uses an edge-based line-by-line stereo correlation scheme, and appears to be fast, robust, and parallel implementable. The processing consists of extracting edge descriptions for a stereo pair of images, linking these edges to their nearest neighbors to obtain the edge connectivity structure, correlating the edge descriptions on the basis of local edge properties, then cooperatively removmg those edge correspondences determined to be in error - those which violate the connectivity structure of the two images. A further correlation process, using a technique similar to that used for the edges, is applied to the image intensity values over intervals defined by the previous correlation The result of the processing is a full image array disparity map of the scene viewed.
---
paper_title: A direct method for stereo correspondence based on singular value decomposition

paper_content:

This paper proposes a new algorithm for matching point features across pairs of images. Despite the well-known combinatorial complexity of the problem, this work shows that an acceptably good solution can be obtained directly by singular value decomposition of an appropriate correspondence strength matrix. The approach draws from the method proposed previously but, besides suggesting its usefulness for stereo matching, in this work a correlation-weighted proximity function is used as correspondence strength to specifically cater for real images.
---
paper_title: Volume/surface octrees for the representation of three-dimensional objects

paper_content:

The octree structure for the representation of 3D objects is an extension of the quadtree representation of 2D (binary) images. It is generated from the 3D binary array of the object it represents. However, the acquisition of a 3D array is not a trivial problem. In this study, we propose a scheme to generate an octree of an object from its three orthogonal views (silhouettes) exploiting a volume intersection technique. A multi-level boundary search algorithm is developed to incorporate surface information into the octree representation. This makes the octree representation compact, informative, and especially useful for graphic displays and object recognition tasks. An algorithm is also designed for computing the moment of inertia matrix, which is useful for object recognition. All the algorithms developed in this study are essentially tree traversal procedures and therefore are suitable for implementation on parallel processors.
---
paper_title: Stereo Correspondence Based on Line Matching in Hough Space Using Dynamic Programming

paper_content:

This paper presents a method of using Hough space for solving the correspondence problem in stereo vision. It is shown that the line-matching problem in image space can readily be converted into a point-matching problem in Hough (/spl rho/-/spl theta/) space. Dynamic programming can be used for searching the optimal matching, now in Hough space. The combination of multiple constraints, especially the natural embedding of the constraint of figural continuity, ensures the accuracy of the matching. The time complexity for searching in dynamic programming is O(pmn), where m and n are the numbers of the lines for each /spl theta/ in the pair of stereo images, respectively, and p is the number of all possible line orientations. Since m and n are usually fairly small, the matching process is very efficient. Experimental results from both binocular and trinocular matchings are presented and analyzed. >
---
paper_title: A theory of self-calibration of a moving camera

paper_content:

There is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displacement. The epipolar transformation imposes two algebraic constraints on the camera calibration. If two epipolar transformations, arising from different camera displacements, are available then the compatible camera calibrations are parameterized by an algebraic curve of genus four. The curve can be represented either by a space curve of degree seven contained in the intersection of two cubic surfaces, or by a curve of degree six in the dual of the image plane. The curve in the dual plane has one singular point of order three and three singular points of order two.
---
paper_title: Stratified self-calibration with the modulus constraint

paper_content:

In computer vision and especially for 3D reconstruction, one of the key issues is the retrieval of the calibration parameters of the camera. These are needed to obtain metric information about the scene from the camera. Often these parameters are obtained through cumbersome calibration procedures. There is a way to avoid explicit calibration of the camera. Self-calibration is based on finding the set of calibration parameters which satisfy some constraints (e.g., constant calibration parameters). Several techniques have been proposed but it often proved difficult to reach a metric calibration at once. Therefore, in the paper, a stratified approach is proposed, which goes from projective through affine to metric. The key concept to achieve this is the modulus constraint. It allows retrieval of the affine calibration for constant intrinsic parameters. It is also suited for use in conjunction with scene knowledge. In addition, if the affine calibration is known, it can also be used to cope with a changing focal length.
---
paper_title: Self-Calibration from Image Triplets

paper_content:

We describe a method for determining affine and metric calibration of a camera with unchanging internal parameters undergoing planar motion. It is shown that affine calibration is recovered uniquely, and metric calibration up to a two fold ambiguity.
---
paper_title: Critical motion sequences for monocular self-calibration and uncalibrated Euclidean reconstruction

paper_content:

In this paper sequences of camera motions that lead to inherent ambiguities in uncalibrated Euclidean reconstruction or self-calibration are studied. Our main contribution is a complete, detailed classification of these critical motion sequences (CMS). The practically important classes are identified and their degrees of ambiguity are derived. We also discuss some practical issues, especially concerning the reduction of the ambiguity of a reconstruction.
---
paper_title: Ground Plane Motion Camera Models

paper_content:

We show that it is possible to build an application-specific motion constraint into a general hierarchy of camera models so that the resulting algorithm is efficient and well conditioned; and the system degrades gracefully if the constraint is violated. The current work arose in the context of a specific application, namely smart convoying of vehicles on highways, and so ground plane motion (GPM) arises naturally. The algorithm for estimating motion from monocular, uncalibrated image sequences under ground plane motion involves the computation of three kinds of structure α,Β and γ for which algorithms are presented. Typical results on real data are shown.
---
paper_title: Multiple view geometry in computer vision

paper_content:

From the Publisher: ::: A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. The book covers the geometric principles and how to represent objects algebraically so they can be computed and applied. The authors provide comprehensive background material and explain how to apply the methods and implement the algorithms directly.
---
paper_title: Rapid octree representation from image sequences

paper_content:

A mercury trap apparatus used in connection with a differential pressure meter comprising a plurality of mercury trap receptacles, each of the mercury trap receptacles having a pipe with a T-shaped nozzle inserted therein, and extending a predetermined distance into the enclosed area of the mercury trap receptacle; each of the mercury trap receptacles are connected to a gas pipeline by a high-pressure conduit and with the trap receptacle pipe being connected to a mercury differential pressure meter by a connector conduit.
---
paper_title: A direct method for stereo correspondence based on singular value decomposition

paper_content:

This paper proposes a new algorithm for matching point features across pairs of images. Despite the well-known combinatorial complexity of the problem, this work shows that an acceptably good solution can be obtained directly by singular value decomposition of an appropriate correspondence strength matrix. The approach draws from the method proposed previously but, besides suggesting its usefulness for stereo matching, in this work a correlation-weighted proximity function is used as correspondence strength to specifically cater for real images.
---

Title: A Survey of Motion-Parallax-Based 3-D Reconstruction Algorithms

Section 1: INTRODUCTION
Description 1: Provide an overview of computer vision's focus on analyzing visual information, the importance of depth cues like motion parallax, and the paper's goals.

Section 2: CLASSIFICATION OF RECONSTRUCTION ALGORITHMS
Description 2: Discuss the classification of different 3-D reconstruction algorithms and their dependence on camera calibration.

Section 3: REVIEW OF PROJECTIVE GEOMETRY
Description 3: Review the fundamental concepts of projective geometry relevant to 3-D reconstruction, including the pinhole camera model, epipolar geometry, the fundamental matrix, and the infinite homography.

Section 4: PRE-CALIBRATED RECONSTRUCTION
Description 4: Examine 3-D reconstruction algorithms that require prior camera calibration, detailing image-based, voxel-based, and object-based approaches.

Section 5: ONLINE CALIBRATED RECONSTRUCTION
Description 5: Explore reconstruction algorithms that do not require prior camera calibration, focusing on projective reconstruction, calibration using scene constraints, and calibration using geometric constraints.

Section 6: CONCLUSION
Description 6: Summarize the surveyed algorithms and discuss open issues and future research directions in motion-parallax-based 3-D reconstruction.