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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Introduction to ITK Segmentation in SimpleITK Notebooks <a href="https
Step1:  Thresholding
Thresholding is the most basic form of segmentation. It simply labels the pixels of an image based on the intensity range without respect to geometry or connectivity.
Step2:  ITK has a number of histogram based automatic thresholding filters including Huang, MaximumEntropy, Triangle, and the popular Otsu's method. These methods create a histogram then use a heuristic to determine a threshold value.
Step3:  Region Growing Segmentation
The first step of improvement upon the naive thresholding is a class of algorithms called region growing. This includes
Step4:  Improving upon this is the ConfidenceConnected filter, which uses the initial seed or current segmentation to estimate the threshold range.
Step5:  Fast Marching Segmentation
The FastMarchingImageFilter implements a fast marching solution to a simple level set evolution problem (eikonal equation). In this example, the speed term used in the differential equation is provided in the form of an image. The speed image is based on the gradient magnitude and mapped with the bounded reciprocal $1/(1+x)$.
Step6:  The output of the FastMarchingImageFilter is a <b>time-crossing map</b> that indicates, for each pixel, how much time it would take for the front to arrive at the pixel location.
Step7:  Level-Set Segmentation
There are a variety of level-set based segmentation filter available in ITK
Step8:  Use the seed to estimate a reasonable threshold range.
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Python Code:
%matplotlib inline
import matplotlib.pyplot as plt
from ipywidgets import interact, FloatSlider
import SimpleITK as sitk
# Download data to work on
%run update_path_to_download_script
from downloaddata import fetch_data as fdata
from myshow import myshow, myshow3d
img_T1 = sitk.ReadImage(fdata("nac-hncma-atlas2013-Slicer4Version/Data/A1_grayT1.nrrd"))
img_T2 = sitk.ReadImage(fdata("nac-hncma-atlas2013-Slicer4Version/Data/A1_grayT2.nrrd"))
# To visualize the labels image in RGB with needs a image with 0-255 range
img_T1_255 = sitk.Cast(sitk.RescaleIntensity(img_T1), sitk.sitkUInt8)
img_T2_255 = sitk.Cast(sitk.RescaleIntensity(img_T2), sitk.sitkUInt8)
myshow3d(img_T1)
Explanation: Introduction to ITK Segmentation in SimpleITK Notebooks <a href="https://mybinder.org/v2/gh/InsightSoftwareConsortium/SimpleITK-Notebooks/master?filepath=Python%2F300_Segmentation_Overview.ipynb"><img style="float: right;" src="https://mybinder.org/badge_logo.svg"></a>
<b>Goal</b>: To become familiar with basic segmentation algorithms available in ITK, and interactively explore their parameter space.
Image segmentation filters process an image to partition it into (hopefully) meaningful regions. The output is commonly an image of integers where each integer can represent an object. The value 0 is commonly used for the background, and 1 ( sometimes 255) for a foreground object.
End of explanation
seg = img_T1 > 200
myshow(sitk.LabelOverlay(img_T1_255, seg), "Basic Thresholding")
seg = sitk.BinaryThreshold(
    img_T1, lowerThreshold=100, upperThreshold=400, insideValue=1, outsideValue=0
)
myshow(sitk.LabelOverlay(img_T1_255, seg), "Binary Thresholding")
Explanation: Thresholding
Thresholding is the most basic form of segmentation. It simply labels the pixels of an image based on the intensity range without respect to geometry or connectivity.
End of explanation
otsu_filter = sitk.OtsuThresholdImageFilter()
otsu_filter.SetInsideValue(0)
otsu_filter.SetOutsideValue(1)
seg = otsu_filter.Execute(img_T1)
myshow(sitk.LabelOverlay(img_T1_255, seg), "Otsu Thresholding")
print(otsu_filter.GetThreshold())
Explanation: ITK has a number of histogram based automatic thresholding filters including Huang, MaximumEntropy, Triangle, and the popular Otsu's method. These methods create a histogram then use a heuristic to determine a threshold value.
End of explanation
seed = (132, 142, 96)
seg = sitk.Image(img_T1.GetSize(), sitk.sitkUInt8)
seg.CopyInformation(img_T1)
seg[seed] = 1
seg = sitk.BinaryDilate(seg, [3] * 3)
myshow(sitk.LabelOverlay(img_T1_255, seg), "Initial Seed")
seg = sitk.ConnectedThreshold(img_T1, seedList=[seed], lower=100, upper=190)
myshow(sitk.LabelOverlay(img_T1_255, seg), "Connected Threshold")
Explanation: Region Growing Segmentation
The first step of improvement upon the naive thresholding is a class of algorithms called region growing. This includes:
<ul>
  <li><a href="http://www.itk.org/Doxygen/html/classitk_1_1ConnectedThresholdImageFilter.html">ConnectedThreshold</a></li>
  <li><a href="http://www.itk.org/Doxygen/html/classitk_1_1ConfidenceConnectedImageFilter.html">ConfidenceConnected</a></li>
  <li><a href="http://www.itk.org/Doxygen/html/classitk_1_1VectorConfidenceConnectedImageFilter.html">VectorConfidenceConnected</a></li>
  <li><a href="http://www.itk.org/Doxygen/html/classitk_1_1NeighborhoodConnectedImageFilter.html">NeighborhoodConnected</a></li>
</ul>
Earlier we used 3D Slicer to determine that index: (132,142,96) was a good seed for the left lateral ventricle.
End of explanation
seg = sitk.ConfidenceConnected(
    img_T1,
    seedList=[seed],
    numberOfIterations=1,
    multiplier=2.5,
    initialNeighborhoodRadius=1,
    replaceValue=1,
)
myshow(sitk.LabelOverlay(img_T1_255, seg), "ConfidenceConnected")
img_multi = sitk.Compose(img_T1, img_T2)
seg = sitk.VectorConfidenceConnected(
    img_multi,
    seedList=[seed],
    numberOfIterations=1,
    multiplier=2.5,
    initialNeighborhoodRadius=1,
)
myshow(sitk.LabelOverlay(img_T2_255, seg))
Explanation: Improving upon this is the ConfidenceConnected filter, which uses the initial seed or current segmentation to estimate the threshold range.
End of explanation
seed = (132, 142, 96)
feature_img = sitk.GradientMagnitudeRecursiveGaussian(img_T1, sigma=0.5)
speed_img = sitk.BoundedReciprocal(
    feature_img
)  # This is parameter free unlike the Sigmoid
myshow(speed_img)
Explanation: Fast Marching Segmentation
The FastMarchingImageFilter implements a fast marching solution to a simple level set evolution problem (eikonal equation). In this example, the speed term used in the differential equation is provided in the form of an image. The speed image is based on the gradient magnitude and mapped with the bounded reciprocal $1/(1+x)$.
End of explanation
fm_filter = sitk.FastMarchingBaseImageFilter()
fm_filter.SetTrialPoints([seed])
fm_filter.SetStoppingValue(1000)
fm_img = fm_filter.Execute(speed_img)
myshow(
    sitk.Threshold(
        fm_img,
        lower=0.0,
        upper=fm_filter.GetStoppingValue(),
        outsideValue=fm_filter.GetStoppingValue() + 1,
    )
)
def fm_callback(img, time, z):
    seg = img < time
    myshow(sitk.LabelOverlay(img_T1_255[:, :, z], seg[:, :, z]))
interact(
    lambda **kwargs: fm_callback(fm_img, **kwargs),
    time=FloatSlider(min=0.05, max=1000.0, step=0.05, value=100.0),
    z=(0, fm_img.GetSize()[2] - 1),
)
Explanation: The output of the FastMarchingImageFilter is a <b>time-crossing map</b> that indicates, for each pixel, how much time it would take for the front to arrive at the pixel location.
End of explanation
seed = (132, 142, 96)
seg = sitk.Image(img_T1.GetSize(), sitk.sitkUInt8)
seg.CopyInformation(img_T1)
seg[seed] = 1
seg = sitk.BinaryDilate(seg, [3] * 3)
Explanation: Level-Set Segmentation
There are a variety of level-set based segmentation filter available in ITK:
<ul>
<li><a href="http://www.itk.org/Doxygen/html/classitk_1_1GeodesicActiveContourLevelSetImageFilter.html">GeodesicActiveContour</a></li>
<li><a href="http://www.itk.org/Doxygen/html/classitk_1_1ShapeDetectionLevelSetImageFilter.html">ShapeDetection</a></li>
<li><a href="http://www.itk.org/Doxygen/html/classitk_1_1ThresholdSegmentationLevelSetImageFilter.html">ThresholdSegmentation</a></li>
<li><a href="http://www.itk.org/Doxygen/html/classitk_1_1LaplacianSegmentationLevelSetImageFilter.html">LaplacianSegmentation</a></li>
<li><a href="http://www.itk.org/Doxygen/html/classitk_1_1ScalarChanAndVeseDenseLevelSetImageFilter.html">ScalarChanAndVese</a></li>
</ul>
There is also a <a href="http://www.itk.org/Doxygen/html/group__ITKLevelSetsv4.html">modular Level-set framework</a> which allows composition of terms and easy extension in C++.
First we create a label image from our seed.
End of explanation
stats = sitk.LabelStatisticsImageFilter()
stats.Execute(img_T1, seg)
factor = 3.5
lower_threshold = stats.GetMean(1) - factor * stats.GetSigma(1)
upper_threshold = stats.GetMean(1) + factor * stats.GetSigma(1)
print(lower_threshold, upper_threshold)
init_ls = sitk.SignedMaurerDistanceMap(seg, insideIsPositive=True, useImageSpacing=True)
lsFilter = sitk.ThresholdSegmentationLevelSetImageFilter()
lsFilter.SetLowerThreshold(lower_threshold)
lsFilter.SetUpperThreshold(upper_threshold)
lsFilter.SetMaximumRMSError(0.02)
lsFilter.SetNumberOfIterations(1000)
lsFilter.SetCurvatureScaling(0.5)
lsFilter.SetPropagationScaling(1)
lsFilter.ReverseExpansionDirectionOn()
ls = lsFilter.Execute(init_ls, sitk.Cast(img_T1, sitk.sitkFloat32))
print(lsFilter)
myshow(sitk.LabelOverlay(img_T1_255, ls > 0))
Explanation: Use the seed to estimate a reasonable threshold range.
End of explanation
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