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  • Bridge
    • VtkGlue
      • Convert an itk::Image to vtkImageData
      • Convert an RGB itk::Image to vtkImageData
      • Convert RGB vtkImageData to an itk::Image
      • Convert vtkImageData to an itk::Image
      • Visualize an Evolving Dense 2D Level Set as Elevation Map
      • Visualize an Evolving Dense 2D Level-Set Zero-Set
      • Visualize a Static Dense 2D Level Set as Elevation Map
      • Visualize a Static Dense 2D Level-Set Zero-Set
      • Visualize a Static Sparse Malcolm 2D Level-Set Layers
      • Visualize a Static Sparse Shi 2D Level-Set Layers
      • Visualize a Static Sparse Whitaker 2D Level-Set Layers
      • VTK Image to ITK Image
    • NumPy
      • Interface ITK with NumPy Array
        • Bridging ITK image data with NumPy array
  • Core
    • Common
      • Add Noise To Binary Image
      • Add Offset To Index
      • Apply a Filter Only to a Specified Region of an Image
      • Apply Custom Operation to Each Pixel in Image
      • Bounding Box of a Point Set
      • Bresenham Line
      • Build a Hello World Program
      • Cast Vector Image to Another Type
      • Check if Module Is Present
      • Compute Time Between Points
      • Concept Checking Is Floating Point
      • Concept Checking Is Same Dimension
      • Concept Checking Is Same Type
      • Convert Array to Image
      • Covariant Vector Dot Product
      • Covariant Vector Norm
      • Create a Backward Difference Operator
      • Create a CovariantVector
      • Create a Fixed Array
      • Create a Index
      • Create a PointSet
      • Create a Size
      • Create a Vector
      • Create an Image
      • Create an Image Region
      • Create an Image of Vectors
      • Create an RGB Image
      • Create Another Instance Of A Filter
      • Create Another Instance of an Image
      • Create Derivative Kernel
      • Create Forward Difference Kernel
      • Create Gaussian Derivative Kernel
      • Create Gaussian Kernel
      • Create Laplacian Kernel
      • Create Sobel Kernel
      • Create Vector Image
      • Crop Image by Specifying Region
      • Deep Copy Image
      • Demonstrate All Operators
      • Direct Warning to File
      • Display Image
      • Distance Between Indices
      • Distance Between Points
      • Do Data Parallel Threading
      • Duplicate an Image
      • Eagerly Load Python Modules
      • Filter and ParallelizeImageRegion Comparison
      • Filter Image
      • Filter Image Using Multiple Threads
      • Filter Image Without Copying Its Data
      • Find Max and Min in Image
      • Generate the Offsets of a Shaped Image Neighborhood
      • Get Image Size
      • Get Name of Class
      • Get or Set Member Variable of ITK Class
      • Get Type Basic Information
      • Iterate Over an Image Buffer and an Index Range
      • Image Region Intersection
      • Image Region Overlap
      • Import Pixel Buffer Into an Image
      • In Place Filter of Image
      • Is Pixel Inside Region
      • Iterate Image Starting at Seed
      • Iterate Line Through Image
      • Iterate Line Through Image Without Write Access
      • Iterate on a Vector Container
      • Iterate Over a Region With a Shaped Neighborhood Iterator
      • Iterate Over a Region With a Shaped Neighborhood Iterator Manually
      • Iterate Over Image While Skipping Specific Region
      • Iterate Region in Image With Access to Index Without Write Access
      • Iterate Region in Image With Access to Current Index With Write Access
      • Iterate Region in Image With Neighborhood
      • Iterate Region in Image With Neighborhood Without Write Access
      • Iterate Region in Image With Write Access
      • Iterate Region in Image Without Write Access
      • Make Out of Bounds Pixels Return Constant Value
      • Make Part of an Image Transparent
      • Matrix
      • Matrix Inverse
      • Mersenne Twister Random Integer Generator
      • Mersenne Twister Random Number Generator
      • Mini Pipeline
      • Multiple Inputs of Different Type
      • Multiple Inputs of Same Type
      • Multiple Outputs of Different Type
      • Multiple Outputs of Same Type
      • Multi-thread Oil Painting
      • Neighborhood Iterator on Vector Image
      • Observe an Event
      • Pass Image to Function
      • Permute Sequence of Indices
      • Pi Constant
      • Print ITK Python Module Loading
      • Produce Image Programmatically
      • Random Selection of Pixels From Region
      • Random Select Pixel From Region Without Replacing
      • Read a PointSet
      • Read Write Vector Image
      • Re-Run Pipeline With Changing Largest Possible Region
      • Return Object From Function
      • Set the Default Number of Threads
      • Set Pixel Value in One Image
      • Sort ITK Index
      • Store Non-Pixel Data In Image
      • Stream a Pipeline
      • Throw Exception
      • Trace Memory Between Points
      • Try Catch Exception
      • Use ParallelizeImageRegion
      • Variable Length Vector
      • Vector Dot Product
      • Watch a Filter
      • Write a PointSet
    • ImageAdaptors
      • Add Constant to Every Pixel Without Duplicating Memory
      • Extract Channel of Image With Multiple Components
      • Present Image After Operation
      • Process Nth Component of Vector Image
      • View Component Vector Image as Scalar Image
    • ImageFunction
      • Compute Median of Image at Pixel
      • Linearly Interpolate Position in Image
      • Multiply Kernel With an Image at Location
      • Resample Segmented Image
    • Mesh
      • Access data in cells
      • Add Points and Edges
      • Calculate Area and Volume of Simplex Mesh
      • Convert Mesh to Unstructered Grid
      • Convert Triangle Mesh to Binary Image
      • Extract Iso Surface
      • Translate One Mesh
      • Working With Point and Cell Data
      • Write Mesh to VTP
    • QuadEdgeMesh
      • Create Triangular Quad Edge Mesh
      • Cut Mesh
      • Extract Vertex on Mesh Boundaries
      • Get List of Faces Around a Given Vertex
      • Print Vertex Neighbors
    • SpatialObjects
      • Blob
      • Contour Spatial Object
      • Convert Spatial Object to Image
      • Create a Line Spatial Object
      • Ellipse
    • TestKernel
      • Generate Random Image
    • Transform
      • Apply Affine Transform From Homogeneous Matrix and Resample
      • Cartesian to Azimuth Elevation
      • Copy a CompositeTransform
      • Copy a Non-CompositeTransform
      • Global Registration Two Images (Affine)
      • Global Registration of Two Images (BSpline)
      • Mutual Information Affine
        • Mutual Information Metric
      • Scale an Image
      • Translate a Vector Image
      • Translate Image
      • Deform a Volume With a Thin Plate Spline
  • External
  • Filtering
    • AnisotropicSmoothing
      • Compute Curvature Anisotropic Diffusion
      • Compute Curvature Flow
      • Compute Gradient Anisotropic Diffusion
      • Perona Malik Anisotropic Diffusion on Grayscale Image
      • Smooth Image While Preserving Edges
      • Smooth Image While Preserving Edges (Curvature)
    • AntiAlias
      • Smooth Binary Image Before Surface Extraction
    • Binary Mathematical Morphology
      • Closing Binary Image
      • Dilate a Binary Image
      • Erode a Binary Image
      • Opening a Binary Image
      • Prune Binary Image
      • Thin Image
    • Colormap
      • Apply a Color Map to an Image
      • Create a Custom Color Map
      • Map Scalars Into Jet Colormap
    • Convolution
      • Color Normalized Correlation
      • Convolve Image With Kernel
      • Normalized Correlation
      • Normalized Correlation of Masked Image
      • Normalized Correlation Using FFT
      • Normalized Correlation Using FFT With Mask Images for Input Images
    • CurvatureFlow
      • Binary Min and Max Curvature Flow of Binary Image
      • Smooth Image Using Curvature Flow
      • Smooth Image Using Min Max Curvature Flow
      • Smooth RGB Image Using Curvature Flow
      • Smooth RGB Image Using Min Max Curvature Flow
    • DistanceMap
      • Approximate Distance Map of Binary Image
      • Maurer Distance Map of Binary Image
      • Mean Distance Between All Points on Two Curves
      • Signed Distance Map of Binary Image
    • FastMarching
      • Compute Geodesic Distance on Mesh
      • Create Distance Map From Seeds
    • FFT
      • Compute Forward FFT
      • Compute Image Spectral Density
      • Compute Inverse FFT of Image
      • Filter Image in Fourier Domain
    • ImageCompare
      • Absolute Value Of Difference Between Two Images
      • Combine Two Images With Checker Board Pattern
      • Squared Difference of Two Images
    • ImageCompose
      • Compose Vector From Three Scalar Images
      • Convert Real and Imaginary Images to Complex Image
      • Create Vector Image From Scalar Images
      • Join Images
    • ImageFeature
      • Add Gaussian Noise to an Image
      • Apply a Filter Only to a Specified Image Region
      • Apply a Filter to a Specified Region of an Image
      • Bilateral Filter an Image
      • Compute Laplacian
      • Detect Edges With Canny Edge Detection Filter
      • Compute Derivative
      • Extract Contours From Image
      • Find Zero Crossings in Signed Image
      • Laplacian Recursive Gaussian Image Filter
      • Segment Blood Vessels
      • Sharpen Image
      • Sobel Edge Detection Image Filter
      • Zero-crossing Based Edge Decor
    • ImageFilterBase
      • Apply Kernel to Every Pixel
      • Apply Kernel to Every Pixel in Non-Zero Image
      • Cast an Image to Another Type
      • Compute Local Noise in Image
      • Custom Operation to Corresponding Pixels in Two Images
      • Predefined Operation to Corresponding Pixels in Two Images
    • ImageFusion
      • Color Boundaries of Labeled Regions
      • Color Labeled Regions in Image
      • Overlay Label Map on Image
      • Overlay Label Map on Top of an Image
    • ImageGradient
      • Apply GradientRecursiveGaussianImageFilter
      • Apply GradientRecursiveGaussianImageFilter on Image With Vector type
      • Compute and Display Gradient of Image
      • Compute Gradient Magnitude of Grayscale Image
      • Compute Gradient Magnitude Recursive Gaussian of Grayscale Image
      • Gradient of Vector Image
      • Implementation of Snakes
    • ImageGrid
      • Append Two 3D Volumes
      • Change Image Origin Spacing or Direction
      • Create 3D Volume
      • Crop Image by Specifying Region
      • Extract Region of Interest in One Image
      • Fit Spline Into Point Set
      • Flip an Image Over Specified Axes
      • Pad an Image by Mirroring
      • Pad an Image With a Constant
      • Pad Image by Wrapping
      • Paste Image Into Another One
      • Permute Axes of an Image
      • Process a 2D Slice of a 3D Image
      • Resample an Image
      • Resample a Scalar Image
      • Resample a Vector Image
      • Run Image Filter on Region of Image
      • Shrink Image
      • Stack 2D Images Into 3D Image
      • Tile Images Side by Side
      • Upsample an Image
      • Warp an Image Using a Deformation Field
    • ImageIntensity
      • Absolute Value of Image
      • Add Constant to Every Pixel
      • Add Two Images Together
      • Apply Atan Image Filter
      • Apply Cos Image Filter
      • Apply Exp Negative Image Filter
      • Apply Sin Image Filter
      • Binary AND Two Images
      • Binary OR Two Images
      • Binary XOR Two Images
      • Cast Image to Another Type but Clamp to Output Range
      • Compare Two Images and Set Output Pixel to Max
      • Compare Two Images and Set Output Pixel to Min
      • Compute Edge Potential
      • Compute Sigmoid
      • Computer Magnitude in Vector Image to Make Magnitude Image
      • Convert RGB Image to Grayscale Image
      • Extract Component of Vector Image
      • Intensity Windowing
      • Inverse of Mask to Image
      • Invert Image
      • Mask Image
      • Multiply Image by Scalar
      • Multiply Two Images
      • Normalize Image
      • Pixel Division of Two Images
      • Rescale an Image
      • Scale All Pixel’s Sum to Constant
      • Square Every Pixel
      • Subtract Constant From Every Pixel
      • Subtract Two Images
      • Transform Magnitude of Vector Valued Image Pixels
    • ImageLabel
      • Extract Inner and Outer Boundaries of Blobs in Binary Image
      • Extract Boundaries of Connected Regions in Binary Image
      • Label Contours of Connect Components
    • ImageStatistics
      • Adaptive Histogram Equalization Image Filter
      • Apply Accumulate Image Filter
      • Compute Min, Max, Variance and Mean of Image
      • Compute PCA Shape From Training Sample
      • Statistical Properties of Labeled Regions
      • Calculate Image Moments
        • Calculate Image Moments of an Ellipse
    • LabelMap
      • Apply Morphological Closing on All Label Objects
      • Apply Morphological Closing on Specific Label Object
      • Convert itk::Image With Labels to Label Map
      • Convert Image With Labeled Regions to ShapeLabelMap
      • Convert Label Map to Normal Image
      • Extract Given Label Object
      • Invert Image Using Binary Not Operation
      • Keep Binary Regions That Meet Specific Properties
      • Keep Regions Above Certain Level
      • Keep Regions That Meet Specific Properties
      • Label Binary Regions and Get Properties
      • Label Binary Regions in Image
      • Mask One Image Given Label Map
      • Merge LabelMaps
      • Remove Holes Not Connected to Image Boundaries
      • Remove Labels From Label Map
      • Shape Attributes for Binary Image
    • MathematicalMorphology
      • Create a Binary Ball Structuring Element
      • Dilate a grayscale image
      • Erode a Grayscale Image
      • Erode Binary Image Using Flat Structure Element
      • Generate Structuring Elements With Accurate Area
      • Regional Maximal
      • Regional Minimal
      • Valued Regional Maxima Image
      • Valued Regional Minimal Image
    • Path
      • Data Structure for Piece-Wise Linear Curve
      • Extract Contours From Image
    • QuadEdgeMeshFiltering
      • Clean Quad Edge Mesh
      • Compute Normals of a Mesh
      • Compute Planar Parameterization of a Mesh
      • Delaunay Conform Edge Flipping
    • Smoothing
      • Blurring an Image Using a Binomial Kernel
      • Computes Smoothing With Gaussian Kernel
      • Find Higher Derivatives of Image
      • Mean Filtering of an Image
      • Median Filtering of an Image
      • Median Filtering of an RGB Image
      • Smooth Image With Discrete Gaussian Filter
    • Thresholding
      • Demonstrate Available Threshold Algorithms
      • Separate Foreround and Background Using Otsu Method
      • Threshold an Image
      • Threshold an Image Using Binary Thresholding
      • Threshold an Image Using Otsu
  • GPU
  • IO
    • GDCM
      • Read and Print DICOM Tags
      • Read DICOM Series and Write 3D Image
      • Resample DICOM Series
    • ImageBase
      • Convert File Formats
      • Convert Image to Another Type
      • Create 3D Volume From Series of 2D Images
      • Create a List of File Names
      • Generate Slices From Volume
      • Process Image Chunks
      • Read an Image
      • Read Unknown Image Type
      • Register IO Factories
      • Write an Image
    • Mesh
      • Read Mesh
    • TIFF
      • Write a TIFF Image
    • TransformBase
      • Read Transform From File
      • Write Transform From File
    • TransformFactory
      • Register Transform With Transform Factory
  • Numerics
    • Optimizers
      • Amoeba Optimizer
      • Exhaustive Optimizer
        • Visualize Parameter Space with Exhaustive Optimizer
      • Levenberg-Marquardt Optimization
    • Statistics
      • 2D Gaussian Mixture Model Expectation Maximum
      • Compute Histogram From Grayscale Image
      • Compute Histogram of Masked Region in Image
      • Compute Texture Features
      • Create Gaussian Distribution
      • Create Histogram From List of Measurements
      • Create List of Sample Measurements
      • Create List of Samples From Image Without Duplication
      • Create List of Samples With Associated ID’s
      • Distribute Sampling Using GMM EM
      • Distribution of Pixels Using GMM EM
      • Histogram Creation and Bin Access
      • Spatial Search
  • Nonunit
    • Review
      • Geometric Properties of Labeled Region
      • Multiphase Chan and Vese Sparse Field Level Set Segmentation
      • Segment Blood Vessels With Multi-Scale Hessian-Based Measure
      • Singlephase Chan and Vese Dense Field Level Set Segmentation
      • Singlephase Chan and Vese Sparse Field Level Set Segmentation
  • Registration
    • Common
      • Compute Mean Squares Metric Between Two Images
      • Global Registration of Two Images
      • Match Feature Points
      • Multiresolution Pyramid From Image
      • Mutual Information
        • Mutual Information Metric
      • Perform 2D Translation Registration With Mean Squares
      • Perform Multi Modality Registration With Viola Wells Mutual Information
      • Register Image to Another Using Landmarks
      • Watch Registration
    • Metricsv4
      • Perform Registration on Vector Images
      • Register Two Point Sets
        • Register Two Point Sets
  • Segmentation
    • Classifiers
      • Cluster Pixels in Grayscale Image
      • K-Means Clustering
      • K Means Cluster of Pixels in Image
    • ConnectedComponents
      • Assign Contiguous Labels to Connected Regions in an Image
      • Extra Largest Connect Component From Binary Image
      • Label Connect Components in Binary Image
      • Label Connect Components in Grayscale Image
    • KLMRegionGrowing
      • Basic Region Growing
    • LabelVoting
      • Iterative Hole Filling
    • LevelSets
      • Segment With Geodesic Active Contour Level Set
    • RegionGrowing
      • Connected Components in Image
      • Segment Pixels With Similar Statistics
    • Voronoi
      • Voronoi Diagram
    • Watersheds
      • Morphological Watershed Segmentation
      • Watershed Image Filter
  • Video
    • BridgeOpenCV
      • Convert an ITK Gray Scale Image to CV Mat
  • Examples
  • Numerics
  • Statistics

Statistics#

  • 2D Gaussian Mixture Model Expectation Maximum
  • Compute Histogram From Grayscale Image
  • Compute Histogram of Masked Region in Image
  • Compute Texture Features
  • Create Gaussian Distribution
  • Create Histogram From List of Measurements
  • Create List of Sample Measurements
  • Create List of Samples From Image Without Duplication
  • Create List of Samples With Associated ID’s
  • Distribute Sampling Using GMM EM
  • Distribution of Pixels Using GMM EM
  • Histogram Creation and Bin Access
  • Spatial Search

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Levenberg-Marquardt Optimization

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2D Gaussian Mixture Model Expectation Maximum
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Creative Commons License
Documentation and code by the Insight Software Consortium is licensed under a
Creative Commons Attribution 3.0 Unported License and Apache 2.0 License, respectively.
Last updated on Oct 31, 2023.
Created using Sphinx 4.4.0, and CMake.