Package inra.ijpb.measure

Class IntrinsicVolumes3D

java.lang.Object
inra.ijpb.measure.IntrinsicVolumes3D
public class IntrinsicVolumes3D
extends java.lang.Object
Collection of static classes for the computation of intrinsic volumes (volume, surface area, mean breadth and Euler number) for binary or label 3D images. Static methods provides computation of either the intrinsic volumes for individual regions / labels, or the density of the intrinsic volumes for porous media. For binary images, a binary stack is expected, together with the spatial calibration of the image. For label images, the list of region labels within images should be specified as an array of integers.
Author:
dlegland
See Also:
IntrinsicVolumes2D, IntrinsicVolumesAnalyzer3D

  • Method Summary

    Modifier and Type Method Description
    static double eulerNumber​(ij.ImageStack image, int conn)
    Measures the Euler number of the region within the binary image, using the specified connectivity.
    static double eulerNumberDensity​(ij.ImageStack image, ij.measure.Calibration calib, int conn)
    Measures the Euler number density of the foreground region within a binary image, using the specified connectivity.
    static double[] eulerNumbers​(ij.ImageStack image, int[] labels, int conn)
    Measures the Euler number of each region given in the "labels" argument, using the specified connectivity.
    static double interfaceSurfaceArea​(ij.ImageStack image, int label1, int label2, ij.measure.Calibration calib, int nDirs)
    Measures the surface area of the interface between two regions in a 3D label image.
    static double meanBreadth​(ij.ImageStack image, ij.measure.Calibration calib, int nDirs, int conn2d)
    Measures the mean breadth of a single region within a 3D binary image.
    static double meanBreadthDensity​(ij.ImageStack image, ij.measure.Calibration calib, int nDirs, int conn2d)
    Measures the mean breadth density of a single region within a 3D binary image.
    static double[] meanBreadths​(ij.ImageStack image, int[] labels, ij.measure.Calibration calib, int nDirs, int conn2d)
    Measures the mean breadth of each region within a label image.
    static double samplingVolume​(ij.ImageStack image, ij.measure.Calibration calib)
    Returns the "inner volume" of the 3D image, i.e. the calibrated volume of the image without taking into account the voxels at the border of the image.
    static double[] sphericity​(double[] volumes, double[] surfaces)
    Helper function that computes the sphericity index of 3D particles, based on the value of volume and surface area.
    static double sphericity​(double volume, double surface)
    Helper function that computes the sphericity index of 3D particles, based on the value of volume and surface area.
    static double surfaceArea​(ij.ImageStack image, ij.measure.Calibration calib, int nDirs)
    Measures the surface area of a single region within a 3D binary image.
    static double surfaceAreaDensity​(ij.ImageStack image, ij.measure.Calibration calib, int nDirs)
    Measures the surface area density of a single region within a 3D binary image.
    static double[] surfaceAreas​(ij.ImageStack image, int[] labels, ij.measure.Calibration calib, int nDirs)
    Measures the surface area of each region within a label image.
    static double volume​(ij.ImageStack image, ij.measure.Calibration calib)
    Measures the volume of a single region within a 3D binary image.
    static double volumeDensity​(ij.ImageStack image)
    Measures the volume density of a single region within a 3D binary image.
    static double[] volumes​(ij.ImageStack labelImage, int[] labels, ij.measure.Calibration calib)
    Measures the volume of each region within a 3D label image.

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • volume

      public static final double volume​(ij.ImageStack image, ij.measure.Calibration calib)
      Measures the volume of a single region within a 3D binary image.
      Parameters:
      image - the binary image containing the region
      calib - the spatial calibration of the image
      Returns:
      the volume of the region in the image
      See Also:
      BinaryImages.countForegroundVoxels(ImageStack)

    • volumes

      public static final double[] volumes​(ij.ImageStack labelImage, int[] labels, ij.measure.Calibration calib)
      Measures the volume of each region within a 3D label image.
      Parameters:
      labelImage - image containing the label of each region
      labels - the set of labels for which volume has to be computed
      calib - the spatial calibration of the image
      Returns:
      the volume of each region within the image

    • volumeDensity

      public static final double volumeDensity​(ij.ImageStack image)
      Measures the volume density of a single region within a 3D binary image.
      Parameters:
      image - the binary image containing the region
      Returns:
      the volume density of the region within the image

    • interfaceSurfaceArea

      public static final double interfaceSurfaceArea​(ij.ImageStack image, int label1, int label2, ij.measure.Calibration calib, int nDirs)
      Measures the surface area of the interface between two regions in a 3D label image.
      Parameters:
      image - the 3D image containing the label of each particle
      label1 - the label of the first region
      label2 - the label of the second region
      calib - the spatial calibration of the image
      nDirs - the number of directions to consider, either 3 or 13
      Returns:
      the surface area of each region within the image
      See Also:
      InterfaceSurfaceArea

    • surfaceArea

      public static final double surfaceArea​(ij.ImageStack image, ij.measure.Calibration calib, int nDirs)
      Measures the surface area of a single region within a 3D binary image. Uses discretization of the Crofton formula, that consists in computing numbers of intersections with lines of various directions.
      Parameters:
      image - image containing the label of each particle
      calib - the spatial calibration of the image
      nDirs - the number of directions to consider, either 3 or 13
      Returns:
      the surface area of each region within the image

    • surfaceAreas

      public static final double[] surfaceAreas​(ij.ImageStack image, int[] labels, ij.measure.Calibration calib, int nDirs)
      Measures the surface area of each region within a label image. Uses discretization of the Crofton formula, that consists in computing numbers of intersections with lines of various directions.
      Parameters:
      image - image containing the label of each particle
      labels - the set of labels in the image
      calib - the spatial calibration of the image
      nDirs - the number of directions to consider, either 3 or 13
      Returns:
      the surface area of each region within the image

    • surfaceAreaDensity

      public static final double surfaceAreaDensity​(ij.ImageStack image, ij.measure.Calibration calib, int nDirs)
      Measures the surface area density of a single region within a 3D binary image. Uses discretization of the Crofton formula, that consists in computing numbers of intersections with lines of various directions.
      Parameters:
      image - image containing the label of each particle
      calib - the spatial calibration of the image
      nDirs - the number of directions to consider, either 3 or 13
      Returns:
      the surface area density of the binary phase within the image

    • sphericity

      public static final double sphericity​(double volume, double surface)
      Helper function that computes the sphericity index of 3D particles, based on the value of volume and surface area. The sphericity is computed using the following formula: sphericity = 36 * PI * V^2 / S^3 A perfect ball would have a sphericity index close to 1, a very complex particle will present a lower sphericity index.
      Parameters:
      volume - the volume of a region
      surface - the surface area of a region
      Returns:
      the sphericity index
      See Also:
      surfaceAreas(ij.ImageStack, int[], ij.measure.Calibration, int), volumes(ij.ImageStack, int[], ij.measure.Calibration)

    • sphericity

      public static final double[] sphericity​(double[] volumes, double[] surfaces)
      Helper function that computes the sphericity index of 3D particles, based on the value of volume and surface area. The sphericity is computed using the following formula: sphericity = 36 * PI * V^2 / S^3 A perfect ball would have a sphericity index close to 1, a very complex particle will present a lower sphericity index.
      Parameters:
      volumes - the volume of each particle
      surfaces - the surface area of each particle
      Returns:
      the sphericity index of each particle
      See Also:
      surfaceAreas(ij.ImageStack, int[], ij.measure.Calibration, int), volumes(ij.ImageStack, int[], ij.measure.Calibration)

    • meanBreadth

      public static final double meanBreadth​(ij.ImageStack image, ij.measure.Calibration calib, int nDirs, int conn2d)
      Measures the mean breadth of a single region within a 3D binary image. The mean breadth is proportional to the integral of mean curvature: mb = 2*pi*IMC.
      Parameters:
      image - image containing the label of each particle
      calib - the spatial calibration of the image
      nDirs - the number of directions to consider, either 3 or 13
      conn2d - the connectivity to use on planar sections with square tiles (either 4 or 8)
      Returns:
      the mean breadth of the binary region within the image

    • meanBreadths

      public static final double[] meanBreadths​(ij.ImageStack image, int[] labels, ij.measure.Calibration calib, int nDirs, int conn2d)
      Measures the mean breadth of each region within a label image. The mean breadth is proportional to the integral of mean curvature: mb = 2*pi*IMC. Uses discretization of the Crofton formula, that consists in computing euler number of intersection with planes of various orientations.
      Parameters:
      image - image containing the label of each region
      labels - the set of labels in the image
      calib - the spatial calibration of the image
      nDirs - the number of directions to consider, either 3 or 13
      conn2d - the connectivity to use on planar sections with square tiles (either 4 or 8)
      Returns:
      the mean breadth of each region within the image

    • meanBreadthDensity

      public static final double meanBreadthDensity​(ij.ImageStack image, ij.measure.Calibration calib, int nDirs, int conn2d)
      Measures the mean breadth density of a single region within a 3D binary image. Uses discretization of the Crofton formula, that consists in computing euler number of intersection with planes of various orientations.
      Parameters:
      image - image containing a binary region
      calib - the spatial calibration of the image
      nDirs - the number of directions to consider, either 3 or 13
      conn2d - the connectivity to use on planar sections with square tiles (either 4 or 8)
      Returns:
      the surface area density of the binary phase within the image

    • eulerNumber

      public static final double eulerNumber​(ij.ImageStack image, int conn)
      Measures the Euler number of the region within the binary image, using the specified connectivity.
      Parameters:
      image - the input 3D binary image
      conn - the connectivity to use (either 6 or 26)
      Returns:
      the Euler number of the region within the binary image

    • eulerNumbers

      public static final double[] eulerNumbers​(ij.ImageStack image, int[] labels, int conn)
      Measures the Euler number of each region given in the "labels" argument, using the specified connectivity.
      Parameters:
      image - the input 3D label image (with labels having integer values)
      labels - the set of unique labels in image
      conn - the connectivity to use (either 6 or 26)
      Returns:
      the Euler number of each region within the image

    • eulerNumberDensity

      public static final double eulerNumberDensity​(ij.ImageStack image, ij.measure.Calibration calib, int conn)
      Measures the Euler number density of the foreground region within a binary image, using the specified connectivity.
      Parameters:
      image - the input 3D binary image
      calib - the spatial calibration of the image
      conn - the connectivity to use (either 6 or 26)
      Returns:
      the Euler number density within the binary image

    • samplingVolume

      public static final double samplingVolume​(ij.ImageStack image, ij.measure.Calibration calib)
      Returns the "inner volume" of the 3D image, i.e. the calibrated volume of the image without taking into account the voxels at the border of the image.
      Parameters:
      image - the input 3D image
      calib - the spatial calibration of the image
      Returns:
      the calibrated volume of the portion of image witout border voxels