inra.ijpb.measure

Class IntrinsicVolumes3D

java.lang.Object

inra.ijpb.measure.IntrinsicVolumes3D

public class IntrinsicVolumes3D
extends 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 and 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.
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

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

Method Detail

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