Inertia

Contains measurements derived from the variance-covariance matrix extracted from the intensity image values, and using the label input image as a mask.

More information about the variance-covariance matrix is available in the Moments of inertia section.

Notes:

The inertia measurements with the name starting with "Gray" are based on the intensity input image. Using them with a label image as an intensity image is not relevant. Using them with a binary image as an intensity image is the same as computing their "non gray" counterpart.
Other inertia measurements ignore the intensity input image.
The Inertia Matrix $M_i$ can be retrieved from the variance-covariance matrix $M_c$ as: $$ M_{i}=I\times tr(M_c)-M_c$$ where $I$ is the identity matrix and $tr$ is the matrix trace; that is, the sum of diagonal elements.

Object members

Measurement name	Description	Element type	Indexing
Moment2X	The centered moment term 2x of the binary covariance matrix.	Floating point	[label]
Moment2Y	The centered moment term 2y of the binary covariance matrix.	Floating point	[label]
Moment2Z	The centered moment term 2z of binary the covariance matrix.	Floating point	[label]
MomentXY	The centered moment term xy of the binary covariance matrix.	Floating point	[label]
MomentXZ	The centered moment term xz of the binary covariance matrix.	Floating point	[label]
MomentYZ	The centered moment term yz of the binary covariance matrix.	Floating point	[label]
Eigenvalue1	The largest eigenvalue of the binary covariance matrix.	Floating point	[label]
Eigenvalue2	The medium 3D eigenvalue or smallest 2D eigenvalue of the binary covariance matrix.	Floating point	[label]
Eigenvalue3	The smallest 3D eigenvalue of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]
Eigenvector1X	The X coordinate of the largest eigenvector of the binary covariance matrix.	Floating point	[label]
Eigenvector1Y	The Y coordinate of the largest eigen vector of the binary covariance matrix.	Floating point	[label]
Eigenvector1Z	The Z coordinate of the largest eigenvector of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]
Eigenvector2X	The X coordinate of the medium 3D eigenvector or smallest 2D eigenvector of the binary covariance matrix.	Floating point	[label]
Eigenvector2Y	The Y coordinate of the medium 3D eigenvector or smallest 2D eigenvector of the binary covariance matrix.	Floating point	[label]
Eigenvector2Z	The Z coordinate of the medium 3D eigenvector or smallest 2D eigenvector of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]
Eigenvector3X	The X coordinate of the 3D smallest eigenvector of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]
Eigenvector3Y	The Y coordinate of the 3D smallest eigenvector of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]
Eigenvector3Z	The Z coordinate of the 3D smallest eigenvector of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]
ExtentMax1	The maximal extent of the data in the direction of the largest eigenvector of the covariance matrix.	Floating point	[label]
ExtentMax2	The maximal extent of the data in the direction of the medium (second) eigenvector of the covariance matrix.	Floating point	[label]
ExtentMax3	The maximal extent of the data in the direction of the smallest eigenvector of the covariance matrix. This value is only available in 3D.	Floating point	[label]
ExtentMin1	The minimal extent of the data in the direction of the largest eigenvector of the covariance matrix.	Floating point	[label]
ExtentMin2	The minimal extent of the data in the direction of the medium (second) eigenvector of the covariance matrix.	Floating point	[label]
ExtentMin3	The minimal extent of the data in the direction of the smallest eigenvector of the covariance matrix. This value is only available in 3D.	Floating point	[label]
GrayMoment2X	The centered moment term 2x of the covariance matrix weighted by the gray level intensities. This measurement is similar to Moment2X based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayMoment2Y	The centered moment term 2y of the covariance matrix weighted by the gray level intensities. This measurement is similar to Moment2Y based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayMoment2Z	The centered moment term 2z of the covariance matrix weighted by the gray level intensities. This measurement is similar to Moment2Z based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayMomentXY	The centered moment term 2xy of the covariance matrix weighted by the gray level intensities. This measurement is similar to Moment2XY based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayMomentXZ	The centered moment term 2xz of the covariance matrix weighted by the gray level intensities. This measurement is similar to Moment2XZ based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayMomentYZ	The centered moment term 2yz of the covariance matrix weighted by the gray level intensities. This measurement is similar to Moment2YZ based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayEigenvalue1	The largest eigenvalue of the gray level covariance matrix. This measurement is similar to Eigenvalue1 based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayEigenvalue2	The medium 3D eigenvalue or smallest 2D eigenvalue of the gray level covariance matrix. This measurement is similar to Eigenvalue2 based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayEigenvalue3	The smallest 3D eigenvalue of the gray level covariance matrix. This measurement is similar to Eigenvalue3 based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayEigenvector1X	The X coordinate of the largest eigenvector of the gray level covariance matrix. This measurement is similar to EigenVec1X based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayEigenvector1Y	The Y coordinate of the largest eigenvector of the gray level covariance matrix. This measurement is similar to EigenVec1Y based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayEigenvector1Z	The Z coordinate of the largest eigenvector of the gray level covariance matrix. This measurement is similar to EigenVec1Z based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayEigenvector2X	The X coordinate of the medium 3D eigenvector or smallest 2D eigenvector of the gray level covariance matrix. This measurement is similar to EigenVec2X based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayEigenvector2Y	The Y coordinate of the medium 3D eigenvector or smallest 2D eigenvector of the gray level covariance matrix. This measurement is similar to EigenVec2Y based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayEigenvector2Z	The Z coordinate of the medium 3D eigenvector or smallest 2D eigenvector of the gray level covariance matrix. This measurement is similar to EigenVec2Z based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayEigenvector3X	The X coordinate of the smallest eigenvector of the gray level covariance matrix. This measurement is similar to EigenVec3X based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayEigenvector3Y	The Y coordinate of the smallest eigenvector of the gray level covariance matrix. This measurement is similar to EigenVec3Y based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayEigenvector3Z	The Z coordinate of the smallest eigenvector of the gray level covariance matrix. This measurement is similar to EigenVec3Z based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayExtent1Max	The maximal extent of the data in the direction of the largest eigenvector of the gray level covariance matrix. This measurement is similar to ExtentMax1 based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayExtent2Max	The maximal extent of the data in the direction of the of the medium 3D eigenvector or smallest 2D eigenvector of the gray level covariance matrix. This measurement is similar to ExtentMax2 based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayExtent3Max	The maximal extent of the data in the direction of the smallest eigenvector of the gray level covariance matrix. This measurement is similar to ExtentMax3 based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayExtent1Min	The minimal extent of the data in the direction of the largest eigenvector of the gray level covariance matrix. This measurement is similar to ExtentMin1 based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayExtent2Min	The minimal extent of the data in the direction of the of the medium 3D eigenvector or smallest 2D eigenvector of the gray level covariance matrix. This measurement is similar to ExtentMin2 based on the covariance matrix weighted by the gray level intensities.	Floating point	[label, channel]
GrayExtent3Min	The minimal extent of the data in the direction of the smallest eigenvector of the gray level covariance matrix. This measurement is similar to ExtentMin3 based on the covariance matrix weighted by the gray level intensities. This value is only available in 3D.	Floating point	[label, channel]
GrayAnisotropy	The anisotropy factor based on the covariance matrix weighted by the gray level intensities. This measurement is similar to the Anisotropy measurement of the Geometry category, but takes into account the gray levels of the intensity image.	Floating point	[label, channel]
GrayElongation	The elongation factor based on the covariance matrix weighted by the gray level intensities. This measurement is similar to the Elongation measurement of the Geometry category, but takes into account the gray levels of the intensity image.	Floating point	[label, channel]
GrayFlatness3d	The flatness factor based on the covariance matrix weighted by the gray level intensities. This measurement is similar to the Flatness measurement of the Geometry category, but takes into account the gray levels of the intensity image. This value is only available in 3D.	Floating point	[label, channel]