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	Physical Information
Moment2X	The centered moment term 2x of the binary covariance matrix.	Floating point	[label]	AREA
Moment2Y	The centered moment term 2y of the binary covariance matrix.	Floating point	[label]	AREA
Moment2Z	The centered moment term 2z of binary the covariance matrix.	Floating point	[label]	AREA
MomentXY	The centered moment term xy of the binary covariance matrix.	Floating point	[label]	AREA
MomentXZ	The centered moment term xz of the binary covariance matrix.	Floating point	[label]	AREA
MomentYZ	The centered moment term yz of the binary covariance matrix.	Floating point	[label]	AREA
Eigenvalue1	The largest eigenvalue of the binary covariance matrix.	Floating point	[label]	COEFFICIENT
Eigenvalue2	The medium 3D eigenvalue or smallest 2D eigenvalue of the binary covariance matrix.	Floating point	[label]	COEFFICIENT
Eigenvalue3	The smallest 3D eigenvalue of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]	COEFFICIENT
Eigenvector1X	The X coordinate of the largest eigenvector of the binary covariance matrix.	Floating point	[label]	COORDINATE
Eigenvector1Y	The Y coordinate of the largest eigen vector of the binary covariance matrix.	Floating point	[label]	COORDINATE
Eigenvector1Z	The Z coordinate of the largest eigenvector of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]	COORDINATE
Eigenvector2X	The X coordinate of the medium 3D eigenvector or smallest 2D eigenvector of the binary covariance matrix.	Floating point	[label]	COORDINATE
Eigenvector2Y	The Y coordinate of the medium 3D eigenvector or smallest 2D eigenvector of the binary covariance matrix.	Floating point	[label]	COORDINATE
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]	COORDINATE
Eigenvector3X	The X coordinate of the 3D smallest eigenvector of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]	COORDINATE
Eigenvector3Y	The Y coordinate of the 3D smallest eigenvector of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]	COORDINATE
Eigenvector3Z	The Z coordinate of the 3D smallest eigenvector of the binary covariance matrix. This value is only available in 3D.	Floating point	[label]	COORDINATE
ExtentMax1	The maximal extent of the data in the direction of the largest eigenvector of the covariance matrix.	Floating point	[label]	LENGTH
ExtentMax2	The maximal extent of the data in the direction of the medium (second) eigenvector of the covariance matrix.	Floating point	[label]	LENGTH
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]	LENGTH
ExtentMin1	The minimal extent of the data in the direction of the largest eigenvector of the covariance matrix.	Floating point	[label]	LENGTH
ExtentMin2	The minimal extent of the data in the direction of the medium (second) eigenvector of the covariance matrix.	Floating point	[label]	LENGTH
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]	LENGTH
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]	AREA
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]	AREA
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]	AREA
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]	AREA
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]	AREA
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]	AREA
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]	COEFFICIENT
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]	COEFFICIENT
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]	COEFFICIENT
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]	COORDINATE
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]	COORDINATE
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]	COORDINATE
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]	COORDINATE
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]	COORDINATE
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]	COORDINATE
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]	COORDINATE
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]	COORDINATE
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]	COORDINATE
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]	LENGTH
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]	LENGTH
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]	LENGTH
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]	LENGTH
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]	LENGTH
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]	LENGTH
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]	RATIO
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]	RATIO
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]	RATIO

Object methods

Method	Description
void toDataFrame()	Convert the measurement to an IOLink.DataFrame

Method	Description
void ToDataFrame()	Convert the measurement to an IOLink.DataFrame

Method	Description
void to_data_frame()	Convert the measurement to an IOLink.DataFrame