Default value is undefined.

It will be ignored by analysis request

1 minus the ratio of the smallest to the largest eigenvalue of the covariance matrix.

Measures a region's deviation from a spherical shape.

Area of the object.

See also the documentation of the OIV.ImageViz.Engines.ImageAnalysis.GlobalMeasures.SoAreaQuantification2d engine.

Area of the object boundary.

See also the documentation of the 3D interpretation of the OIV.ImageViz.Engines.ImageAnalysis.GlobalMeasures.SoAreaQuantification2d engine.

Ratio between the label area and the image area in 2D: Ratio between the label volume and the image volume in 3D: .

X coordinate of the center of gravity.

See Moments of inertia.

Y coordinate of the center of gravity.

See Moments of inertia.

Z coordinate of the center of gravity.

See Moments of inertia.

Centered moment term (XX) of the covariance matrix.

See Moments of inertia.

Centered moment term (YY) of the covariance matrix.

See Moments of inertia.

Centered moment term (ZZ) of the covariance matrix.

See Moments of inertia.

Centered moment term (XY) of the covariance matrix.

See Moments of inertia.

Centered moment term (XZ) of the covariance matrix.

See Moments of inertia.

Centered moment term (YZ) of the covariance matrix.

See Moments of inertia.

Some components of the image volume might be intersected by the Bounding Box of the image volume.

This value is the number of voxels that are touching this boundary. The component might not be fully within the image.

Width of the Bounding Box.

Height of the Bounding Box.

Depth of the Bounding Box.

X coordinate of the upper-left corner of the Bounding Box.

Y coordinate of the upper-left corner of the Bounding Box.

Z coordinate of the upper-left corner of the Bounding Box.

Difference between the object area A and the area of the smoothing circle AS ( Union(A,AS) - Intersection(A,AS) ).

The smoothing circle is computed on the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary and verifies :

• the center of the circle is the barycenter of the object

• the distance between the circle and the approximated polygon minimizes the least squares criteria

Area of the convex hull of the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

Perimeter of the convex hull of the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

For each of the 8 intercept measures, the diametral variation is the product of intercept with the distance between interception points.

The Crofton perimeter is the average of those 8 diametral variation measures. See Intercept count.

Gives the shortest edge to edge distance from the current object to its nearest neighbor.

The distance measure is computed from the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundaries.

The largest eigenvalue of the covariance matrix.

The medium 3D eigenvalue or smallest 2D eigenvalue of the covariance matrix.

The smallest 3D eigenvalue of the covariance matrix.

This value is only available in 3D.

X coordinate of the largest eigenvector of the covariance matrix.

Y coordinate of the largest eigen vector of the covariance matrix.

Z coordinate of the largest eigenvector of the covariance matrix.

This value is only available in 3D.

X coordinate of the medium 3D eigenvector or smallest 2D eigenvector of the covariance matrix.

Y coordinate of the medium 3D eigenvector or smallest 2D eigenvector of covariance matrix.

Z coordinate of the medium 3D eigenvector or smallest 2D eigenvector of the covariance matrix.

This value is only available in 3D.

X coordinate of the 3D smallest eigenvector of the covariance matrix.

This value is only available in 3D.

Y coordinate of the 3D smallest eigenvector of the covariance matrix.

This value is only available in 3D.

Z coordinate of the 3D smallest eigenvector of the covariance matrix.

This value is only available in 3D.

Difference between the area A of the studied particle and the area of its enclosing ellipse EA ( Union(A,EA) - Intersection(A,EA) ).

The enclosing ellipse is computed on the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary and verifies:

• the center of the ellipse is the barycenter of the object

• the major axis of the ellipse is parallel to the inertia axis of the object

• the length of the minor and major axis is given by the extent size of the eigenvectors of the covariance matrix.

The ratio of the medium and the largest eigenvalue of the covariance matrix.

Elongated objects will have small values close to 0.

Difference between the object area A and the area of the enclosing circle EA ( Union(A,EA) - Intersection(A,EA) ).

The enclosing circle is computed on the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

The diameter of the circular particle of same area in 2D: The diameter of the spherical particle of same volume in 3D: .

1 minus the number of holes.

See Euler Number section.

The eccentricity is defined as: and are the covariance matrix eigenvalues.

A disk or a cross has a null eccentricity since . The eccentricity increases with the difference between the eigenvalues, and thus measures the elongation of the object. It also indicates in some cases a privileged direction, corresponding to a large eigenvalue and a small one, i.e.: has a high value, though two orthogonal privileged directions mean two large eigenvalues and a smaller difference .

See Moments of inertia.

The maximal extent of the data in the direction of the largest eigenvector of the covariance matrix.

The maximal extent of the data in the direction of the medium (second) eigenvector of the covariance matrix.

The maximal extent of the data in the direction of the smallest eigenvector of the covariance matrix.

This value is only available in 3D.

The minimal extent of the data in the direction of the largest eigenvector of the covariance matrix.

The minimal extent of the data in the direction of the medium (second) eigenvector of the covariance matrix.

The minimal extent of the data in the direction of the smallest eigenvector of the covariance matrix.

This value is only available in 3D.

Distribution of the length of Bounding Boxes oriented along the specified directions.

See also Feret's Diameter.

X coordinate of input point for Feret Distribution.

Y coordinate of input point for for Feret Distribution.

X coordinate of output point for for Feret Distribution.

Y coordinate of output point for for Feret Distribution.

This shape factor is defined as (D/d), where d is the minimum Feret's Diameter and D is the maximum Feret diameter in the orthogonal direction (90 deg from the minimum Feret diameter).

Feret measures rely on sampling in a distribution of different directions (31 directions by default).

X coordinate of the first point of each object encountered when scanning the input image from top to bottom, and left to right.

Y coordinate of the first point of each object encountered when scanning the input image from top to bottom, and left to right.

Z coordinate of the first point of each object encountered when scanning the input image from top to bottom, and left to right.

The ratio of the smallest and the medium eigenvalue of the covariance matrix.

Flat objects have small values close to 0. See Variance-covariance matrix. This value is only available in 3D.

X coordinate of the center of gravity weighted by the gray level intensities.

Y coordinate of the center of gravity weighted by the gray level intensities.

Z coordinate of the center of gravity weighted by the gray level intensities.

Kurtosis of the histogram of intensity values within the object.

Mean of the histogram of intensity values within the object.

Peak of the histogram of intensity values within the object.

10% quantile of the histogram of intensity values within the object.

25% quantile of the histogram of intensity values within the object.

50% quantile of the histogram of intensity values within the object.

75% quantile of the histogram of intensity values within the object.

90% quantile of the histogram of intensity values within the object.

Modifiable quantile of the histogram of intensity values within the object (default is 20%).

The quantile value can be customized with the OIV.ImageViz.Nodes.Measures.SoDataMeasureAttributes.quantilePercents field.

Modifiable quantile of the histogram of intensity values within the object (default is 30%).

The quantile value can be customized with the OIV.ImageViz.Nodes.Measures.SoDataMeasureAttributes.quantilePercents field.

Modifiable quantile of the histogram of intensity values within the object (default is 40%).

The quantile value can be customized with the OIV.ImageViz.Nodes.Measures.SoDataMeasureAttributes.quantilePercents field.

Modifiable quantile of the histogram of intensity values within the object (default is 50%).

The quantile value can be customized with the OIV.ImageViz.Nodes.Measures.SoDataMeasureAttributes.quantilePercents field.

Modifiable quantile of the histogram of intensity values within the object (default is 60%).

The quantile value can be customized with the OIV.ImageViz.Nodes.Measures.SoDataMeasureAttributes.quantilePercents field.

Modifiable quantile of the histogram of intensity values within the object (default is 70%).

The quantile value can be customized with the OIV.ImageViz.Nodes.Measures.SoDataMeasureAttributes.quantilePercents field.

Skewness of the histogram of intensity values within the object.

Standard deviation of the histogram of intensity values within the object.

Variance of the histogram of intensity values within the object.

Length of the skeleton of the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

Maximum of the Feret Diameters.

Maximum of the Feret Diameters.

Angle Phi of the maximum of the Feret's Diameter, in degrees (not radians) [-90,90].

Angle Theta of the maximum of the Feret's Diameter, in degrees (not radians) [0,180].

Angle of the maximum of the Feret Diameters.

The most represented pixel intensity value inside the particle.

It uses the nearest value with the average intensity of the particle if several intensities met this criterion.

Maximum pixel intensity of the particle.

Average pixel intensity intensity.

Minimum pixel intensity of the particle.

Number of holes of the particle.

Orientation of the particle in degrees (not radians) [-90,+90] computed with the inertia moments.

See Moments of inertia.

Phi minor orientation of the particle in degrees (not radians) [0,+90], computed with the inertia moments.

See Moments of inertia.

Theta minor orientation of the particle in degrees (not radians) [-180,+180], computed with the inertia moments.

See Moments of inertia.

Phi orientation of the particle in degrees (not radians) [0,+90], computed with the inertia moments.

See Moments of inertia.

Theta orientation of the particle in degrees (not radians) [-180,+180], computed with the inertia moments.

See Moments of inertia.

The perimeter measure designates the length of the object boundary.

In the continuous case, let and be a parametric representation of the boundary curve , its perimeter is thus obtained as: This formula has no obvious discrete equivalent, and is therefore mostly useless for our purposes. In the discrete case, the perimeter can be simply estimated as the number of points which lie on the object boundary, i.e., points with at least one zero in their neighborhood.

The factor of rugosity determines if the contour of a shape is smooth or not.

A value close to 0 represents a smooth edges particle, a value close to 1 a rough edges particle. A value of -1 is returned when the rugosity can't be computed (i.e., object made up of few pixels).

It is defined by the following formula where is defined as the mean operator over all the basis length , which is defined as the distance in figure below. is defined as the shape perimeter. is defined as follows: where . is the mean operator for all the points between the basis defined by the points and . The angles and are defined as in figure below, with . If the weight is counted as 0.

Area of the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

X coordinate of the center of the Rectangle of Minimum Area computed on the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

Y coordinate of the center of the Rectangle of Minimum Area computed on the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

Length of the Rectangle of Minimum Area computed on the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

Orientation of the Rectangle of Minimum Area computed on the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

Width of the Rectangle of Minimum Area computed on the OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

Number of holes of the particles represented by inner and outer chains.

Length of OIV.ImageViz.Engines.ImageSegmentation.ComputationalGeometry of the object boundary.

Circularity Shape factor, close to 1 for a disk, and lower for star-shaped objects: .

The shape factor defined as : .

Standard deviation of the pixel intensities.

The measure of symmetry determines the trend of a shape to be symmetric or not.

It is close to 1 for a symmetric shape and decreases with asymmetry. It is lower to 0.5 if the gravity center is outside the particle as illustrated on the figure below. It is measured using the following formula for a particle P : with , and the minimum value operator over all the angles .

Sum of the of pixel intensity values.

Sum of the squares of pixel intensity values.

Volume of the object.

Sum of voxel surfaces that are on the outside of each connected component.

Minimum of the 2D Feret Diameters.

Minimum of the 3D Feret Diameters.

Angle Phi of the minimum of the 3D Feret Diameters, in degrees (not radians) [0,90].

Angle Theta of the minimum of the 3D Feret Diameters, in degrees (not radians) [-180,+180].

Angle of the minimum of the 2D Feret Diameters.

Largest distance between two parallel lines touching the object without intersecting it and lying in a plane orthogonal to the maximum 3D Feret diameter (LENGTH_ORIENTATION_PHI_3D, LENGTH_ORIENTATION_THETA_3D).

See Feret's Diameter and OIV.ImageViz.Nodes.Measures.SoDataMeasureAttributes.feretAngles2D.

Angle Phi of the BREADTH_3D in degrees (not radians) [-90,90].

Angle Theta of the BREADTH_3D in degrees (not radians) [0,180].

Largest distance between two parallel lines touching the object without intersecting it and lying in a plane orthogonal to the maximum 3D Feret diameter (LENGTH_ORIENTATION_PHI_3D, LENGTH_ORIENTATION_THETA_3D) and also orthogonal to the BREADTH_3D diameter.

Angle Phi of the THICKNESS_3D in degrees (not radians) [-90,90].

Angle Theta of the THICKNESS_3D in degrees (not radians) [0,180].

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.ANISOTROPY based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VALUE1 based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VALUE2 based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VALUE3_3D based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VECTOR1X based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VECTOR1Y based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VECTOR1Z_3D based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VECTOR2X based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VECTOR2Y based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VECTOR2Z_3D based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VECTOR3X_3D based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VECTOR3Y_3D based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EIGEN_VECTOR3Z_3D based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.ELONGATION based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EXTENT_MAX1 based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EXTENT_MAX2 based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EXTENT_MAX3_3D based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EXTENT_MIN1 based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EXTENT_MIN2 based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.EXTENT_MIN3_3D based on the covariance matrix weighted by the gray level intensities.

Same measure as OIV.ImageViz.Nodes.Measures.SoDataMeasurePredefined.PredefinedMeasures.FLATNESS_3D based on the covariance matrix weighted by the gray level intensities.

Centered moment term (XX) of the covariance matrix weighted by the gray level intensities.

See Moments of inertia.

Centered moment term (YY) of the covariance matrix weighted by the gray level intensities.

See Moments of inertia.

Centered moment term (ZZ) of the covariance matrix weighted by the gray level intensities.

See Moments of inertia.

Centered moment term (XY) of the covariance matrix weighted by the gray level intensities.

See Moments of inertia.

Centered moment term (XZ) of the covariance matrix weighted by the gray level intensities.

See Moments of inertia.

Centered moment term (YZ) of the covariance matrix weighted by the gray level intensities.

See Moments of inertia.

Number of different label intersecting each particle.

Number of neighbors located at a given distance from the object boundaries.

X coordinate of the Length3d diameter input point.

Y coordinate of the Length3d diameter input point.

Z coordinate of the Length3d diameter input point.

X coordinate of the Length3d diameter output point.

Y coordinate of the Length3d diameter output point.

Z coordinate of the Length3d diameter output point.

X coordinate of the Width3d diameter input point.

Y coordinate of the Width3d diameter input point.

Z coordinate of the Width3d diameter input point.

X coordinate of the Width3d diameter output point.

Y coordinate of the Width3d diameter output point.

Z coordinate of the Width3d diameter output point.

X coordinate of the Breadth3d diameter input point.

Y coordinate of the Breadth3d diameter input point.

Z coordinate of the Breadth3d diameter input point.

X coordinate of the Breadth3d diameter output point.

Y coordinate of the Breadth3d diameter output point.

Z coordinate of the Breadth3d diameter output point.

X coordinate of the Thickness3d diameter input point.

Y coordinate of the Thickness3d diameter input point.

Z coordinate of the Thickness3d diameter input point.

X coordinate of the Thickness3d diameter output point.

Y coordinate of the Thickness3d diameter output point.

Z coordinate of the Thickness3d diameter output point.

Number of voxels of the object.

X coordinate of the inside length center which is extracted from the skeleton of the object boundary polygonal approximation.

Contrarily to the barycenter, this measurement ensures to return a point belonging to the object.

Y coordinate of the inside length center which is extracted from the skeleton of the object boundary polygonal approximation.

Contrarily to the barycenter, this measurement ensures to return a point belonging to the object.