Object shape

Object shape features

Circularity

Measures how much an object resembles a circle. Perfect circle is 1. All other shapes have circularity smaller than 1.

Circularity = \frac{4 π \cdot Area}{Perimeter ^{2}}

Convexity

Convexity = \frac{Area}{ConvexHullArea}

Elongation

Characterizes the object shape. In 2d it is the ratio of MaxFeret and MinFeret features.

Elongation_{2 D} = \frac{MaxFeret}{MinFeret}

In 3D it is calculated as a ratio of axes lengths.

Elongation_{3 D} = \frac{Major}{( Minor + Minor2 ) /2}

Fill Ratio

The ratio of Area and FillArea. The feature ranges from 0 to 1.

If an object does not contain holes, FillRatio = 1. If an object contains holes, FillRatio is less than 1. This feature helps distinguish objects with and without holes.

FillRatio = \frac{Area}{FillArea}

Major axis length

The longest (1.) objects axis (in µm).

Axis length of the object based on its PCA model. λ = eigenvalue. When PCA is applied to binary voxels, it gives us three orthonormal axes 1, 2, 3 ordered by the length of the object along each axis.

Minor axis length

The second longest (2.) objects axis (in µm).

Axis length (in µm) of the object based on its PCA model. λ = eigenvalue. When PCA is applied to binary voxels, it gives us three orthonormal axes 1, 2, 3 ordered by the length of the object along each axis.

Minor2 axis length

The shortest (3.) objects axis (in µm).

Mean Chord

The mean value of secants in the 0, 45, 90 and 135 degrees directions. It is a derived feature and is calculated from the Area and mean projection according to the following formula.

MeanChord = \frac{4 \cdot Area}{P _{0} + P _{45} + P _{90} + P _{135}}

Orientation

The object is the angle (in degrees) between the positive x-axis and the object’s axis measured counter-clockwise. It ranges from 0 to 180.

In 2D it is the angle at which MaxFeret is measured. Feret’s diameters are calculated with 5 degrees angle increments.

In 3D it is the objects’s major axis projected on the XY plane.

Pitch

Angle (in degrees) between the Major axis and its projection in the XY plane. It ranges from 0 to 90 degrees.

Rectangularity

Measures how much an object resembles a rectangle. A perfect rectangle has a Rectangularity of 1. All other shapes have Rectangularity smaller than 1.

The measurement uses the minimum-area oriented enclosing rectangle, which is rotated to achieve the smallest possible area while still containing the entire object.

Rectangularity = \frac{Area}{RectangleArea}

Roughness

Indicates how much the object is rough. 1 means the object is is circular. It ranges from 0 to 1.

Roughness = \frac{ConvexHullPerimeter}{Perimeter}

Roughness Inf

Indicates how much the object is rough. 1 means the object is is circular. It ranges from 1 to $\infty$

RoughnessInf = \frac{1}{Roughness}

Shape Factor

This feature indicates whether the object is rough or not.

ShapeFactor = \frac{4 π \cdot Area}{ConvexHullPerimeter ^{2}}

Sphericity

Similarity to a sphere, computed as the ratio of the object surface and the surface of a sphere with matching volume. A sphere has the maximum Sphericity = 1.

Sphericity = 3 \frac{π ( 6 \cdot Volume ) ^{2}}{Surface}

Object size Object position