Parameters for shapes and particles

Outline

The outline of a feature is the projection of the feature's boundaries on a 2-dimensional horizontal plane.

Contour

The contour of a feature is its 3-dimensional boundary, with varying Z-heights along the contour.

Parameter

Explanation

TD

WD

ED

CD

Method

Detection methods:

▪Threshold detection

▪Watershed detection

▪Edge detection

▪Circle detection

Particles to detect

When using "Threshold detection", detect particles:

▪Above a threshold value

▪Below a threshold value

▪Between two threshold values

▪Outside two threshold values

Motifs to detect

When using "Watershed detection", detect:

▪Hill motifs

▪Dale motifs

Features to detect

When using "Circle detection", detect:

▪Particles (protruding objects)

▪Holes (receding objects)

Parameter

Explanation

TD

WD

ED

CD

Reference (for threshold)

Reference used as a threshold

Threshold 1

Custom threshold

Threshold 2

Custom threshold

Threshold

Custom threshold

Min diameter (for detection)

Minimum custom diameter for circle detection

Max diameter (for detection)

Maximum custom diameter for circle detection

Pruning

Pruning type (height pruning or area pruning) and pruning values

Number of particles

Detected number of particles

Density

Density of particles

Coverage

Coverage in percent of the whole surface area

Parameter

Explanation

TD

WD

ED

CD

Shape

Projected area

Projected horizontal area enclosed by the outline of the particle.

Parameter

Explanation

TD

WD

ED

CD

Shape

Perimeter

Projected perimeter.

Length of the outline of the particle, including the perimeters of perhaps existing holes in the particle.

External perimeter

Projected external perimeter.

Length of the (projected) perimeter of the particle, without taking into account the perimeters of perhaps existings holes in the particle.

Radius (circle)

Radius of the circle.

Diameter (circle)

Diameter of the circle.

Equivalent radius

Radius of the disk whose area is equal to the area of the particle.

Equivalent diameter

Diameter of the disk whose area is equal to the area of the particle.

Also called "Heywood diameter".

Mean diameter

Mean diameter of the particle, measured from its center of gravity.

Min diameter

Smallest diameter of the particle, measured from its center of gravity.

Max diameter

Maximum diameter of the particle, measured from its center of gravity.

Note: The maximum diameter is the diameter of the minimum enclosing circle.

Maximum caliber

Longest distance between any two points on the particle's outline.

Also called "Maximum Feret's diameter".

X-extent

Size of the particle along the X-axis.

Note: X-size of the axis-oriented minimum bounding rectangle.

Y-extent

Size of the particle along the Y-axis.

Note: X-size of the axis-oriented minimum bounding rectangle.

Parameter

Explanation

TD

WD

ED

CD

Shape

Volume

Maximum volume (volume of material or volume of void).

Volume of material

Volume of all points having a Z-value higher than the mean contour height.

Volume of void

Volume of all points having a Z-value lower than the mean contour height.

Local volume

Hill: Material volume of the motif, above the highest saddle point.

Dale: Void volume of the motif, below the lowest saddle point.

Parameter

Explanation

TD

WD

ED

CD

Sphere

Radius (sphere)

X of sphere center

X-coordinate of the center of the sphere.

Y of sphere center

Y-coordinate of the center of the sphere.

Z of sphere center

Z-coordinate of the center of the sphere.

Parameter

Explanation

TD

WD

ED

CD

Skeleton

Shape

Skeleton length

Result of thinning the particle into a one-pixel-wide line with branches.

Sum of the lengths of all branches of the skeleton.

Note: Ellipses are not skeletonized.

Note: This parameter may increase the computation time.

Fiber length

Length of the longest path in the skeleton.

Relevant parameter for measuring the length of long thin shapes (e.g. DNA).

Note: This parameter may increase the computation time.

Fiber width

Ratio between the area of the particle and the skeleton length.

For a normal worm-like particle, it will be the mean width perpendicular to the fiber.

Note: Should be more accurately called "Skeleton width".

Note: This parameter may increase the computation time.

Parameter

Explanation

TD

WD

ED

CD

Shape

Local height

Hill: Height difference between highest saddle point and peak.

Dale: Height difference between pit and lowest saddle point.

Z-min

Minimum Z-value of all points inside the smoothed outline of the particle.

Z-max

Maximum Z-value of all points inside the smoothed outline of the particle.

Z-mean

Average of the Z-values of all points inside the outline of the particle.

Z-extremum

Minimum or maximum Z-value inside the outline of the particle.

Detection of hills: Z-extremum = Z-max

Detection of dales: Z-extremum = Z-min

Mean contour height

Average Z-value of the points on the particle's contour.

Min contour height

Minimum Z-value of the points on the particle's contour.

Max contour height

Maximum Z-value of the points on the particle's contour.

Maximum depth

Maximum depth inside the outline of the particle.

Value relative to the mean contour height.

Mean depth

Average of Z-values of all points inside the contour of the particle that are smaller than the mean contour height.

Values are relative to the mean contour height.

Maximum height

Maximum height inside the outline of the particle.

Value relative to the mean contour height.

Mean height

Average of Z-values of all points inside the outline of the particle that are bigger than the mean contour height.

Values are relative to the mean contour height.

Parameter

Explanation

TD

WD

ED

CD

Shape

X of Z-min

X-position of Z-min:

X-coordinate of the lowest point inside the outline of the particle.

Y of Z-min

Y-position of Z-min:

Y-coordinate of the highest point inside the outline of the particle.

X of Z-max

X-position of Z-max:

X-coordinate of the highest point inside the outline of the particle.

Y of Z-max

Y-position of Z-max:

Y-coordinate of the highest point inside the outline of the particle.

X of Z-extremum

Y of Z-extremum

X of geometric center

Y of geometric center

X of gravity center /

Y of gravity center

The gravity center is based on the particle's outline.

X of gravity center (material) /

Y of gravity center (material)

Center of gravity of the material volume, i.e. for those points inside the outline of the particle with Z-values above the mean contour height.

Center of gravity relevant for particles (protruding features, i.e. features above the background).

X of gravity center (void) /

Y of gravity center (void)

Center of gravity of the void volume, i.e. for those points inside the contour of the particle with Z-values below the mean contour height.

Center of gravity relevant for pores (receding features, i.e. features below the background)

X of circle center /

Y of circle center

Parameter

Explanation

TD

WD

ED

CD

Shape

Edge/Interior

▪Edge: Partial or open particle in contact with or cutting the edge of the studiable.

▪Interior: Complete particle without contact with the edge of the studiable.

Form factor

Ratio between the area of the particle and its squared perimeter.

Describes the shape of a feature.

Aspect ratio

Ratio between the max diameter and the min diameter.

If the value is close to 1, the form of the particle is close to the form of a disk.

If the value is high, the particle is oblong.

Roundness

Ratio between the area of the particle and the area of the disk having as diameter the max diameter of the particle.

This value is close to 1 for a circular particle, and smaller than 0.5 for an oblong particle.

Note: This parameter may increase the computation time.

Compactness

Ratio between the equivalent diameter and the max diameter.

This ratio is close to 1 for a particle with the form of a disk, or smaller than 0.5 for an oblong particle.

Compactness = Equivalent diameter / Max diameter

Note:

The compactness of a circle is 1.

The compactness of a square is √(2/π) ≈0.79784.

Convexity

Ratio between the perimeter of the minimum bounding polygon (convex perimeter) (in green) and the perimeter of the particle itself (in red).

Elongation

Indicates how elongated a particle is. A square or circle have an elongation of 0. The longer the rectangle or the ellipse, the closer the value will be to 1.

Solidity

Describes the similarity of the particle's area with its convex area.

Ratio between the area and the area inside the minimum bounding polygon (convex area).

Orientation

Angle between the biggest axis of the smoothed particle and the X-axis.

Note: Angle expressed in degrees, in trigonometric direction, with 0° at the right side.

Angle of min diameter

Angle between the X-axis and the smallest diameter of the particle (diameter measured trough the particle's center of gravity).

Note: Angle expressed in degrees, in trigonometric direction, with 0° at the right side.

Angle of max diameter

Angle between the X-axis and the maximum diameter of the particle (diameter measured trough the particle's center of gravity).

Note: Angle expressed in degrees, in trigonometric direction, with 0° at the right side.

Length

Length of the particle's oriented bounding rectangle.

Note: The bounding rectangle is parallel to the biggest axis of the particle.

For a circle: Length = Diameter

For an ellipse: Length = Length of major axis

Width

Width of the particle's oriented bounding rectangle.

Note: The bounding rectangle is parallel to the biggest axis of the particle.

For an ellipse: Width = Length of minor axis

Parameter

Explanation

TD

WD

ED

CD

Shape

Number of neighbors

Number of adjacent particles in direct contact with the respective particle.

Pitch

Hill: Mean horizontal distance between the peak of this particle and the peaks of adjacent particles.

Dale: Mean horizontal distance between the pit of this particle and the pits of adjacent particles.

Max pitch

Hill: Maximum horizontal distance between the peak of this particle and the peak of an adjacent particle.

Dale: Maximum horizontal distance between the pit of this particle and the pit of an adjacent particle.

Min pitch

Hill: Minimum horizontal distance between the peak of this particle and the peak of an adjacent particle.

Dale: Minimum horizontal distance between the pit of this particle and the pit of an adjacent particle.

Coflatness

Hill: Maximum vertical distance between the peak of this particle and the peak of an adjacent particle.

Dale: Maximum vertical distance between the pit of this particle and the pit of an adjacent particle.

Parameter

Explanation

TD

WD

ED

CD

Shape

Height

Height difference between the mean height of the smoothed particle and the lowest point of the surface.