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Measurement Features

Coordinate System

Some feature descriptions contain images with a coordinate system for illustrative purposes. Note that the actual coordinate system in the software is different and has its point of origin (0/0) in the top left corner of the image.

The software can automatically detect and measure various properties of objects.

Some general terms relevant for several feature descriptions are the following:

  • Filled: A measurement feature with Filled in its name takes the entire region for the respective calculation, i.e. any holes the region might contain are included in the calculation.
  • Unscaled: For features that are titled as Unscaled, the scaling of the image is not taken into account for the measurement. The values returned by these features have the unit pixel.

ACP X Unscaled

Gray irregular polygon with small inner hole between vertical and horizontal axes, blue top marker and blue down arrow.

The x coordinate of the last pixel in the last line of a region.

To identify measurement objects, the image is scanned from bottom left to top right. The so-called ACP (anti-coincidence point) is the last point that has been identified for a new object. The parameter ACP X indicates the x-coordinate of this point.

  • Unit: pixels
  • Value range: 1 ... image size in x-direction

ACP X Unscaled WCS

Irregular polygon with two interior cutouts, blue top marker and downward blue arrow, and X/Y axes at left and bottom

The x coordinate of the last pixel in the last line of a region.

To identify measurement objects, the image is scanned from bottom left to top right. The so-called ACP (anti-coincidence point) is the last point that has been identified for a new object. The parameter ACP X indicates the x-coordinate of this point in the world coordinate system (WCS).

  • Unit: pixels
  • Value range: 1 ... image size in x-direction

ACP Y Unscaled

Gray irregular polygon with a central cutout, blue dot and left-pointing horizontal arrow at top left, black axes.

The y coordinate of the last pixel in the last line of a region.

To identify measurement objects, the image is scanned from bottom left to top right. The so-called ACP (anti-coincidence point) is the last point that has been identified for a new object. The parameter ACP Y indicates the y-coordinate of this point.

  • Unit: pixels
  • Value range: 1 ... image size in y-direction

ACP Y Unscaled WCS

Gray irregular polygon with two inner cutouts, blue dot at top with left arrow, corner axes and dashed vertical guide

The y coordinate of the last pixel in the last line of a region.

To identify measurement objects, the image is scanned from bottom left to top right. The so-called ACP (anti-coincidence point) is the last point that has been identified for a new object. The parameter ACP Y indicates the y-coordinate of this point in the world coordinate system (WCS).

  • Unit: pixels
  • Value range: 1 ... world coordinate size in y-direction

Area

Blue outlined irregular polygon with diagonal hatch, a smaller internal hole, and a horizontal double arrow below

Area of a region.

Area of a region excluding any holes it may contain. The areas of the holes are not included in the measurement. If you want to include them, use the Area filled parameter.

  • Unit: Unit of area of the scaling assigned to the image (e.g. μm²)

Area Convex (arivis)

Area of convex hull of a region.

The current region is surrounded by a convex polyline. The (filled!) area of the resulting region is then measured.

  • Unit: Unit of area of the scaling assigned to the image (e.g. μm²)

Area Cut

Area of a region including the parts cut by a frame. Note that if you define Cut at Frame in the Frame step of the image analysis, the value of this parameter is identical to the value delivered by the Area feature.

  • Unit: Unit of area of the scaling assigned to the image (e.g. μm²)

Area Cut Unscaled

Unscaled area of a region including the parts cut by a frame. Note that if you define Cut at Frame in the Frame step of the image analysis, the value of this parameter is identical to the value delivered by the Area Unscaled feature.

  • Unit: pixels

Area Filled

Irregular blue outlined polygon with diagonal blue hatch fill and three black irregular holes

Area of filled region.

Area of a region including any holes it contains. The holes are interpreted as belonging to the region or are filled prior to the measurement. If you do not want the holes to be measured, use the Area parameter.

  • Unit: Unit of area of the scaling assigned to the image (e.g. μm²)

Area Filled Unscaled

Irregular blue polygon with diagonal gray hatch fill and a small white polygonal hole inside

Area of filled region.

Area of a region including any holes it contains. The holes are interpreted as belonging to the region or are filled prior to the measurement. If you do not want the holes to be measured, use the Area parameter.

  • Unit: pixels²

Area Frame

Returns the area of the measurement frame used in the image. If a ROI is defined in the Frame step of the wizard, this area is displayed, otherwise the area of the entire image is indicated. This also includes image areas without pixel values.

  • Unit: µm2

Area Frame Unscaled

Returns the area of the measurement frame used in the image. If a ROI is defined in the Frame step of the wizard, this area is displayed, otherwise the area of the entire image is indicated. This also includes image areas without pixel values.

  • Unit: pixels

Area Percentage of Holes

Area of the holes as a percentage of the overall area, i.e. the area of holes divided by the area of the segmented region.

Area Unscaled

Irregular blue-outlined polygon with diagonal blue-striped fill and a central white geometric cutout

Area of a region unscaled.

The Area unscaled parameter corresponds to the Area parameter. However, the scaling of the image is not taken into account for the measurement. The (unfilled!) area of a region is displayed in pixels in each case.

  • Unit: pixels²

Bound Back

Indicates the back coordinate (highest value in z-direction) of the bounding box of a region. The box is drawn in parallel to the x, y and z axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Back Unscaled

Indicates the back coordinate (highest value in z-direction) of the unscaled bounding box of a region. The box is drawn in parallel to the x, y and z axis.

  • Unit: pixels

Bound Back Unscaled WCS

Indicates the back coordinate (highest value in z-direction) of the unscaled bounding box of a region in the world coordinate system (WCS). The box is drawn in parallel to the x, y and z axis.

  • Unit: pixels

Bound Back WCS

Indicates the back coordinate (highest value in z-direction) of the bounding box of a region in the world coordinate system (WCS). The box is drawn in parallel to the x, y and z axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Bottom

Gray irregular polygon with white inner holes inside dashed blue rectangle, blue horizontal double-arrow below

Minimum y-coordinate of the bounding box of a region.

Indicates the y-coordinate of the bottom edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Bottom Unscaled

Blue dashed bounding box, gray irregular polygon with two white polygonal holes, blue double-headed horizontal arrow at bottom

Minimum y-coordinate of the bounding box of a region.

Indicates the y-coordinate of the bottom edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: pixels

Bound Bottom Unscaled WCS

Gray irregular polygon with white interior cutouts inside a dashed blue bounding box next to axes arrows and a globe icon

Minimum y-coordinate of the bounding box of a region.

Indicates the y-coordinate in the world coordinate system (WCS) of the bottom edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: pixels

Bound Bottom WCS

Diagram of irregular gray polygon with internal white shapes inside dashed blue bounding box on coordinate axes

Minimum y-coordinate of the bounding box of a region.

Indicates the y-coordinate in the world coordinate system (WCS) of the bottom edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Center

Bound Center X/Y/Z.

Indicates the x, y or z coordinate of the center of the bounding box for a region.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Center Unscaled

Bound Center X/Y/Z Unscaled.

Indicates the x, y or z coordinate of the unscaled center of the bounding box for a region.

  • Unit: pixels

Bound Center Unscaled WCS

Bound Center X/Y/Z Unscaled WCS.

Indicates the x, y or z coordinate of the unscaled center of the bounding box for a region in the world coordinate system (WCS).

  • Unit: pixels

Bound Center WCS

Bound Center X/Y/Z WCS.

Indicates the x, y or z coordinate of the center of the bounding box for a region in the world coordinate system (WCS).

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Depth

Indicates the depth of the bounding box of a region, i.e. the "length" of the bounding box in z.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Depth Unscaled

Indicates the depth of the unscaled bounding box of a region, i.e. the "length" of the bounding box in z.

  • Unit: pixels

Bound Front

Indicates the front coordinate (smallest value in z-direction) of the bounding box of a region. The box is drawn in parallel to the x, y and z axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Front Unscaled

Indicates the front coordinate (smallest value in z-direction) of the unscaled bounding box of a region. The box is drawn in parallel to the x, y and z axis.

  • Unit: pixels

Bound Front Unscaled WCS

Indicates the front coordinate (smallest value in z-direction) of the unscaled bounding box of a region in the world coordinate system (WCS). The box is drawn in parallel to the x, y and z axis.

  • Unit: pixels

Bound Front WCS

Indicates the front coordinate (smallest value in z-direction) of the bounding box of a region in the world coordinate system (WCS). The box is drawn in parallel to the x, y and z axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Height

Gray polygon with two white holes inside dashed blue bounding box with vertical double-arrow indicating height

Indicates the height (size in y-direction) of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)
  • Formula: Bound top - Bound bottom

Bound Height Unscaled

Gray irregular polygon with two white holes inside a blue dashed bounding box and blue double-headed vertical arrow

Indicates the height (size in y-direction) of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: pixels
  • Formula: Bound top - Bound bottom

Bound Left

Gray irregular polygon with small inner cutout inside dashed blue rectangle and left blue vertical measurement arrow

Minimum x-coordinate of the bounding box of a region.

Indicates the x coordinate of the left-hand edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Left Unscaled

Gray irregular polygon with inner hole inside dashed blue bounding box, blue vertical arrow at left edge

Minimum x-coordinate of the bounding box of a region.

Indicates the x coordinate of the left-hand edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: pixels

Bound Left Unscaled WCS

Gray irregular polygon inside blue dashed bounding box with blue left edge and a downward blue arrow on a vertical axis

Minimum x-coordinate of the bounding box of a region.

Indicates the x coordinate in the world coordinate system (WCS) of the left-hand edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: pixels

Bound Left WCS

Gray polygon in dashed blue bounding box with axes and arrows labeled Minimum x-coordinate

Minimum x-coordinate of the bounding box of a region.

Indicates the x coordinate in the world coordinate system (WCS) of the left-hand edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Right

Gray irregular polygon with white interior shapes inside dashed blue rectangle and blue vertical arrow at right.

Maximum x-coordinate of the bounding box of a region.

Indicates the x coordinate of the right-hand edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Right Unscaled

Gray irregular polygon with internal cutouts inside a dashed blue bounding box with a blue right-edge arrow

Maximum x-coordinate of the bounding box of a region.

Indicates the x coordinate of the right-hand edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: pixels

Bound Right Unscaled WCS

Irregular gray polygon inside dashed blue bounding box and larger solid blue box, axis arrows at left and bottom-right

Maximum x-coordinate of the bounding box of a region.

Indicates the x coordinate in the world coordinate system (WCS) of the right-hand edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: pixels

Bound Right WCS

Gray irregular polygon with two white interior shapes inside a dashed blue bounding box, axes and a downward blue arrow

Maximum x-coordinate of the bounding box of a region.

Indicates the x coordinate in the world coordinate system (WCS) of the right-hand edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Top

Gray irregular polygon with two white holes inside a dashed blue bounding box and blue horizontal arrows above

Maximum y-coordinate of the bounding box of a region.

Indicates the y-coordinate of the top edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Top Unscaled

Irregular gray polygon with two white interior polygons inside a dashed blue bounding box and a top blue horizontal arrow

Maximum y-coordinate of the bounding box of a region.

Indicates the y-coordinate of the top edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: pixels

Bound Top Unscaled WCS

Gray irregular polygon with two interior cutouts inside dashed blue bounding box with axis arrows

Maximum y-coordinate of the bounding box of a region.

Indicates the y coordinate in the world coordinate system (WCS) of the top edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: pixels

Bound Top WCS

Gray irregular polygon with white holes inside a dashed blue bounding box and blue horizontal double-arrow dimension

Maximum y-coordinate of the bounding box of a region.

Indicates the y coordinate in the world coordinate system (WCS) of the top edge of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Width

Gray irregular polygon with holes inside a blue dashed rectangular bounding box with horizontal double-headed arrows

Indicates the width (size in x-direction) of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Formula: Bound right - Bound left
  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Bound Width Unscaled

Gray irregular polygon inside a blue dashed bounding box with bottom double-headed arrow indicating width

Indicates the width (size in x-direction) of a bounding box for a region. The box is drawn in parallel to the x and y axis.

  • Formula: Bound right - Bound left
  • Unit: pixels

Center X

Gray irregular polygon with inner hole, blue dot inside, and arrows indicating horizontal, vertical and downward.

The x coordinate of the geometric center of gravity of a region.

Depending on the shape of the object, this point may also lie outside a region. The associated y-coordinate is determined via the Center Y parameter.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Center X Unscaled

Gray polygon with hole in black border, blue dot inside, upward arrow top-left and blue downward arrow below

The x coordinate of the geometric center of gravity of a region.

Depending on the shape of the object, this point may also lie outside a region. The associated y-coordinate is determined via the Center Y parameter.

  • Unit: pixels

Center X Unscaled WCS

Irregular polygon with blue dot at geometric center, axes and arrows showing WCS x coordinate in pixels

The x coordinate in the world coordinate system (WCS) of the geometric center of gravity of a region.

Depending on the shape of the object, this point may also lie outside a region. The associated y-coordinate is determined via the Center Y parameter.

  • Unit: pixels

Center X WCS

Irregular gray polygon with interior cutouts and a blue dot, overlaid axes with origin globe icon and a downward blue arrow.

The x coordinate in the world coordinate system (WCS) of the geometric center of gravity of a region.

Depending on the shape of the object, this point may also lie outside a region. The associated y-coordinate is determined via the Center Y parameter.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Center Y

Gray irregular polygon with inner white hole, blue center dot, blue left-pointing arrow and black edge measurement arrows

The y coordinate of the geometric center of gravity of a region.

Depending on the shape of the object, this point may also lie outside a region. The associated x coordinate is determined via the Center X parameter.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Center Y Unscaled

Diagram of a gray polygon with inner hole and blue dot marking its geometric center y coordinate; axes and left arrow.

The y coordinate of the geometric center of gravity of a region.

Depending on the shape of the object, this point may also lie outside a region. The associated x coordinate is determined via the Center X parameter.

  • Unit: pixels

Center Y Unscaled WCS

Gray irregular polygon with inner hole and blue center dot; blue left arrow pointing to dashed vertical axis.

The y coordinate in the world coordinate system (WCS) of the geometric center of gravity of a region.

Depending on the shape of the object, this point may also lie outside a region. The associated x coordinate is determined via the Center X parameter.

  • Unit: pixels

Center Y WCS

y coordinate diagram: gray irregular polygon with hole, blue center dot and left-pointing blue arrow

The y coordinate in the world coordinate system (WCS) of the geometric center of gravity of a region.

Depending on the shape of the object, this point may also lie outside a region. The associated x coordinate is determined via the Center X parameter.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Center Z

Indicates the z coordinate of the geometric center of gravity of a region.

Depending on the shape of the object, this point can also lie outside a region. The associated x and y coordinates are determined by the Center X and Center Y features.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Center Z Unscaled

Indicates the z coordinate of the unscaled geometric center of gravity of a region.

Depending on the shape of the object, this point can also lie outside a region. The associated x and y coordinates are determined by the Center X Unscaled and Center Y Unscaled features.

  • Unit: pixels

Center Z Unscaled WCS

Indicates the z coordinate of the unscaled geometric center of gravity of a region in the world coordinate system (WCS).

Depending on the shape of the object, this point can also lie outside a region. The associated x and y coordinates are determined by the Center X Unscaled WCS and Center Y Unscaled WCS features.

  • Unit: pixels

Center Z WCS

Indicates the z coordinate of the geometric center of gravity of a region in the world coordinate system (WCS).

Depending on the shape of the object, this point can also lie outside a region. The associated x and y coordinates are determined by the Center X WCS and Center Y WCS features.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Circularity (arivis)

Sqrt(Roundness) = Sqrt(4 × Area / (π × Feret Maximum (arivis)²))

Compactness (arivis)

4 × π × Area / Perimeter Convex (arivis)²

Convexity (arivis)

(Perimeter Convex (arivis) / Perimeter Crofton)2

Count

Returns the count of analyzed objects.

Count Objects Direct Subclasses

Returns the count of analyzed objects in the direct subclasses.

Note that this feature only considers values of direct subclasses of a class, i.e. subclasses that are directly on the next lower hierarchy level in the class list. Values of subclasses on lower hierarchy levels ("subclass of a subclass") are not considered.

Count per mm2

Returns the count of analyzed objects per mm2.

Diameter

Gray octagonal outline with a blue circle inside and horizontal double-headed blue arrow marking the circle's diameter

Diameter of a circle/sphere with an area/volume equal to that of the object.

The object is measured using the Area feature. A circle with the same area as the object is created. The diameter of this circle is returned.
In case of a three dimensional analysis, the equivalent sphere with the Volume of the region is measured and the diameter of the sphere is returned.

  • Formula 2D: Sqrt ((4/π)*Area)
  • Formula 3D: Pow(6*Volume/π, 1/3)
  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Diameter Maximum Inscribed Circle

Gray irregular polygon with interior holes and a blue-outlined inscribed circle touching its right edge, axes with arrowheads

Diameter of the largest circle that can be inscribed inside an area.

The object is transformed into a binary image. A distance transform is applied on the binary image which calculates the largest distance to the outline of the object or any holes the object contains. Extracting the point with the largest distance yields the maximum inscribed circle. The diameter is twice the largest distance.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Diameter Maximum Inscribed Circle Filled

Diameter of the largest circle that can be inscribed inside an entire object.

The object is transformed into a binary image. A distance transform is applied on the binary image to find the point with the largest distance to the outline of the entire object. The diameter returned by this feature is equal to twice the value of the largest distance. All holes inside the object are ignored for the calculation.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Diameter Maximum Inscribed Circle Filled Unscaled

Unscaled diameter of the largest circle that can be inscribed inside an entire object.

The object is transformed into a binary image. A distance transform is applied on the binary image to find the point with the largest distance to the outline of the entire object. The diameter returned by this feature is equal to twice the value of the largest distance. All holes inside the object are ignored for the calculation.

  • Unit: pixel

Diameter Maximum Inscribed Circle Unscaled

Gray irregular polygon with interior holes and a blue-outlined inscribed circle touching its right edge, axes with arrowheads

Diameter of the largest circle that can be inscribed inside an area.

The object is transformed into a binary image. A distance transform is applied on the binary image which calculates the largest distance to the outline of the object or any holes the object contains. Extracting the point with the largest distance yields the maximum inscribed circle. The diameter is twice the largest distance.

  • Unit: pixel

Diameter Unscaled

Blue circle with horizontal double-headed arrow across overlaying gray irregular polygon with triangular cutouts

Unscaled diameter of a circle/sphere with an area/volume equal to that of the object.

The object is measured using the Area Unscaled feature. A circle with the same area as the object is created. The diameter of this circle is returned.
In case of a three dimensional analysis, the equivalent sphere with the Volume Unscaled of the region is measured and the diameter of the sphere is returned.

  • Formula 2D: Sqrt ((4/π)*Area Unscaled)
  • Formula 3D: Pow(6*Volume Unscaled/π, 1/3)
  • Unit: pixels

Ellipse Angle

Dashed blue ellipse around gray region, solid blue diagonal major axis and curved arrow indicating angle to x-axis

Angle of the major axis of the ellipse.

The major axis of an ellipse with the same geometric moment of inertia as the current region is determined in accordance with the Ellipse major parameter. The angle to the x-axis is then determined. The indication of the angle always relates to a counterclockwise direction.

  • Unit: degrees
  • Value range: 0 ... 180°

Ellipse Angle Unscaled

Gray irregular region with inner white rotated rectangle, dashed blue ellipse, blue diagonal axis and angle arc to horizontal

Angle of the major axis of the ellipse.

The major axis of an ellipse with the same geometric moment of inertia as the current region is determined in accordance with the Ellipse major parameter. The angle to the x-axis is then determined. The indication of the angle always relates to a counterclockwise direction.

  • Unit: degrees
  • Value range: 0 ... 180°

This tool uses unscaled pixels for calculating the angle. The results may differ from the results of Ellipse Angle.

Ellipse Semi-Major

Gray irregular region with blue dashed ellipse, a horizontal double-headed arrow for semi-major axis and vertical blue arrow

Length of the semi-major axis of the ellipse.

Length of the semi-major axis of an ellipse with the same geometric moment of inertia as the region. The moment of inertia is calculated about the center of gravity of the region.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Ellipse Semi-Major Unscaled

Diagram of irregular region with dashed blue outline and double-headed blue arrow indicating semi-major axis length

Length of the semi-major axis of the ellipse.

Length of the semi-major axis of an ellipse with the same geometric moment of inertia as the region. The moment of inertia is calculated about the center of gravity of the region.

  • Unit: pixels

Ellipse Semi-Minor

Gray irregular region with two cutouts, dashed blue ellipse around it, horizontal blue arrow to center and double arrow above

Length of the semi-minor axis of the ellipse.

Length of the semi-minor axis of an ellipse with the same geometric moment of inertia as the region. The moment of inertia is calculated about the center of gravity of the region.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Ellipse Semi-Minor Unscaled

Gray region inside dashed blue ellipse with horizontal double-headed arrow indicating semi-minor axis length

Length of the semi-minor axis of the ellipse.

Length of the semi-minor axis of an ellipse with the same geometric moment of inertia as the region. The moment of inertia is calculated about the center of gravity of the region.

  • Unit: pixels

Ellipsoid Semi-Major

Gray irregular region with blue dashed ellipse, a horizontal double-headed arrow for semi-major axis and vertical blue arrow

Calculates the length of the semi-major axis of the equivalent ellipsoid of the region.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Ellipsoid Semi-Major Unscaled

Diagram of irregular region with dashed blue outline and double-headed blue arrow indicating semi-major axis length

Calculates the length of the semi-major axis of the equivalent unscaled ellipsoid of the region.

  • Unit: pixels

Ellipsoid Semi-Mean

Calculates the length of the semi-mean axis of the equivalent ellipsoid of the region, i.e. half the length of the medium/middle axis of the three dimensional ellipsoid.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Ellipsoid Semi-Mean Unscaled

Calculates the length of the semi-mean axis of the equivalent unscaled ellipsoid of the region, i.e. half the length of the medium/middle axis of the three dimensional ellipsoid.

  • Unit: pixels

Ellipsoid Semi-Minor

Gray irregular region with two cutouts, dashed blue ellipse around it, horizontal blue arrow to center and double arrow above

Calculates the length of the semi-minor axis of the equivalent ellipsoid of the region.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Ellipsoid Semi-Minor Unscaled

Gray region inside dashed blue ellipse with horizontal double-headed arrow indicating semi-minor axis length

Calculates the length of the semi-minor axis of the equivalent unscaled ellipsoid of the region.

  • Unit: pixels

Feret Maximum

Gray region with central diamond hole and blue angled measurement lines and arrows illustrating the maximum feret of a region

Maximum feret of a region.

The maximum feret of a region is determined on the basis of distance measurements. Two straight lines are positioned on opposite sides of the object, like a sliding caliper, at 128 angle positions. The corresponding distance is measured for each angle position. The maximum value determined is the maximum feret.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Feret Maximum (arivis)

Gray region with central diamond hole and blue angled measurement lines and arrows illustrating the maximum feret of a region

Maximum feret of a region.

The maximum feret of a region is determined on the basis of distance measurements. The calculation uses the method of rotating calipers. Two parallel tangent lines are positioned on opposite sides of the object and rotated around the object to determine the largest distance. The corresponding distance is measured for each angle position. The maximum value determined is the maximum feret.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Feret Maximum Angle (arivis)

Gray irregular polygon with inner hole and blue diagonal maximum feret line and arrows indicating angle to x-axis

Angle of the maximum feret of a region in relation to the x-axis.

The maximum feret is determined as described in Feret Maximum (arivis). The angle of the maximum feret in relation to the x-axis is then determined. The indication of the angle always relates to a counterclockwise direction.

  • Unit: degrees
  • Value range: -90° ... 90°

Feret Maximum Unscaled (arivis)

Gray polygonal region with blue rotated-calipers arrows and lines illustrating the maximum feret measurement

Maximum feret of a region.

The maximum feret of a region is determined on the basis of distance measurements. The calculation uses the method of rotating calipers. Two parallel tangent lines are positioned on opposite sides of the object and rotated around the object to determine the largest distance. The corresponding distance is measured for each angle position. The maximum value determined is the maximum feret.

  • Unit: pixels

Feret Minimum

Gray octagonal region with an inner polygon and blue slanted lines, arrows and bracket indicating distance.

Minimum feret of a region.

The minimum feret of a region is determined on the basis of distance measurements. Two straight lines are positioned on opposite sides of the object, like a sliding caliper, at 128 angle positions. The corresponding distance is measured for each angle position. The minimum value determined is the minimum feret.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Feret Minimum (arivis)

Gray octagonal region with an inner polygon and blue slanted lines, arrows and bracket indicating distance.

Minimum feret of a region.

The minimum feret of a region is determined on the basis of distance measurements. The calculation uses the method of rotating calipers. Two parallel tangent lines are positioned on opposite sides of the object and rotated around the object to determine the smallest distance. The corresponding distance is measured for each angle position. The minimum value determined is the minimum feret.

  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Feret Minimum Angle (arivis)

Gray irregular polygon with blue arrows marking minimum feret and angle relative to x-axis

Angle of the minimum feret of a region in relation to the x-axis.

The minimum feret is determined as described in Feret Minimum (arivis). The angle of the minimum feret in relation to the x-axis is then determined. The indication of the angle always relates to a counterclockwise direction.

  • Unit: degrees
  • Value range: -90° ... 90°

Feret Minimum Unscaled (arivis)

Gray polygon with blue rotated caliper lines and arrows showing minimum feret distance

Minimum feret of a region.

The minimum feret of a region is determined on the basis of distance measurements. The calculation uses the method of rotating calipers. Two parallel tangent lines are positioned on opposite sides of the object and rotated around the object to determine the smallest distance. The corresponding distance is measured for each angle position. The minimum value determined is the minimum feret.

  • Unit: pixels

Feret Ratio (arivis)

Gray irregular polygon with inner rotated rectangle and blue arrows labeled a (vertical), b (top horizontal), and text a:b

Feret ratio.

The ratio of Feret Minimum (arivis) to Feret Maximum (arivis) is calculated. This ratio makes it possible to make statements on the form of the measured objects. If the feret ratio has a low value, long, elongated objects are present. Values approaching 1 indicate the presence of compact or circular objects, as in this case Feret Minimum (arivis) and Feret Maximum (arivis) have very similar values. The Form Circle is also suitable for making statements on the circularity of an object.

  • Formula: Feret Minimum (arivis) / Feret Maximum (arivis)
  • Unit: none
  • Value range: 0 ... 1

Feret Vertical to Maximum (arivis)

The feret perpendicular to the maximum feret of a region.

  • Unit: Unit of the scaling assigned to the image (e.g. µm)

Fiber Length

Length of a fiber-like region.

To calculate the fiber length, a structure that is actually similar to a fiber is required. Here it is not the distance between a start and end point that is determined. The check can be done using the Form circle, among other things.

  • Formula: ¼ × (Perimeter + (Sqrt (Perimeter² - 16 × Area))
  • Unit: Unit of the scaling assigned to the image (e.g. μm)

Fiber Length Unscaled

Length of a fiber-like region.

To calculate the fiber length, a structure that is actually similar to a fiber is required. Here it is not the distance between a start and end point that is determined. The check can be done using the Form Circle, among other things.

  • Formula: ¼ × (Perimeter Unscaled + (Sqrt (Perimeter Unscaled² - 16 × Area Unscaled))
  • Unit: pixels

Form Circle

Two gray irregular blobs inside blue-outlined circular regions, each containing small white polygonal shapes

Form factor of a region.

Describes the form of a region on the basis of its circularity. A perfect circle is given the value 1. The more elongated the region is, the smaller the form factor. The calculation is based on the Area filled and Perimeter Crofton parameters.

  • Formula: 4 × π × Area / PerimeterCrofton²
  • Unit: none
  • Value range: 0...1

Frame Area Percentage

Grid of gray dots on black; yellow translucent square highlights a cell with a pale rectangle and orange dot

The percentage of the area of the regions in relation to the area of all frames in the respective scene. This also includes image areas without pixel values. If you have defined no frame, this feature returns the percentage in relation to the whole image, i.e. the same value as Image Plane Area Percentage. In case of images with multiple scenes, the features is always calculated based on the area of a single scene.

Note that if your image does not contain areas without pixel values and you have not drawn a frame into the image, the following features all have the same result: Frame Area Percentage, Frame Data Area Percentage, Image Plane Area Percentage, and Image Plane Data Area Percentage.

Frame Area Percentage Cut

Yellow square with white inner square, orange circle and red arc on black background patterned with gray circular dots

The percentage of the area of the regions including regions that are cut by the frame in relation to the area of all frames in the respective scene. This also includes image areas without pixel values. In case of images with multiple scenes, the features is always calculated based on the area of a single scene.

Frame Data Area

Returns the area of the measurement frame used in the image. If a ROI is defined in the Frame step of the wizard, this area is displayed, otherwise the area of the entire image is indicated. This only incorporates image areas which contain pixel values.

  • Unit: Unit of area of the scaling assigned to the image (e.g. μm2)

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