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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

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

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

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 Filled

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 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

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 Unscaled

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 WCS

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 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 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 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 Left

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

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

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 Right Unscaled

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 WCS

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 Unscaled

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 Width Unscaled

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

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

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 WCS

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

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

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

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

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 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

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.

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 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

Ellipse Angle Unscaled

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

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-Minor

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)

Ellipsoid Semi-Major

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

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

  • Unit: pixels

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

Feret Maximum

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)

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)

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)

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

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 Ratio (arivis)

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

Frame Area Percentage

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 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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