Object size

Object size features

Eq Diameter

The equivalent diameter (in µm) in 2D represents a diameter a circle with the same area would have had. This feature has better characteristics: it grows linearly not quadratically as the area or cubically in case of volume.

EqDiameter_{2D} = \frac{4 \cdot Area}{π}

The equivalent diameter (in µm) in 3D represents a diameter a sphere with the same volume would have had.

EqDiameter_{3D} = 3 \frac{6 \cdot Volume}{π}

Fill Area

Is the area (in µm²) of the object with all holes filled.

Incircle Diameter

Diameter of the largest inscribed circle that can be fully contained in the object.

Length

Length is a derived feature appropriate for elongated or thin structures. Since it is based on the rod model, it is useful for calculating length of medial axis of thin rods.

Length = \frac{Perimeter + Perimeter ^{2} - 16 \cdot Area}{4}

Line Length

It is the length of an object with elongated shape.

Max Feret

It is the maximal value of the set of Feret’s diameters. Generally (for convex objects), Feret’s diameter at angle α equals the projected length of the object at angle α , α (0,180); NIS-Elements calculates Feret’s diameters for α =0, 10, 20, 30, …, 180.

Max Feret 90

It is a length projected across (perpendicular to) the MaxFeret angle.

Min Feret

The minimal value of the set of Feret’s diameters. Generally (for convex objects), Feret’s diameter at angle α equals the projected length of object at angle α , α (0,180); NIS-Elements calculates Feret’s diameter for α =0,10,20, 30, …, 180.

Min Rect Area

Area of the minimum-area enclosing rectangle of the object. The rectangle may be rotated and is chosen so that it fully contains the object while having the smallest possible area.

Object Pixel Count

Number of pixels in the object.

Object Voxel Count

Number of voxels in the object.

Object Area

Is the calibrated area of the object (in µm²).

ObjectArea = ObjectPixelCount \cdot Calibration^{2}

Object Volume

Is the calibrated volume of the object (in µm³).

ObjectVolume = ObjectVoxelCount \cdot Calibration^{2} \cdot ZStep

Outer Perimeter

Length of the outer perimeter (unlike in Perimeter, holes inside the object do not count).

Perimeter

The total boundary length. It includes both the outer and inner boundaries (if there are holes inside an object). The perimeter is calculated from four projections in the directions 0, 45, 90 and 135 degrees using Crofton’s formula

Perimeter = \frac{π \cdot ( P _{0} + P _{45} + P _{90} + P _{135} )}{4}

Surface

The surface (in µm²) of a 3D object.

Perimeter Contour

Total boundary length computed from object contours. Compared to Perimeter, it is more accurate (especially on elongated objects) but the calculation is slower.

Volume Eq Cylinder

This parameter is based on the rod model. Length is interpreted as height and Width is interpreted as the base diameter of a cylinder.

VolumeEqCylinder = \frac{( π \cdot d ^{2} ) ( l - d )}{4} + \frac{π \cdot d ^{3}}{6}

l = max (MaxFeret, Length)

d = min (MinFeret, Width)

Volume Eq Sphere

Volume of a sphere whose diameter is equal to EqDiameter of the measured 2D object.

VolumeEqSphere = \frac{π \cdot EqDiameter ^{3}}{6}

Width

Width is a derived feature appropriate for elongated or thin structures. It is based on the rod model.

Width = \frac{Area}{Length}

Object field Object shape