Object field

Object field features

Object Count

Number of objects in the field of view.

N

Total Pixel Count

Number of pixels under the binary in the frame.

TotalPixelCount = i = 1 \sum N ObjectPixelCount_{i}

Total Voxel Count

Number of voxels under the binary in the volume.

TotalVoxelCount = i = 1 \sum N ObjectVoxelCount_{i}

Total Object Area

Calibrated binary area (in µm²). Sum of the area of all objects in the frame.

TotalObjectArea = i = 1 \sum N ObjectArea_{i}

Total Object Volume

Calibrated binary volume (in µm³). Sum of the volume of all objects in the z-stack.

TotalObjectVolume = i = 1 \sum N ObjectVolume_{i}

Area Fraction

The ratio of the area occupied by objects to the whole frame area. Ranges from 0 to 1.

AreaFraction = \frac{TotalObjectArea}{MeasuredArea}

Volume Fraction

The ratio of the volume occupied by objects to the whole z-stack. Ranges from 0 to 1.

VolumeFraction = \frac{TotalObjectVolume}{MeasuredVolume}

Measured Area

The area that has been measured (in µm²): the whole frame.

MeasuredArea = FrameSize_{x} \cdot FrameSize_{y}

Measured Volume

The volume that has been measured (in µm³): the whole volume.

MeasuredVolume = VolumeSize_{x} \cdot VolumeSize_{y} \cdot VolumeSize_{z}

Perimeter

The estimated total boundary length (in µm) of the binary objects in the frame. It is calculated from projections of the whole binary field in the 0, 45, 90 and 135 degree directions, using the same projection-based formula as Object Perimeter.

Here, $P_{0}$ , $P_{45}$ , $P_{90}$ and $P_{135}$ are the calibrated directional projections of the binary field, with diagonal projections corrected for pixel spacing.

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

Mean Chord

The mean chord length (in µm) of the binary field, calculated by dividing the total area occupied by objects by the mean of its four directional projections. This uses the same formula as Object Mean Chord, applied to the whole field rather than to each object separately. It is not the arithmetic mean of the individual object measurements.

In the formula, Area is Total Object Area, and the projections are the same as for Perimeter. The result is zero for an empty binary field.

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

Surf Volume Ratio

The ratio of the surface to volume.

SurfVolumeRatio = \frac{\frac{4}{π} \cdot Perimeter}{MeasuredArea}

Intensity Object size