2D+Time Measurement Data

3D Measurement Data

Shape metrics are extracted from binary images obtained from the
segmentation of the 3D volumes.

Two types of primary shape metrics are extracted : 3D shape metrics,
extracted from the segmented 3D volume, and 2D shape metrics,
extracted from 2D projections of the segmented 3D volume.

Secondary shape metrics are also computed using the primary shape
metrics.

For this experiment, the shape metrics are extracted and computed
for two channels: actin and nucleus.

L = Axis of interest.

ROI = Region Of Interest in image, the foreground object.
It defines the voxels/pixels over which features are extracted.

N = Number of voxels/pixels in the ROI.

X dimension = dimension along X axis of the voxel/pixel in the
image.

Y dimension = dimension along Y axis of the voxel/pixel in the
image.

Z dimension = dimension along Z axis of the voxel in the
image.

Each shape metric computation is associated with one formula. For metrics related to axis, the computation can yield up to six values per channel:

- Three measures denoted with X, Y, Z and obtained from the image stack without orientation.
- Three measures denoted with L1, L2, L3 and obtained from the oriented cell and correspond to gyration moments.

To calculate the gyration tensors, S_{ij}, the position vectors of
each cell were centered about its mass (CM) to measure the deviation
of the cell from its center and to neglect effects due to cell
orientation:

The principal moments (eigenvalues), L1, L2, and L3, of the
gyration tensor, S, were calculated, where L1 < L2 < L3. The square
roots of the eigenvalues (L1^{0.5}, L2^{0.5},
L3^{0.5}) are the characteristic
semi-axis lengths (radii) of the ellipsoid that describes the shape
of the cell, while the eigenvectors of S describe the cellâ€™s original
orientation.

These shape metrics are computed on the binary mask of the 3D image.

Caliper length along the axis of interest, computed projecting each foreground voxel on the axis of interest in physical dimension. The depth is the length of the segment formed between the minimum and the maximum of the projections.

Notation: L-Depth

Six values are computed over the six axis of interest.

Computed from the gyration tensors, square root of gyration moments.

Notation: Sqrt(L)

Three values are computed over the three gyration moments.

Surface area of the ROI, computed using the
Marching Cube algorithm affecting local surface area to each
cube configuration. The surface area of the object is the sum of
all the computed local surface areas.
For more details, please refer to the initial paper
^{
[1]
}.

Notation: Surface Area

Coordinates of the center of mass of the ROI.

Notation: Center of mass (x,y,z)

Volume of the foreground object is the sum of the volumes of each voxel part of the ROI.

Notation: Volume

These shape metrics are computed on max projections of the segmented 3D image.

Perimeter is computed from the max projection of the foreground
object along the axis of interest. The computation is done using
the Marching Square algorithm affecting local perimeter to each
square configuration.

The perimeter of the projected object is the sum of all the
computed local perimeters.
For more details, please refer to the initial paper
^{
[1]
}.

Notation: L-Perimeter

Six values are computed over the six axis of interest.

Area is computed from the max projection of the foreground object along the axis of interest. The area is the sum of the areas of all the projected ROI pixels.

Notation: L-Area

Six values are computed over the six axis of interest.

Bounding box aspect ratio is computed from the max projection of the foreground object along the axis of interest. The bounding box of the ROI is computed to determine the aspect ratio.

Notation: L-Aspect Ratio

Six values are computed over the six axis of interest.

These metrics are computed using the primary shape metrics extracted from the 3D segmented image and its projections.

Ratio of shortest gyration moment to longest gyration moment.

Notation: sqrt(L1)/sqrt(L3)

Ratio of middle gyration moment to longest gyration moment.

Notation: sqrt(L2)/sqrt(L3)

Ratio of shortest gyration moment to middle gyration moment.

Notation: sqrt(L1)/sqrt(L2)

Ratio of longest gyration moment to shortest gyration moment.

Notation: sqrt(L3)/sqrt(L1)

Ratio of longest gyration moment to middle gyration moment.

Notation: sqrt(L3)/sqrt(L2)

Ratio of middle gyration moment to shortest gyration moment.

Notation: sqrt(L2)/sqrt(L1)

Notation: Radius of gyration

Notation: Asphericity

Notation: Acylindricity

Notation: Anisotropy

Ratio of nucleus to actin surface area.

Notation: Nucleus to Actin Surface Area

Ratio of nucleus to actin volume.

Notation: Nucleus to Actin Volume

Ratio of nucleus to actin L1-Depth.

Notation: Nucleus to Actin L1-Depth

Distance from center of mass of nucleus to center of mass of actin using Euclidian distance.

Notation: Nucleus to Actin Distance

[1]
^
Lindblad, Joaquim,
"Surface area estimation of digitized 3D objects using weighted local configurations", Image and Vision Computing , Volume 23, Issue 2,
pp.111-122, Feb. 2005

https://www.sciencedirect.com/science/article/pii/S0262885604001507