regionprops3

Measure properties of 3-D volumetric image regions

Syntax

stats = regionprops3(BW,properties)

stats = regionprops3(CC,properties)

stats = regionprops3(L,properties)

stats = regionprops3(___,V,properties)

Description

stats = regionprops3(BW,properties) measures a set of properties for each connected component (object) in the 3-D volumetric binary image BW. The output stats denote different properties for each object.

For all syntaxes, if you do not specify the properties argument, regionprops3 returns the 'Volume', 'Centroid', and 'BoundingBox' measurements.

stats = regionprops3(CC,properties) measures a set of properties for each connected component (object) in CC, which is a structure returned by bwconncomp.

stats = regionprops3(L,properties) measures a set of properties for each labeled region in the 3-D label image L.

stats = regionprops3(___,V,properties) measures a set of properties for each labeled region in the 3-D volumetric grayscale image V. The first input (BW, CC, or L) identifies the regions in V.

Examples

Estimate Centers and Radii of Objects in 3-D Volumetric Image

Create a binary image with two spheres.

[x,y,z] = meshgrid(1:50,1:50,1:50);
bw1 = sqrt((x-10).^2 + (y-15).^2 + (z-35).^2) < 5;
bw2 = sqrt((x-20).^2 + (y-30).^2 + (z-15).^2) < 10;
bw = bw1 | bw2;

Get the centers and radii of the two spheres.

s = regionprops3(bw,"Centroid","PrincipalAxisLength");
centers = s.Centroid

centers = 2×3

    20    30    15
    10    15    35

diameters = mean(s.PrincipalAxisLength,2)

diameters = 2×1

   17.8564
    8.7869

radii = diameters/2

radii = 2×1

    8.9282
    4.3935

Get All Statistics for Cube Within a Cube

Make a 9-by-9 cube of 0s that contains a 3-by-3 cube of 1s at its center.

innercube = ones(3,3,3);
cube_in_cube = padarray(innercube,[3 3],0,'both');

Get all statistics on the cube within the cube.

stats = regionprops3(cube_in_cube,'all')

stats=1×18 table
    Volume     Centroid      BoundingBox                 SubarrayIdx                     Image         EquivDiameter    Extent    VoxelIdxList       VoxelList         PrincipalAxisLength        Orientation    EigenVectors    EigenValues      ConvexHull        ConvexImage      ConvexVolume    Solidity    SurfaceArea
    ______    ___________    ____________    ___________________________________    _______________    _____________    ______    _____________    _____________    __________________________    ___________    ____________    ____________    _____________    _______________    ____________    ________    ___________

      27      5    5    2    [1x6 double]    {[4 5 6]}    {[4 5 6]}    {[1 2 3]}    {3x3x3 logical}       3.7221          1       {27x1 double}    {27x3 double}    3.4641    3.4641    3.4641    0    0    0    {3x3 double}    {3x1 double}    {24x3 double}    {3x3x3 logical}         27            1           41.07   

Input Arguments

BW — Volumetric binary image

3-D logical array

Volumetric binary image, specified as a 3-D logical array.

Data Types: logical

CC — Connected components

structure

Connected components of a 3-D volumetric image, specified as a structure returned by bwconncomp using a 3-D connectivity value, such as 6, 18, or 26. CC.ImageSize must be a 1-by-3 vector.

Data Types: struct

L — Label image

3-D numeric array | 3-D categorical array

Label image, specified as one of the following.

• A 3-D numeric array. Voxels labeled 0 are the background. Voxels labeled 1 make up one object; voxels labeled 2 make up a second object; and so on. regionprops3 treats negative-valued voxels as background and rounds down input voxels that are not integers. You can get a numeric label image from labeling functions such as watershed or labelmatrix.

• A 3-D categorical array. Each category corresponds to a different region.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | categorical

properties — Type of measurement

'basic' (default) | comma-separated list of strings or character vectors | cell array of strings or character vectors | 'all'

Type of measurement, specified as a comma-separated list of strings or character vectors, a cell array of strings or character vectors, 'all' or 'basic'.

• If you specify 'all', then regionprops3 computes all the shape measurements. If you also specify a grayscale image, then regionprops3 returns all of the voxel value measurements.

• If you specify 'basic' or do not specify the properties argument, then regionprops3 computes only the 'Volume', 'Centroid', and 'BoundingBox' measurements.

The following table lists all the properties that provide shape measurements. The Voxel Value Measurements table lists additional properties that are valid only when you specify a grayscale image.

Shape Measurements

Property Name	Description
'BoundingBox'	Smallest cuboid containing the region, returned as a 1-by-6 vector of the form [ulf_x ulf_y ulf_z width_x width_y width_z]. ulf_x, ulf_y, and ulf_z specify the upper-left front corner of the cuboid. width_x, width_y, and width_z specify the width of the cuboid along each dimension.
'Centroid'	Center of mass of the region, returned as a 1-by-3 vector of the form [centroid_x centroid_y and centroid_z]. The first element, centroid_x, is the horizontal coordinate (or x-coordinate) of the center of mass. The second element, centroid_y, is the vertical coordinate (or y-coordinate). The third element, centroid_z, is the planar coordinate (or z-coordinate).
'ConvexHull'	Smallest convex polygon that can contain the region, returned as a p-by-3 matrix. Each row of the matrix contains the x-, y-, and z-coordinates of one vertex of the polygon.
'ConvexImage'	Image of the convex hull, returned as a volumetric binary image (logical) with all voxels within the hull filled in (set to on). The image is the size of the bounding box of the region.
'ConvexVolume'	Number of voxels in 'ConvexImage', returned as a scalar.
'EigenValues'	Eigenvalues of the voxels representing a region, returned as a 3-by-1 vector. regionprops3 uses the eigenvalues to calculate the principal axes lengths.
'EigenVectors'	Eigenvectors of the voxels representing a region, returned as a 3-by-3 vector. regionprops3 uses the eigenvectors to calculate the orientation of the ellipsoid that has the same normalized second central moments as the region.
'EquivDiameter'	Diameter of a sphere with the same volume as the region, returned as a scalar. Computed as (6*Volume/pi)^(1/3).
'Extent'	Ratio of voxels in the region to voxels in the total bounding box, returned as a scalar. Computed as the value of Volume divided by the volume of the bounding box. [Volume/(bounding box width * bounding box height * bounding box depth)]
'Image'	Bounding box of the region, returned as a volumetric binary image (logical) that is the same size as the bounding box of the region. The on voxels correspond to the region, and all other voxels are off.
'Orientation'	Euler angles [2], returned as a 1-by-3 vector. The angles are based on the right-hand rule. regionprops3 interprets the angles by looking at the origin along the x-, y-, and z-axis representing roll, pitch, and yaw respectively. A positive angle represents a rotation in the counterclockwise direction. Rotation operations are not commutative so they must be applied in the correct order to have the intended effect.
'PrincipalAxisLength'	Length (in voxels) of the major axes of the ellipsoid that have the same normalized second central moments as the region, returned as 1-by-3 vector. regionprops3 sorts the values from highest to lowest.
'Solidity'	Proportion of the voxels in the convex hull that are also in the region, returned as a scalar. Computed as Volume/ConvexVolume.
'SubarrayIdx'	Indices used to extract elements inside the object bounding box, returned as a cell array such that L(idx{:}) extracts the elements of L inside the object bounding box.
'SurfaceArea'	Distance around the boundary of the region [1], returned as a scalar.
'Volume'	Count of the actual number of 'on' voxels in the region, returned as a scalar. Volume represents the metric or measure of the number of voxels in the regions within the volumetric binary image, BW.
'VoxelIdxList'	Linear indices of the voxels in the region, returned as a p-element vector.
'VoxelList'	Locations of voxels in the region, returned as a p-by-3 matrix. Each row of the matrix has the form [x y z] and specifies the coordinates of one voxel in the region.

The voxel value measurement properties in the following table are valid only when you specify a grayscale volumetric image, V.

Voxel Value Measurements

Property Name	Description
'MaxIntensity'	Value of the voxel with the greatest intensity in the region, returned as a scalar.
'MeanIntensity'	Mean of all the intensity values in the region, returned as a scalar.
'MinIntensity'	Value of the voxel with the lowest intensity in the region, returned as a scalar.
'VoxelValues'	Value of the voxels in the region, returned as a p-by-1 vector, where p is the number of voxels in the region. Each element in the vector contains the value of a voxel in the region.
'WeightedCentroid'	Center of the region based on location and intensity value, returned as a p-by-3 vector of coordinates. The first element of WeightedCentroid is the horizontal coordinate (or x-coordinate) of the weighted centroid. The second element is the vertical coordinate (or y-coordinate). The third element is the planar coordinate (or z-coordinate).

Data Types: char | string | cell

V — Volumetric grayscale image

3-D numeric array

Volumetric grayscale image, specified as a 3-D numeric array. The size of the image must match the size of the binary image BW, connected component structure CC, or label matrix L.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32

Output Arguments

stats — Measurement values

table

Measurement values, returned as a table. The number of rows in the table corresponds to the number of objects in BW, CC.NumObjects, or max(L(:)). The variables (columns) in each table row denote the properties calculated for each region, as specified by properties. If the input image is a categorical label image L, then stats includes an additional variable with the property 'LabelName'.

References

[1] Lehmann, Gaetan and David Legland. Efficient N-Dimensional surface estimation using Crofton formula and run-length encoding, The Insight Journal, 2012. (https://insight-journal.org/browse/publication/852)

[2] Shoemake, Ken, Graphics Gems IV. Edited by Paul S. Heckbert, Morgan Kaufmann, 1994, pp. 222–229.