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regionprops3

Measure properties of 3-D volumetric image regions

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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 denotes different properties for each object.

regionprops3 finds unique objects in volumetric binary images using 26-connected neighborhoods. For more information, see Pixel Connectivity. To find objects using other types of connectivity, instead use bwconncomp to create the connected components, and then pass the result to regionprops3 using the CC argument.

For all syntaxes, you can omit the properties argument. In this case, regionprops3 returns the "Volume", "Centroid", and "BoundingBox" measurements.

example

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

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Open Live Script

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

   19.9641
    9.8241


radii = diameters/2
radii = 2×1

    9.9820
    4.9120
Open Live Script

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    3.5    3.5    0.5      3      3      3    {[4 5 6]}    {[4 5 6]}    {[1 2 3]}    {3x3x3 logical}       3.7221          1       {27x1 double}    {27x3 double}    3.873    3.873    3.873    0    0    0    {3x3 double}    {3x1 double}    {24x3 double}    {3x3x3 logical}         27            1           41.07

Input Arguments

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

regionprops3 sorts the objects in the volumetric binary image from left to right based on the top-left extremum of each component. When multiple objects have the same horizontal position, the function then sorts those objects from top to bottom, and again along the third dimension. regionprop3 returns the measured properties, stats, in the same order as the sorted objects.

Data Types: logical

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

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

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 NameDescriptionCode Generation
"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.Yes
"Centroid"

Center of mass of the region, returned as a 1-by-3 vector. The three elements specify the (x, y, z) coordinates of the center of mass.

Yes
"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.No
"ConvexImage"Image of the convex hull, returned as a volumetric binary image with all voxels within the hull filled in (set to on). The image is the size of the bounding box of the region. No
"ConvexVolume"Number of voxels in ConvexImage, returned as a scalar.No
"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.Yes
"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.Yes
"EquivDiameter"Diameter of a sphere with the same volume as the region, returned as a scalar. Computed as (6*Volume/pi)^(1/3).Yes
"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)]Yes
"Image"Bounding box of the region, returned as a volumetric binary image 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.Yes
"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.

Yes
"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.Yes
"Solidity"Proportion of the voxels in the convex hull that are also in the region, returned as a scalar. Computed as Volume/ConvexVolume.No
"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.Yes
"SurfaceArea"Distance around the boundary of the region [1], returned as a scalar.No
"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.Yes
"VoxelIdxList"Linear indices of the voxels in the region, returned as a p-element vector.Yes
"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.Yes

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 DescriptionCode Generation
"MaxIntensity"Value of the voxel with the greatest intensity in the region, returned as a scalar. Yes
"MeanIntensity"Mean of all the intensity values in the region, returned as a scalar. Yes
"MinIntensity"Value of the voxel with the lowest intensity in the region, returned as a scalar. Yes
"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.Yes
"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).Yes

Data Types: char | string | cell

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

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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".

The order of the measurement values in stats is the same as the sorted objects in binary image BW, or the ordered objects specified by CC or L.

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.

Extended Capabilities

Version History

Introduced in R2017b

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See Also

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