# regionprops

Measure properties of image regions

## Description

The regionprops function measures properties such as area, centroid, and bounding box, for each object (connected component) in an image. regionprops supports both contiguous regions and discontiguous regions.

regionprops finds unique objects in binary images using 8-connected neighborhoods for 2-D images and maximal connectivity for higher dimension images. For more information, see Pixel Connectivity. To find objects using other types of connectivity, use bwconncomp to create the connected components, and then pass the result to regionprops using the CC argument instead.

Note

To measure properties of objects in a 3-D volumetric image, consider using regionprops3 instead. Although regionprops can accept 3-D images, regionprops3 supports more statistics for 3-D images.

When you call the regionprops function, you can omit the properties argument, in which case the function returns the "Area", "Centroid", and "BoundingBox" measurements.

example

stats = regionprops(BW,properties) measures properties for each object in the binary image BW.

stats = regionprops(CC,properties) measures properties for each connected component CC.

stats = regionprops(L,properties) measures properties for each labeled region in label image L.

stats = regionprops(regions,I,properties) also measures pixel value properties for each labeled region in the grayscale image I. The first input argument, regions, must be a valid value for the BW, CC, or L argument.

example

stats = regionprops(outputFormat,___) also specifies the format of the returned measurements as an array of structures or a table, using the outputFormat argument.

## Examples

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Read a binary image into workspace.

Calculate centroids for connected components in the image using regionprops. The regionprops function returns the centroids in a structure array.

s = regionprops(BW,'centroid');

Store the x- and y-coordinates of the centroids into a two-column matrix.

centroids = cat(1,s.Centroid);

Display the binary image with the centroid locations superimposed.

imshow(BW)
hold on
plot(centroids(:,1),centroids(:,2),'b*')
hold off

Estimate the center and radii of circular objects in an image and use this information to plot circles on the image. In this example, regionprops returns the measured region properties in a table.

Turn the input image into a binary image.

bw = a < 50;
imshow(bw)
title("Image with Circles")

Calculate properties of regions in the image and return the data in a table.

stats = regionprops("table",bw,"Centroid", ...
"MajorAxisLength","MinorAxisLength")
stats=3×3 table
Centroid        MajorAxisLength    MinorAxisLength
________________    _______________    _______________

300       120        79.517             79.517
330.29    369.92        109.49              108.6
450       240        99.465             99.465

Get centers and radii of the circles.

centers = stats.Centroid;
diameters = mean([stats.MajorAxisLength stats.MinorAxisLength],2);

Plot the circles.

hold on
ans =
Group with properties:

Children: [2x1 Line]
Visible: on
HitTest: on

Use GET to show all properties

hold off

Read a binary image and detect the connected components.

CC = bwconncomp(BW);

Measure the area of each connected component and return the results as a table.

p = regionprops("table",CC,"Area");

Create a binary image that contains only the 2nd through 10th largest connected components. Display the result.

[~,idx] = sort(p.Area,"descend");
BWfilt = cc2bw(CC,ObjectsToKeep=idx(2:10));
imshow(BWfilt)

Read a grayscale image of grains of rice, then convert the image to binary.

BW = imbinarize(I);
imshow(BW)

Measure the area and bounding box of each region.

CC = bwconncomp(BW);
stats = regionprops("table",CC,"Area","BoundingBox");

Select regions for whom these conditions apply:

• The area is greater than 50 pixels

• The bounding box is less than 15 pixels wide and is greater than or equal to 20 pixels tall.

area = stats.Area;
bbox = stats.BoundingBox;
selection = (area > 50) & (bbox(:,3) < 15) & (bbox(:,4) >= 20);
BW2 = cc2bw(CC,ObjectsToKeep=selection);

Display the filtered image.

imshow(BW2)

## Input Arguments

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Binary image, specified as a logical array of any dimension.

regionprops sorts the objects in the 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 any higher dimensions. regionprops returns the measured properties, stats, in the same order as the sorted objects.

Data Types: logical

Connected components, specified as a structure with four fields. You can get a connected components structure by using the bwconncomp or bwpropfilt function.

FieldDescription
ConnectivityConnectivity of the connected components (objects)
ImageSizeSize of the binary image
NumObjectsNumber of connected components (objects) in the binary image
PixelIdxList1-by-NumObjects cell array where the k-th element in the cell array is a vector containing the linear indices of the pixels in the k-th object

Data Types: struct

Label image, specified as one of the following.

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

• A 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 string scalars or character vectors, an array of string scalars, a cell array of character vectors, or as "all" or "basic".

• If you specify "all", then regionprops computes all the shape measurements and, for grayscale images, the pixel value measurements as well.

• If you specify "basic", then regionprops computes only the "Area", "Centroid", and "BoundingBox" measurements.

The following tables list all the properties that provide shape measurements. The properties listed in the Pixel Value Measurements table are valid only when you specify a grayscale image.

Shape Measurements

Property NameDescriptionN-D SupportGPU SupportCode Generation
"Area"

Actual number of pixels in the region, returned as a scalar. This value might differ slightly from the value returned by bwarea, which weights different patterns of pixels differently.

To find the equivalent to the area of a 3-D volume, use the "Volume" property of regionprops3.

YesYesYes
"BoundingBox"

Position and size of the smallest box containing the region, returned as a 1-by-(2*Q) vector, where Q is the image dimensionality. The first Q elements are the coordinates of the minimum corner of the box. The second Q elements are the size of the box along each dimension. For example, a 2-D bounding box with value [5.5 8.5 11 14] indicates that the (x,y) coordinate of the top-left corner of the box is (5.5, 8.5), the horizontal width of the box is 11 pixels, and the vertical height of the box is 14 pixels.

YesYesYes
"Centroid"

Center of mass of the region, returned as a 1-by-Q vector, where Q is the image dimensionality. The first element of Centroid is the horizontal coordinate (or x-coordinate) of the center of mass. The second element is the vertical coordinate (or y-coordinate). All other elements of Centroid are in order of dimension.

This figure illustrates the centroid and bounding box for a discontiguous region. The region consists of the white pixels. The green box is the bounding box, and the red dot is the centroid.

YesYesYes
"Circularity"

Roundness of objects, returned as a structure with field Circularity. The structure contains the circularity value for each object in the input image. The circularity value is computed as:

(4*pi*Area/Perimeter^2)*(1 - 0.5/r)^2 where r = Perimeter/(2*pi) + 0.5

The maximum circularity value is 1. The input must be a label matrix or binary image with contiguous regions. If the image contains discontiguous regions, regionprops returns unexpected results.

2-D onlyNoYes
"ConvexArea"Number of pixels in ConvexImage, returned as a scalar.2-D onlyNoNo
"ConvexHull"Smallest convex polygon that can contain the region, returned as a p-by-2 matrix. Each row of the matrix contains the x- and y-coordinates of one vertex of the polygon.2-D onlyNoNo
"ConvexImage"Image that specifies the convex hull, with all pixels within the hull filled in (set to on), returned as a binary image. The image is the size of the bounding box of the region. For pixels that the boundary of the hull passes through, regionprops uses the algorithm described by Classify Pixels That Are Partially Enclosed by ROI.2-D onlyNoNo
"Eccentricity"Eccentricity of the ellipse that has the same second-moments as the region, returned as a scalar. The eccentricity is the ratio of the distance between the foci of the ellipse and its major axis length. The value is between 0 and 1. (0 and 1 are degenerate cases. An ellipse whose eccentricity is 0 is actually a circle, while an ellipse whose eccentricity is 1 is a line segment.)2-D onlyYesYes
"EquivDiameter"Diameter of a circle with the same area as the region, returned as a scalar. Computed as sqrt(4*Area/pi).2-D onlyYesYes
"EulerNumber"Number of objects in the region minus the number of holes in those objects, returned as a scalar. This property is supported only for 2-D label matrices. regionprops uses 8-connectivity to compute the Euler number (also known as the Euler characteristic). To learn more about connectivity, see Pixel Connectivity.2-D onlyNoYes
"Extent"Ratio of pixels in the region to pixels in the total bounding box, returned as a scalar. Computed as the Area divided by the area of the bounding box.2-D onlyYesYes
"Extrema"

Extrema points in the region, returned as an 8-by-2 matrix. Each row of the matrix contains the x- and y-coordinates of one of the points. The format of the vector is [top-left top-right right-top right-bottom bottom-right bottom-left left-bottom left-top]. For some shapes, multiple extrema points can have identical coordinates.

This figure illustrates the extrema of two different regions. In the region on the left, each extrema point is distinct. For the region on the right, certain extrema points (such as top-left and left-top) are identical.

2-D onlyYesYes
"FilledArea"Number of on pixels in FilledImage, returned as a scalar.YesNoYes
"FilledImage"

Image the same size as the bounding box of the region, returned as a binary array. The on pixels correspond to the region, with all holes filled in, as shown in this figure.

YesNoYes
"Image"Image the same size as the bounding box of the region, returned as a binary array. The on pixels correspond to the region, and all other pixels are off.YesYesYes
"MajorAxisLength"Length (in pixels) of the major axis of the ellipse that has the same normalized second central moments as the region, returned as a scalar.2-D onlyYesYes
"MaxFeretProperties"

Feret properties that include maximum Feret diameter, its relative angle, and coordinate values, returned as a structure with fields:

 Field Description MaxFeretDiameter Maximum Feret diameter measured as the maximum distance between any two boundary points on the antipodal vertices of convex hull that enclose the object. MaxFeretAngle Angle of the maximum Feret diameter with respect to horizontal axis of the image. MaxFeretCoordinates Endpoint coordinates of the maximum Feret diameter.

The input can be a binary image, connected component, or a label matrix.

2-D onlyNoNo
"MinFeretProperties"

Feret properties that include minimum Feret diameter, its relative angle, and coordinate values, returned as a structure with fields:

 Field Description MinFeretDiameter Minimum Feret diameter measured as the minimum distance between any two boundary points on the antipodal vertices of convex hull that enclose the object. MinFeretAngle Angle of the minimum Feret diameter with respect to horizontal axis of the image. MinFeretCoordinates Endpoint coordinates of the minimum Feret diameter.

The input can be a binary image, a connected component, or a label matrix.

2-D onlyNoNo
"MinorAxisLength"Length (in pixels) of the minor axis of the ellipse that has the same normalized second central moments as the region, returned as a scalar.2-D onlyYesYes
"Orientation"

Angle between the x-axis and the major axis of the ellipse that has the same second-moments as the region, returned as a scalar. The value is in degrees, ranging from -90 degrees to 90 degrees. This figure illustrates the axes and orientation of the ellipse. The left side of the figure shows an image region and its corresponding ellipse. The right side shows the same ellipse with the solid blue lines representing the axes. The red dots are the foci. The orientation is the angle between the horizontal dotted line and the major axis.

2-D onlyYesYes
"Perimeter"

Distance around the boundary of the region returned as a scalar. regionprops computes the perimeter by calculating the distance between each adjoining pair of pixels around the border of the region. If the image contains discontiguous regions, regionprops returns unexpected results. This figure illustrates the pixels included in the perimeter calculation for this object.

2-D onlyNoYes
"PixelIdxList"Linear indices of the pixels in the region, returned as a p-element vector. YesYesYes
"PixelList"Locations of pixels in the region, returned as a p-by-Q matrix. Each row of the matrix has the form [x y z ...] and specifies the coordinates of one pixel in the region.YesYesYes
"Solidity"

Proportion of the pixels in the convex hull that are also in the region, returned as a scalar. The solidity is calculated as Area/ConvexArea.

regionprops can calculate the solidity only of 2-D images. To calculate the solidity of 3-D images, use regionprops3.

2-D onlyNoNo
"SubarrayIdx"Elements of L inside the object bounding box, returned as a cell array that contains indices such that L(idx{:}) extracts the elements.YesYesNo

The pixel value measurement properties in the following table are valid only when you specify a grayscale image, I.

Pixel Value Measurements

Property Name DescriptionN-D SupportGPU SupportCode Generation
"MaxIntensity"Value of the pixel with the greatest intensity in the region, returned as a scalar.YesYesYes
"MeanIntensity"Mean of all the intensity values in the region, returned as a scalar.YesYesYes
"MinIntensity"Value of the pixel with the lowest intensity in the region, returned as a scalar.YesYesYes
"PixelValues"Number of pixels in the region, returned as a p-by-1 vector, where p is the number of pixels in the region. Each element in the vector contains the value of a pixel in the region.YesYesYes
"WeightedCentroid"Center of the region based on location and intensity value, returned as a p-by-Q 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). All other elements of WeightedCentroid are in order of dimension. YesYesYes

Data Types: char | string | cell

Image to be measured, specified as a grayscale image. The size of the image must match the size of the binary image BW, connected component structure CC, or label image L.

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

Output format of the measurement values stats, specified as either of the following values.

ValueDescription
"struct"Returns an array of structures with length equal to the number of objects in BW, CC.NumObjects, or max(L(:)). The fields of the structure array denote different properties for each region, as specified by properties.
"table"

Returns a table with height (number of rows) equal to the number of objects in BW, CC.NumObjects, or max(L(:)). The variables (columns) denote different properties for each region, as specified by properties.

Data Types: char | string

## Output Arguments

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Measurement values, returned as an array of structures or a table. The number of structures in the array or the number of rows in the table is equal to the number of objects in BW, CC.NumObjects, or max(L(:)). The fields of each structure or the variables in each 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 field or 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.

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### Contiguous Regions and Discontiguous Regions

Contiguous regions are also called objects, connected components, or blobs. A label image L containing contiguous regions might look like this:

1 1 0 2 2 0 3 3
1 1 0 2 2 0 3 3

Elements of L equal to 1 belong to the first contiguous region or connected component; elements of L equal to 2 belong to the second connected component; and so on.

Discontiguous regions are regions that can contain multiple connected components. A label image containing discontiguous regions might look like this:

1 1 0 1 1 0 2 2
1 1 0 1 1 0 2 2
Elements of L equal to 1 belong to the first region, which is discontiguous and contains two connected components. Elements of L equal to 2 belong to the second region, which is a single connected component.

## Tips

• regionprops takes advantage of intermediate results when computing related measurements. Therefore, it is fastest to compute all the desired measurements in a single call to regionprops.

• Most of the measurements take little time to compute. However, these measurements can take longer, depending on the number of regions in L:

• "ConvexHull"

• "ConvexImage"

• "ConvexArea"

• "FilledImage"

• The cc2bw function is useful for creating a binary image containing only a subset of objects or regions that meet certain criteria.

## Version History

Introduced before R2006a

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