# bwferet

Measure Feret properties

## Description

example

out = bwferet(BW,properties) measures the Feret properties of objects in an image and returns the measurements in a table. The input properties specifies the Feret properties to be measured for each object in input binary image BW. The measured Feret properties include the minimum and maximum Feret diameters, Feret angles, and endpoint coordinates of Feret diameters.

example

out = bwferet(CC,properties) measures the Feret properties for each connected component in structure CC.

out = bwferet(L,properties) measures the Feret properties for each object in the input label matrix L.

out = bwferet(input) measures the maximum Feret diameter, its relative angle, and coordinate values measured from the input. The function returns the measurements in a table. The input can be binary image BW, connected component CC, or label matrix L.

[out,LM] = bwferet(___) also returns a label matrix containing label values that represent the row indices of the table out. You can use any of the input arguments from previous syntaxes. Each row entry in out corresponds to a labeled region (object) in label matrix LM.

## Examples

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Read an image into the workspace.

Convert the image into a binary image.

Extract the first two largest objects from the binary image.

bw = bwareafilt(bw,2);

Fill holes in the extracted object regions.

bw = imfill(bw,'holes');

Calculate the minimum Feret properties and the label matrix of the extracted objects.

[out,LM] = bwferet(bw,'MinFeretProperties');

Get the maximum number of objects in the output label matrix.

maxLabel = max(LM(:));

Display the output containing the table of minimum Feret properties.

out
out=2×3 table
MinDiameter    MinAngle    MinCoordinates
___________    ________    ______________

116.23        99.462      {2x2 double}
132.08       -159.27      {2x2 double}

Display the minimum Feret properties of the object with label-value 1 from the output label matrix.

out.MinDiameter(1)
ans = 116.2301
out.MinAngle(1)
ans = 99.4623
out.MinCoordinates{1}
ans = 2×2

120.5000  311.5000
139.6081  196.8514

Display the minimum Feret properties of the object with label-value 2 from the output label matrix.

out.MinDiameter(2)
ans = 132.0776
out.MinAngle(2)
ans = -159.2744
out.MinCoordinates{2}
ans = 2×2

215.5000  197.5000
339.0304  244.2412

Display the output label matrix. Plot the endpoint coordinates and minimum Feret diameter of objects with different label values from the output label matrix.

h = imshow(LM,[]);
axis = h.Parent;
for labelvalues = 1:maxLabel
xmin = [out.MinCoordinates{labelvalues}(1,1) out.MinCoordinates{labelvalues}(2,1)];
ymin = [out.MinCoordinates{labelvalues}(1,2) out.MinCoordinates{labelvalues}(2,2)];
imdistline(axis,xmin,ymin);
end
title(axis,'Minimum Feret Diameter of Objects');
colorbar('Ticks',1:maxLabel)

Read an image into the workspace.

Convert the image into a binary image.

Fill holes in the object regions of the input binary image.

bw = imfill(bw,'holes');

Use the bwconncomp function to generate connected components from the resulting image.

cc = bwconncomp(bw);

Measure the maximum Feret properties of the connected components.

[out,LM] = bwferet(cc,'MaxFeretProperties');

Get the maximum number of objects in the output label matrix.

maxLabel = max(LM(:));

Inspect the table to verify the measured maximum Feret properties.

out
out=4×3 table
MaxDiameter    MaxAngle    MaxCoordinates
___________    ________    ______________

162.6       -175.06      {2x2 double}
156.21       -127.46      {2x2 double}
187.96        121.07      {2x2 double}
63.781       -131.19      {2x2 double}

Display the maximum Feret diameters of objects with different label values from output label matrix.

out.MaxDiameter(1:maxLabel)
ans = 4×1

162.6038
156.2082
187.9628
63.7809

Display the directional angles of the maximum Feret diameters specific to objects with different label values from output label matrix.

out.MaxAngle(1:maxLabel)
ans = 4×1

-175.0608
-127.4568
121.0683
-131.1859

Display the endpoint coordinates of the maximum Feret diameters specific to objects with different label values from output label matrix.

out.MaxCoordinates{1:maxLabel}
ans = 2×2

186.5000  113.5000
24.5000   99.5000

ans = 2×2

156.5000  315.5000
61.5000  191.5000

ans = 2×2

337.5000  174.5000
240.5000  335.5000

ans = 2×2

288.5000  129.5000
246.5000   81.5000

Display the output label matrix. Plot the endpoint coordinates and the maximum Feret diameter of objects with different label values from output label matrix.

h = imshow(LM,[]);
axis = h.Parent;
for labelvalues = 1:maxLabel
xmax = [out.MaxCoordinates{labelvalues}(1,1) out.MaxCoordinates{labelvalues}(2,1)];
ymax = [out.MaxCoordinates{labelvalues}(1,2) out.MaxCoordinates{labelvalues}(2,2)];
imdistline(axis,xmax,ymax);
end
title(axis,'Maximum Feret Diameter of Objects');
colorbar('Ticks',1:maxLabel)

## Input Arguments

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Binary image, specified as a logical or numeric matrix. BW must be a binary image where nonzero pixels correspond to an object and zero-valued pixels correspond to the background.

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

Connected components, specified as a structure with the four fields shown in this table.

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

You can use the bwconncomp function to generate connected components from a binary image.

Data Types: struct

Label matrix of contiguous regions, specified as a matrix of nonnegative integers. The pixels labeled 0 are the background. The pixels labeled 1 make up one object; the pixels labeled 2 make up a second object; and so on. The number of objects represented by L is equal to the maximum value of L. You can use the bwlabel function to generate label matrix from a binary image.

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

Label for Feret properties, specified as MaxFeretProperties, MinFeretProperties, or all.

Data Types: char | string

Generic input, specified as one of these values:

• Numeric matrix or logical matrix — When input is a binary image, BW.

• Structure — When input is the connected component, CC.

• Matrix of nonnegative integers — When input is the label matrix, L.

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

## Output Arguments

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Table of Feret properties, returned as an m-by-n table. m is the number of objects for which the Feret properties are measured. n is 3 or 6, depending on the properties input.

• If properties is 'MaxFeretProperties', then the table out is of size m-by-3 with columns MaxDiameter, MaxAngle, and MaxCoordinates.

• If properties is 'MinFeretProperties', then the table out is of size m-by-3 with columns MinDiameter, MinAngle, and MinCoordinates.

• If properties is 'all', then the table out is of size m-by-6 with all columns listed in this table.

Column NameDescription
MaxDiameterMaximum Feret diameter of an object, measured as the maximum distance between any two boundary points on the antipodal vertices of the convex hull that encloses that object
MaxAngle

Directional angle of the maximum Feret diameter with respect to the horizontal axis of the image. The value, in degrees, is in the range [–180o,180o]

MaxCoordinatesEndpoint coordinates of the maximum Feret diameter, returned in the form $\left[\begin{array}{l}{x}_{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{y}_{1}\\ {x}_{2}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{y}_{2}\end{array}\right]$
MinDiameterMinimum Feret diameter of an object, measured as the minimum distance between any two boundary points on the antipodal vertices of the convex hull that encloses that object
MinAngle

Directional angle of the minimum Feret diameter with respect to the horizontal axis of the image. The value, in degrees, is in the range [–180o,180o]

MinCoordinatesEndpoint coordinates of the minimum Feret diameter, returned in the form $\left[\begin{array}{l}{x}_{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{y}_{1}\\ {x}_{2}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{y}_{2}\end{array}\right]$

Label matrix of contiguous regions, specified as a matrix of nonnegative integers. The pixels labeled 0 are the background. The pixels labeled 1 make up one object; the pixels labeled 2 make up a second object; and so on. The Feret properties in the kth row entry of out correspond to the kth region (object) in LM that have the value k. The number of objects represented by LM is equal to the maximum value of LM.

Note

If the input to bwferet is a label matrix, then the output label matrix LM is same as the input label matrix.

Data Types: uint8

## Algorithms

The Feret properties of an object are measured by using boundary points on the antipodal vertices of the convex hull that encloses that object.

Given the endpoint coordinates of the maximum (or minimum) Feret diameter, $\left[\begin{array}{l}{x}_{1}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{y}_{1}\\ {x}_{2}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{y}_{2}\end{array}\right]$, the maximum (or minimum) Feret angle is measured as $angle\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\mathrm{tan}}^{-1}\left(\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\right)$.