# bwboundaries

Trace region boundaries in binary image

## Description

example

B = bwboundaries(BW) traces the exterior boundaries of objects, as well as boundaries of holes inside these objects, in the binary image BW. bwboundaries also descends into the outermost objects (parents) and traces their children (objects completely enclosed by the parents). Returns B, a cell array of boundary pixel locations.

B = bwboundaries(BW,conn) traces the exterior boundaries of objects, where conn specifies the connectivity to use when tracing parent and child boundaries.

example

B = bwboundaries(BW,conn,options) traces the exterior boundaries of objects, where options is either 'holes' or 'noholes', specifying whether you want to include the boundaries of holes inside other objects.

example

[B,L]= bwboundaries(___) returns a label matrix L where objects and holes are labeled.

example

[B,L,n,A] = bwboundaries(___) returns n, the number of objects found, and A, an adjacency matrix.

## Examples

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Read grayscale image into the workspace.

Convert grayscale image to binary image using local adaptive thresholding.

BW = imbinarize(I);

Calculate boundaries of regions in image and overlay the boundaries on the image.

[B,L] = bwboundaries(BW,'noholes');
imshow(label2rgb(L, @jet, [.5 .5 .5]))
hold on
for k = 1:length(B)
boundary = B{k};
plot(boundary(:,2), boundary(:,1), 'w', 'LineWidth', 2)
end

Read binary image into the workspace.

Calculate boundaries of regions in the image.

[B,L,N,A] = bwboundaries(BW);

Display the image with the boundaries overlaid. Add the region number next to every boundary (based on the label matrix). Use the zoom tool to read individual labels.

imshow(BW); hold on;
colors=['b' 'g' 'r' 'c' 'm' 'y'];
for k=1:length(B),
boundary = B{k};
cidx = mod(k,length(colors))+1;
plot(boundary(:,2), boundary(:,1),...
colors(cidx),'LineWidth',2);

%randomize text position for better visibility
rndRow = ceil(length(boundary)/(mod(rand*k,7)+1));
col = boundary(rndRow,2); row = boundary(rndRow,1);
h = text(col+1, row-1, num2str(L(row,col)));
set(h,'Color',colors(cidx),'FontSize',14,'FontWeight','bold');
end

Display the adjacency matrix using the spy function.

figure
spy(A);

Calculate boundaries.

[B,L,N] = bwboundaries(BW);

Display object boundaries in red and hole boundaries in green.

imshow(BW); hold on;
for k=1:length(B),
boundary = B{k};
if(k > N)
plot(boundary(:,2), boundary(:,1), 'g','LineWidth',2);
else
plot(boundary(:,2), boundary(:,1), 'r','LineWidth',2);
end
end

Display parent boundaries in red and their holes in green.

[B,L,N,A] = bwboundaries(BW);
figure; imshow(BW); hold on;
% Loop through object boundaries
for k = 1:N
% Boundary k is the parent of a hole if the k-th column
% of the adjacency matrix A contains a non-zero element
if (nnz(A(:,k)) > 0)
boundary = B{k};
plot(boundary(:,2),...
boundary(:,1),'r','LineWidth',2);
% Loop through the children of boundary k
for l = find(A(:,k))'
boundary = B{l};
plot(boundary(:,2),...
boundary(:,1),'g','LineWidth',2);
end
end
end

## Input Arguments

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Binary input image, specified as a 2-D logical or numeric matrix. BW must be a binary image where nonzero pixels belong to an object and zero-valued pixels constitute the background. The following figure illustrates these components.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Pixel connectivity, specified as one of the values in this table.

Value

Meaning

Two-Dimensional Connectivities

4-connected

Pixels are connected if their edges touch. Two adjoining pixels are part of the same object if they are both on and are connected along the horizontal or vertical direction.

8-connected

Pixels are connected if their edges or corners touch. Two adjoining pixels are part of the same object if they are both on and are connected along the horizontal, vertical, or diagonal direction.

Data Types: double

Determine whether to search for both parent and child boundaries, specified as either of the following:

Option

Meaning

'holes'

Search for both object and hole boundaries. This is the default.

'noholes'

Search only for object (parent and child) boundaries. This can provide better performance.

Data Types: char | string

## Output Arguments

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Row and column coordinates of boundary pixels, returned as a p-by-1 cell array, where p is the number of objects and holes. Each cell in the cell array contains a q-by-2 matrix. Each row in the matrix contains the row and column coordinates of a boundary pixel. q is the number of boundary pixels for the corresponding region.

Label matrix of contiguous regions, returned as a 2-D matrix of nonnegative integers. The kth region includes all elements in L that have value k. The number of objects and holes represented by L is equal to max(L(:)). The zero-valued elements of L make up the background.

Data Types: double

Number of objects found, returned as a nonnegative integer.

Data Types: double

Parent-child dependencies between boundaries and holes, returned as a square, sparse, logical matrix of class double with side of length max(L(:)). The rows and columns of A correspond to the positions of boundaries stored in B. The first n cells in B are object boundaries. A(i,j)=1 means that object i is a child of object j. .The boundaries that enclose or are enclosed by the k-th boundary can be found using A as follows:

enclosing_boundary  = find(A(m,:));
enclosed_boundaries = find(A(:,m));

## Algorithms

The bwboundaries function implements the Moore-Neighbor tracing algorithm modified by Jacob's stopping criteria. This function is based on the boundaries function presented in the first edition of Digital Image Processing Using MATLAB, by Gonzalez, R. C., R. E. Woods, and S. L. Eddins, New Jersey, Pearson Prentice Hall, 2004.

## References

[1] Gonzalez, R. C., R. E. Woods, and S. L. Eddins, Digital Image Processing Using MATLAB, New Jersey, Pearson Prentice Hall, 2004.