bwlabel.m

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function [L,numComponents] = bwlabel(BW,mode)
%BWLABEL Label connected components in binary image.
%   L = BWLABEL(BW,N) returns a matrix L, of the same size as BW,
%   containing labels for the connected components in BW. N can
%   have a value of either 4 or 8, where 4 specifies 4-connected
%   objects and 8 specifies 8-connected objects; if the argument
%   is omitted, it defaults to 8. 
%
%   The elements of L are integer values greater than or equal to
%   0.  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. 
%
%   [L,NUM] = BWLABEL(BW,N) returns in NUM the number of
%   connected objects found in BW.
%
%   Class Support
%   -------------
%   The input image BW can be of class double or uint8. The
%   output matrix L is of class double.
%
%   Example
%   -------
%       BW = [1 1 1 0 0 0 0 0
%             1 1 1 0 1 1 0 0
%             1 1 1 0 1 1 0 0
%             1 1 1 0 0 0 1 0
%             1 1 1 0 0 0 1 0
%             1 1 1 0 0 0 1 0
%             1 1 1 0 0 1 1 0
%             1 1 1 0 0 0 0 0];
%       L = bwlabel(BW,4);
%       [r,c] = find(L == 2);
%
%   See also BWEULER.

%   Steven L. Eddins, August 1995
%   Copyright 1993-1998 The MathWorks, Inc.  All Rights Reserved.
%   $Revision: 1.14 $  $Date: 1997/11/24 15:34:07 $

if (nargin < 2)
    mode =8;
end

[M,N] = size(BW);

%
% Compute run-length encoding
%
rowZeros = repmat(uint8(0), 1, size(BW,2));
BW1 = [rowZeros ; BW];
BW2 = [BW ; rowZeros];   % BW1 and BW2 are now uint8 arrays
temp = BW2 > BW1;
[sr,sc] = find(temp);
[er,ec] = find(BW2 < BW1);
numRuns = length(sr);
if (numRuns == 0)
    runs = [];
else
    runs = [sc sr (er-1)];
end
runsPerCol = sum(temp,1);
cumRunsPerCol = cumsum(runsPerCol);

% 
% First labeling pass
%
labels = zeros(numRuns,1);
A = sparse([],[],[],numRuns,numRuns,3*numRuns);
currentLabel = 1;
currentColumn = 1;
lastColRuns = [];
first = 1;
last = 0;
for k = 1:numRuns
    column = runs(k,1);
    rowStart = runs(k,2);
    rowEnd = runs(k,3);
    if (column ~= currentColumn)
        % We've started a new column.  Extract the runs
        % belonging to the previous column.
        last = cumRunsPerCol(column - 1);
        first = last - runsPerCol(column - 1) + 1;
        lastColRuns = runs(first:last,:);
        currentColumn = column;
    end
    if (isempty(lastColRuns))
        labels(k) = currentLabel;
        currentLabel = currentLabel + 1;
    else
        if (mode == 8)
            % Find eight-connected objects
            overlaps = find(((rowEnd >= (lastColRuns(:,2)-1)) & ...
                    (rowStart <= (lastColRuns(:,3)+1))));
        else
            overlaps = find(((rowEnd >= lastColRuns(:,2)) & ...
                    (rowStart <= lastColRuns(:,3))));
        end
        if (isempty(overlaps))
            labels(k) = currentLabel;
            currentLabel = currentLabel + 1;
        elseif (length(overlaps) == 1)
            labels(k) = labels(first + overlaps - 1);
        else
            firstIdx = first + overlaps(1) - 1;
            labels(k) = labels(firstIdx);
            for n = 2:length(overlaps)
                nIdx = first + overlaps(n) - 1;
                if (labels(firstIdx) ~= labels(nIdx))
                    i = labels(firstIdx);
                    j = labels(nIdx);
                    A(i,j) = A(i,j) + 1;
                    A(j,i) = A(j,i) + 1;
                end
            end
        end
    end
end
numLabels = currentLabel - 1;

% Resolve equivalence classes
A = A(1:numLabels, 1:numLabels);
newLabels = 1:numLabels;
for i = 1:numLabels
    % Find all labels equivalent to i.
    % Use a queue-based breadth-first search starting from the
    % node i.  The vector equivs holds the queue.
    equivs = find(A(:,i));
    while (~isempty(equivs))
        j = equivs(1);
        newEquivs = find(A(:,j));
        if (~isempty(newEquivs))
            newEquivs(newEquivs == i) = [];
            equivs = [equivs ; newEquivs];
        end
        newLabels(j) = newLabels(i);
        A(:,j) = 0;
        A(j,:) = 0;
        equivs(1) = [];
    end
end

% Now we have a set of labels, but the set
% may skip some numbers.  We want the set
% to go from 1 to numComponents.
[newLabels,sortIdx] = sort(newLabels);
newLabels = 1 + cumsum(diff([1 newLabels]) ~= 0);
newLabels(sortIdx) = newLabels;

% Create the output image and fill in each run
% with its label.
L = zeros(M,N);
for k = 1:numRuns
    column = runs(k,1);
    rowStart = runs(k,2);
    rowEnd = runs(k,3);
    L(rowStart:rowEnd,column) = newLabels(labels(k));
end

numComponents = max(newLabels);