Coffee beans separation algorithm

Question

What is proper algorithm for separating (counting) coffee beans on binary image? Beans can touch and partially overlap.

_{(source: beucher at cmm.ensmp.fr)}

Answer 1

There are some elegant answers, but I thought of sharing what I tried because it is bit different to other approaches.

After thresholding and finding the distance transform, I propagate the local maxima of the distance-transformed image. By adjusting the extent of maxima propagation I segment the distance transformed image, then filter these segments by their area, rejecting smaller segments.

This way I can achieve a reasonably good segmentation of the given image, though it does not clearly define the boundaries. For the given image I get a segment count of 42 using the parameter values that I use in the Matlab code to control the extent of maxima propagation and the area threshold.

Results:

Here's the Matlab code:

clear all;
close all;

im = imread('ex2a.gif');
% threshold: coffee beans are black
bw = im2bw(im, graythresh(im));
% distance transform
di = bwdist(bw);
% mask for coffee beans
mask = double(1-bw);

% propagate the local maxima. depending on the extent of propagation, this
% will transform finer distance image to coarser segments 
se = ones(3);   % 8-neighbors
% this controls the extent of propagation. it's some fraction of the max
% distance of the distance transformed image (50% here)
mx = ceil(max(di(:))*.5);
peaks = di;
for r = 1:mx
    peaks = imdilate(peaks, se);
    peaks = peaks.*mask;
end

% how many different segments/levels we have in the final image
lvls = unique(peaks(:));
lvls(1) = []; % remove first, which is 0 that corresponds to background
% impose a min area constraint for segments. we can adjust this threshold
areaTh = pi*mx*mx*.7;
% number of segments after thresholding by area
nseg = 0;

% construct the final segmented image after thresholding segments by area
z = ones(size(bw));
lblid = 10;  % label id of a segment
for r = 1:length(lvls)
    lvl = peaks == lvls(r); % pixels having a certain value(level)
    props = regionprops(lvl, 'Area', 'PixelIdxList'); % get the area and the pixels
    % threshold area
    area = [props.Area];
    abw = area > areaTh;
    % take the count that passes the imposed area threshold
    nseg = nseg + sum(abw);
    % mark the segments that pass the imposed area threshold with a unique
    % id
    for i = 1:length(abw)
        if (1 == abw(i))
            idx = props(i).PixelIdxList;
            z(idx) = lblid; % assign id to the pixels
            lblid = lblid + 1; % increment id
        end
    end
end

figure,
subplot(1, 2, 1), imshow(di, []), title('distance transformed')
subplot(1, 2, 2), imshow(peaks, []), title('after propagating maxima'), colormap(jet)
figure,
subplot(1, 2, 1), imshow(label2rgb(z)), title('segmented')
subplot(1, 2, 2), imshow(im), title('original')