matlab - How to create a polygon out of the outer cells of a contiguous patch of cells

Question

I have below a contiguous patch of cells plotted in Matlab.

The outer cells of the red patch have to be determined and then a polygon joining the centers of these cells will give me a polygon. How do i compute the outer cells of the contiguous patch?

I have an array of integers whose elements denote the cell in the red patch, for example,

a=[1;64;23;456;345];

Each element , say 64 corresponds to a cell in the image, and it is the cell belonging to the red patch.

The motivation to solve the problem is to deal with a polygon with minimal number of edges rather than so many cells. it slows down computation. Convex hull is not good enough. I don't want the resulting polygon to overlap with the brown area at all.

What i am suggesting is the case on the left in image below but it seems ugly. So a better way would be as in right to just skip the cells only sharing a single point with the outer brown area. I would like my outer cells to then be only those that share more than just a single point with the outer brown area.

But we want to avoid large number of edges in the resultant polygon!

Answer 1

I first processed the sample image from your question to create a logical mask (you already have an example of how to do that here).

Once you have this mask, there is a really easy way to generate the polygon you want using the bwtraceboundary function from the Image Processing Toolbox. This will give you a set of pixel indices in order around the perimeter of your masked region:

[r, c] = find(mask, 1);
coords = bwtraceboundary(mask, [r c], 'N');

And we can visualize it like so:

imagesc(mask);
colormap([0.9 0.9 0.9; 0.6 0.6 0.6]);
axis equal
set(gca, 'XLim', [0.5 0.5+size(mask, 2)], 'YLim', [0.5 0.5+size(mask, 1)]);
hold on;
plot(coords(:, 2), coords(:, 1), 'r', 'LineWidth', 2);
plot(coords(1, 2), coords(1, 1), 'go', 'LineWidth', 2);

The coordinates for the red line are ordered starting from the green circle and moving clockwise around the perimeter pixels of the masked region.

If you would prefer to generate a boundary outline that follows along the perimeter pixel edges of the region instead of the perimeter pixel centers, you can use the solution from my answer to a related question. This will yield the following: