How can I properly fit the skeleton in the first image?

I tried 4th, 5th & 6th order polynomial fitting using polyfit. The curve needs to be split into 8 segments (shown in different colors) after the fitting. I need the tangent slope of each colored segment.

[Krishnashish Bose]

The points representing the skeleton are in the attached csv file.

[yanqi liu]

yes，sir，what is split rule？use index to 8 equal space？

[Krishnashish Bose]

The split rule is 8 nearly equal segments. It is hard to maintain the length of the segments as the tail bends. That is another challenge different from what I asked about.

Answer 1

[Image Analyst]

Why is it hard? Just figure out how many rows 1/8 of the total number of rows is and take those with regular indexing.

xy = rand(75, 2); % my (x,y) coordinates
[rows, columns] = size(xy);
startingRows = round(linspace(1, rows+1, 9)) % Use 9 instead of 8
endingRows = startingRows(2:end) - 1
for k = 1 : 8
    fprintf('\nChunk %d had %d rows:\n', k, endingRows(k) -  startingRows(k) + 1)
    thisChunk = xy(startingRows(k) : endingRows(k), :)
    fprintf('Chunk %d:\n', k)
    % Now do something with this 1/8 chunk of the total array.
end

[Krishnashish Bose]

That would work if the points (x,y) are sorted correctly. When the tail curves backward, some of the points towards the end of tail are found with the points corresponding to the beginning of the tail. If the points are arranged as per the shortest tour (Travelling Salseman/Hamiltonian path), then you can group the points very easily using your code.

[yanqi liu]

yes，sir，is it mean the points should sort counterclockwise or clockwise? may be use trace bound to get the line

[Krishnashish Bose]

Here is how your code incorrectly grouped the points:

[Image Analyst]

Why did you sort the values by x? You need to sort them in order of moving along the curve of course. bwtraceboundary can do that buy you need to take only half the points because we don't want a "round trip" all the way around the blob. Or of course you could do it manually, or use bwdistgeodesic().

https://blogs.mathworks.com/steve/2011/11/01/exploring-shortest-paths-part-1/

Find endpoints to get starting locations with bwmorph(bw, 'endpoints');