Connecting branch points using a straight line as dictated by the skeleton

I want to connect the branch points and endpoints of a skeleton (see sample skeleton below) via straight lines. However, the lines should be along the path of the skeleton. It's like "straightening" the skeleton. I've drawn a sample picture below describing how the branchpoints should be connected by the blue straight lines.

I'm thinking that this would probably involve a traversal algorithm.

[KSSV]

You have the image and you want to connect that on the image?

[WR]

Yes that's right. Basically, getting rid of the "curved" lines in the skeleton by connecting the nodes with straight lines instead

Answer 1

[Image Analyst]

Why? Why do you think you need that?

Here's what I'd do:

1. Call bwmorph to find the branchpoints.
2. Loop over each branchpoint and find the closest other branchpoint.
3. In a new image, use linspace to determine the "in between" coordinates and set them to true.

Here's a start, with a "to do for you":

% Initialization steps.
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 18;

skelImage = logical(imread('skeleton.png'));
% The sample image has a huge white frame around it, so get rid of that.
skelImage = imclearborder(skelImage);
subplot(2, 2, 1);
imshow(skelImage);
bpImage = bwmorph(skelImage, 'Branchpoints');
subplot(2, 2, 2);
imshow(bpImage);
[bpRows, bpCols] = find(bpImage)
fprintf('Found %d branchpoints.\n', numel(bpRows))
% It's hard to see them so put a marker over each one.
hold on;
plot(bpCols, bpRows, 'r.', 'MarkerSize', 10);
outputImage = false(size(bpImage));
for k = 1 : numel(bpRows)
    x1 = bpCols(k);
    y1 = bpRows(k);
    
    % Find distances to others.
    distances = sqrt((x1 - bpCols) .^ 2 + (y1 - bpRows) .^ 2);
    % Find mins
    [minDistances, indexes] = sort(distances, 'ascend');
    
    % IMPORTANT.  TO DO FOR YOU.
	% Make sure we don't "backtrack" by making sure we have not
	% used these exact (x1, y1) and (x2,y2) before by seeing if
	% both those points are true in the output image.
    x2 = bpCols(indexOfClosest);
    y2 = bpRows(indexOfClosest);
    
    % Find number of pixels between the two points.
    numSamples = ceil(sqrt((x2-x1)^2 + (y2-y1)^2));
    % Make sure we won't have any gaps due to rounding.
    % Then get a line between the two points.
    x = linspace(x1, x2, ceil(2*numSamples));
    y = linspace(y1, y2, ceil(2*numSamples));
    % Set those pixels to true in the output image
    for k2 = 1 : numel(x)
        row = round(y(k2));
        col = round(x(k2));
        outputImage(row, col) = true;
    end
end
subplot(2, 2, 2);
imshow(outputImage);