minimum distance between 2 objects

I plotted boundries with bwboundries and smoothed them with the sgolay filter then plotted these boundries over RGB image. Could you kindly help me in finding the  shortest distance between these two boundaries (the shortest distance of the area in-between the red and yellow lines)?

Answer 1

[Walter Roberson]

Trace the boundaries of the two objects. https://www.mathworks.com/help/images/boundary-tracing-in-images.html

Then with the coordinates of each point for each of the two objects, use pdist2() and then min()

If you do not have Statistics and Machine Learning Toolbox for pdist2() you can use

D = sqrt((x1(:) - x2(:).').^2 + (y1(:) - y2(:).').^2);

Answer 2

[Image Analyst]

If xy is an N by 2 array of (x,y) coordinates, then (untested)

allDistances = pdist2(xy1, xy2);
minDistance = min(allDistances(:))
% Find index of closest pair
[row, column] = find(allDistances == minDistance);
% Draw a line between them
x1 = xy1(row, 1);
y1 = xy1(row, 2);
x2 = xy2(col, 1);
y2 = xy2(col, 2);
hold on;
line([x1, x2], [y1, y2], 'LineWidth', 2, 'Color', 'b')