Shortest distance between a specific object to other objects - image

Question

Following these two posts that deals with finding the distance between objects in binary image, how can I only output/calculate only the shortest distance between a specific object to the rest (for examples, {1->3}, {2->5}, {3->1}, {4->7)?
https://www.mathworks.com/matlabcentral/answers/164955-distance-between-several-objects-in-binary-image
Pairwise distance between all centroid coordinate combinations - Matlab
Script:
clc;
clear all;
I = rgb2gray(imread('E:/NCircles.png'));
imshow(I);
BW = imbinarize(I,'adaptive');
BW = imfill(BW, 'holes');
BW = bwlabel(BW);
s = regionprops(BW,'Area', 'BoundingBox', 'Eccentricity', 'MajorAxisLength', 'MinorAxisLength', 'Orientation', 'Perimeter','Centroid');
imshow(BW)
hold on
for k = 1:numel(s)
c = s(k).Centroid;
text(c(1), c(2), sprintf('%d', k), 'HorizontalAlignment', 'center', 'VerticalAlignment', 'middle');
end
boundaries = bwboundaries(BW);
numberOfBoundaries = size(boundaries, 1);
for k = 1 : numberOfBoundaries
thisBoundary = boundaries{k};
plot(thisBoundary(:,2), thisBoundary(:,1), 'r', 'LineWidth', 3);
end
hold off;
% Define object boundaries
numberOfBoundaries = size(boundaries, 1)
for b1 = 1 : numberOfBoundaries
for b2 = 1 : numberOfBoundaries
if b1 == b2
% Can't find distance between the region and itself
continue;
end
boundary1 = boundaries{b1};
boundary2 = boundaries{b2};
boundary1x = boundary1(:, 2);
boundary1y = boundary1(:, 1);
x1=1;
y1=1;
x2=1;
y2=1;
overallMinDistance = inf; % Initialize.
% For every point in boundary 2, find the distance to every point in boundary 1.
for k = 1 : size(boundary2, 1)
% Pick the next point on boundary 2.
boundary2x = boundary2(k, 2);
boundary2y = boundary2(k, 1);
% For this point, compute distances from it to all points in boundary 1.
allDistances = sqrt((boundary1x - boundary2x).^2 + (boundary1y - boundary2y).^2);
% Find closest point, min distance.
[minDistance(k), indexOfMin] = min(allDistances);
if minDistance(k) < overallMinDistance
x1 = boundary1x(indexOfMin);
y1 = boundary1y(indexOfMin);
x2 = boundary2x;
y2 = boundary2y;
overallMinDistance = minDistance(k);
end
end
% Find the overall min distance
minDistance = min(minDistance);
% Report to command window.
fprintf('The minimum distance from region %d to region %d is %.3f pixels\n', b1, b2, minDistance);
% Draw a line between point 1 and 2
line([x1, x2], [y1, y2], 'Color', 'y', 'LineWidth', 3);
end
end

Answer 1

Given BW and boundaries as defined above, and a source object from which to calculate distances to all other objects:
source_object = 1; % label of source object in BW
Construct a distance image such that the value of each pixel is its distance from the source object using bwdist:
% anonymous function to convert cell array of subsripts
% into cell array of indices
indsfun = #(a) sub2ind(size(BW), a(:,1), a(:,2));
% use function on all of the cell's boundary objects
object_inds = cellfun(indsfun, boundaries, 'UniformOutput', false);
source_image = zeros(size(BW)); % create image containing only source object
source_image(object_inds{source_object}) = 1;
% compute distance from source to all other pixels in image
dist_image = bwdist(source_image, 'euclidean'); % replace with desired metric
imagesc(dist_image); % not necessary, but gives a cool image
Now, for each object in the original image, find the minimum distance of its boundary to the source object boundary:
min_dist = zeros(1,numel(boundaries)); % hold minimum distances
for target_object = 1:numel(boundaries)
% get the distance values at the indices of the target object
% and store the minimum.
min_dist(target_object) = min(dist_image(object_inds{target_object}));
end
In the end, min_dist will contain the minimum (boundary) distance from the source object to all other objects. A sample run on your image gives the following Euclidean distances:
min_dist =
Columns 1 through 7:
0.00000 67.54258 60.00000 207.23416 154.48625 168.79869 319.01410
Columns 8 through 13:
236.05296 324.71063 344.05814 367.00000 469.07996 509.00000