Calculate distances from region props centroid data to edge of binary shape

I have a list of centroid coordinates givebn by region props and a binary map of a structure given made by a freehand trace. Any ideas on how to find the distance to the nearest edge of the binary shape?

I need to also have the regionprops area data for each point presered.

let me know what other information I can provide!

Answer 1

[DGM]

Depends on how your objects are shaped, but this should be a start:

inpict = rgb2gray(imread('blobs.png'))>32;

S = regionprops(inpict,'centroid');
C = vertcat(S.Centroid);
dmap = bwdist(inpict); % distance from exterior points to edge
dmapi = bwdist(~inpict); % distance from interior points to edge
% shortest distance to edge for either case
D = interp2(dmap,C(:,1),C(:,2)) + interp2(dmapi,C(:,1),C(:,2))

D = 5×1

17.4449 25.0672 8.6016 30.9511 5.0000

imshow(inpict,[]); hold on
plot(C(:,1),C(:,2),'x')

Note that depending on the convexity of the object, the centroid may lie inside or outside the object. This method covers both cases.

[Theodore Fisher]

I think this is along the right lines, but i need to calculate each centroids distance from the edge of 1 object across all of them. I can attach my objects if that helps! Thanks so much for the assistance

The centroids are from the objects .mat and I need the distance to the edge of the Map(edge) freehand

[Image Analyst]

So, if you have N blobs, you have N centroids, and N outlines, like gotten from bwboundaries(). But I'm not sure what "each centroids distance from the edge of 1 object across all of them" actually means. So do you have one particular object, like blob #3 with its boundary/edge, and then want to find, for each of the other (N-1) blobs, the distance from their (n-1) centroids to all the edge pixels of blob #3? Attaching a diagram might help where you indicate the distances you want/need to measure.

[Theodore Fisher]

Hi there, sorry for the confusing phrasing, I need to calculate the distance of each centroid of objects in objects.mat to the nearest edge of the mask in Map(edge)

hope that clears it up?

[Image Analyst]

@Theodore Fisher, not really. Do you think you could show the diagram showing exactly what distances are to be computed? Like I did in my answer below?

[DGM]

This isn't significantly different from what I already suggested. Just use the edgemap as the basis for distance map generation instead of the object/label image.

S = load('objects.mat');
L = logical(S.L);
S = load('Map(edge).mat');
edgemap = S.labeledImage;

S = regionprops(L,'centroid'); % or you could use the .mat file
C = vertcat(S.Centroid);
dmap = bwdist(edgemap); % distance from exterior points to edge
dmapi = bwdist(~edgemap); % distance from interior points to edge
D = interp2(dmap,C(:,1),C(:,2)) + interp2(dmapi,C(:,1),C(:,2))

imshow(L,[]); hold on
plot(C(:,1),C(:,2),'x')

This gives the distance from each point in C to the nearest interior edge of the edgemap. The image boundary is treated as open. If you want to treat the image boundary as a closed edge, you can use temporary padding.

dmap = bwdist(padarray(edgemap,[1 1],1,'both'));
dmapi = bwdist(padarray(~edgemap,[1 1],1,'both'));
dmap = dmap(2:end-1); % crop off excess
dmapi = dmapi(2:end-1); % crop off excess
D = interp2(dmap,C(:,1),C(:,2)) + interp2(dmapi,C(:,1),C(:,2))

[Theodore Fisher]

Cool! wow thank you this seems to do the trick :)

One last thing, is it possible to have the final output be 3 columns, centroids, area of object, and the distance calculated above?

[DGM]

Again, assuming the "closed boundary" method from the prior example (modify if desired):

S = regionprops(L,'centroid','area');
C = vertcat(S.Centroid);
A = vertcat(S.Area);

dmap = bwdist(addborder(edgemap,[1 1],1)); % distance from exterior points to edge
dmapi = bwdist(addborder(~edgemap,[1 1],1)); % distance from interior points to edge
dmap = cropborder(dmap,[1 1]);
dmapi = cropborder(dmapi,[1 1]);
D = interp2(dmap,C(:,1),C(:,2)) + interp2(dmapi,C(:,1),C(:,2))

out = [C A D]

Of course, that's 4 columns, since the list of centroids is 2 columns. You could also use a table instead:

out = table(C,A,D)

Answer 2

[Image Analyst]

Is this what you mean by "each centroids distance from the edge of 1 object across all of them"?

% Demo by Image Analyst
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 = 20;

%--------------------------------------------------------------------------------------------------------
%    READ IN IMAGE
grayImage = peaks(300)'; % Create sample image of 3 blobs.

% Get the dimensions of the image.
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage)
if numberOfColorChannels > 1
	% It's not really gray scale like we expected - it's color.
	% Extract the red channel (so the magenta lines will be white).
	grayImage = grayImage(:, :, 1);
end

%--------------------------------------------------------------------------------------------------------
% Display the image.
subplot(2, 2, 1);
imshow(grayImage, []);
axis('on', 'image');
title('Original Image', 'FontSize', fontSize, 'Interpreter', 'None');
impixelinfo;
hFig = gcf;
hFig.WindowState = 'maximized'; % May not work in earlier versions of MATLAB.
drawnow;

% Binarize
max(grayImage(:))
mask = grayImage > 2.5;
% Display the image.
subplot(2, 2, 2);
imshow(mask, []);
axis('on', 'image');
title('Mask', 'FontSize', fontSize, 'Interpreter', 'None');
impixelinfo;

% Find the centroids
props = regionprops(mask, 'Centroid');
xy = vertcat(props.Centroid)
% Plot centroids over image
subplot(2, 2, 3);
imshow(grayImage, []); % Optional : show the original image again.  Or you can leave the binary image showing if you want.
hold on;
for k = 1 : size(xy, 1)
	hold on;
	xCentroid = xy(k, 1);
	yCentroid = xy(k, 2);
	plot(xCentroid, yCentroid, 'r+', 'LineWidth', 2, 'MarkerSize', 15);
	str = sprintf('   %d', k);
	text(xCentroid, yCentroid, str, 'FontSize', 20, 'Color', 'r', 'FontWeight', 'bold');	
end

% Find boundaries
% Plot the borders of all the blobs in the overlay above the original grayscale image 
% using the coordinates returned by bwboundaries().
% bwboundaries() returns a cell array, where each cell contains the row/column coordinates for an object in the image.
% Here is where we actually get the boundaries for each blob.
boundaries = bwboundaries(mask);
% boundaries is a cell array - one cell for each blob.
% In each cell is an N-by-2 list of coordinates in a (row, column) format.  Note: NOT (x,y).
% Column 1 is rows, or y.    Column 2 is columns, or x.
numberOfBoundaries = size(boundaries, 1); % Count the boundaries so we can use it in our for loop
% Here is where we actually plot the boundaries of each blob in the overlay.
hold on; % Don't let boundaries blow away the displayed image.
for k = 1 : numberOfBoundaries
	thisBoundary = boundaries{k}; % Get boundary for this specific blob.
	x = thisBoundary(:,2); % Column 2 is the columns, which is x.
	y = thisBoundary(:,1); % Column 1 is the rows, which is x.
	plot(x, y, 'r-', 'LineWidth', 2); % Plot boundary in red.
end
hold off;
caption = sprintf('%d Outlines, from bwboundaries()', numberOfBoundaries); 
title(caption, 'FontSize', fontSize); 
axis('on', 'image'); % Make sure image is not artificially stretched because of screen's aspect ratio.

% Display mask again.
subplot(2, 2, 4);
imshow(mask);
hold on;
axis('on', 'image');
title('Lines from other centroids to boundary of blob #3', 'FontSize', fontSize, 'Interpreter', 'None');
impixelinfo;

% Draw lines from every centroid to points along the boundary of blob %3.
% First get boundary #3
b3 = boundaries{3};
xb3 = b3(:, 2);
yb3 = b3(:, 1);
% Now draw lines from each centroid to every 10'th pixel on boundary 3
for k = 1 : numberOfBoundaries
	if k == 3
		continue; % Skip blob #3
	end
	thisXCentroid = xy(k, 1);
	thisYCentroid = xy(k, 2);
	% Just go to every 10th one otherwise it's too crowded to see.
	x = xb3(1:10:end);
	y = yb3(1:10:end);
	for k2 = 1 : length(x)
		xLine = [thisXCentroid; x(k2)];
		yLine = [thisYCentroid; y(k2)];
		distance(k, k2) = sqrt(diff(xLine).^2 + diff(yLine).^2);
		plot(xLine, yLine, '-', 'LineWidth', 2); % Plot boundary in red.
	end
end