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

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Theodore Fisher
Theodore Fisher on 10 Jul 2021
Commented: DGM on 12 Jul 2021
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!

Answers (2)

DGM on 10 Jul 2021
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
Note that depending on the convexity of the object, the centroid may lie inside or outside the object. This method covers both cases.
DGM on 12 Jul 2021
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)

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Image Analyst
Image Analyst on 11 Jul 2021
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;
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);
% Display the image.
subplot(2, 2, 1);
imshow(grayImage, []);
axis('on', 'image');
title('Original Image', 'FontSize', fontSize, 'Interpreter', 'None');
hFig = gcf;
hFig.WindowState = 'maximized'; % May not work in earlier versions of MATLAB.
% Binarize
mask = grayImage > 2.5;
% Display the image.
subplot(2, 2, 2);
imshow(mask, []);
axis('on', 'image');
title('Mask', 'FontSize', fontSize, 'Interpreter', 'None');
% 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');
% 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.
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);
hold on;
axis('on', 'image');
title('Lines from other centroids to boundary of blob #3', 'FontSize', fontSize, 'Interpreter', 'None');
% 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
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.

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