Calculating Surface Curvature from Image Data

Hello,

I'm trying to calculate the curvature of each surface point from a morphology picture. However, when using surfature(), I do not get the results I want. A lot of points have a gaussian curvature of 0, which is not plausible for the example I use.

I tried a lot of different methods for calculating and ploting, but never got a good result...

I wrote the following:

% reading in picture
data = imread("Morphology.PNG");

% if not yet, convert to gray image
if size(data, 3) == 3
    data = rgb2gray(data);
end

% smoothing image
data = imgaussfilt(data, 4);

% converting to double
data = double(data);
z = data;

% generating 2D arrays for X and Y with size of data-dimensions
[Rows, Cols] = size(data); 
[x, y] = meshgrid(1:Cols, 1:Rows);

% calculating gaussian and normal curvature
[K, H] = surfature(x, y, data);

% display surface
figure;
surf(x, y, z, "EdgeColor","none");
title('Surface Morphology');
colorbar;

% ploting the results
figure;
surf(x, y, z, K, "EdgeColor","none");
title('3D Surface Gaussian Curvature Map');
colorbar;

disp(K);

Answer 1

[Mathieu NOE]

hello

I think this is because your K array contains some high amplitude spikes that avoid you see the smaller amplitude signals

so I decide to scale the imagesc (and not surf) plot using the mean of abs(K) as a starting point (then you can also add another scaling factor from there) and then the K plot shows up correctly

as I don't have the Image Processing Tbx , I replaced imgaussfilt with a Fex submission (smooth2a) but that is secondary in the problem - you can of course use imgaussfilt on your side as you did in the first place

this is my K plot so far :

code updated :

% reading in picture
data = imread("Morphology.png");
% if not yet, convert to gray image
if size(data, 3) == 3
    data = rgb2gray(data);
end

% smoothing image
% data = imgaussfilt(data, 4);    % you

% converting to double
data = double(data);

% smoothing image
data = smooth2a(data,10,10); % me 

% generating 2D arrays for X and Y with size of data-dimensions
[Rows, Cols] = size(data); 
[x, y] = meshgrid(1:Cols, 1:Rows);
% calculating gaussian and normal curvature
[K, H] = surfature(x, y, data);
% display surface
figure;
imagesc(data);
title('Surface Morphology');
colorbar;
% ploting the results
figure;
imagesc(K);
K_mean = mean(abs(K),'all');
amplitude = 3*K_mean; % eventually apply a scaling factor to K_mean
caxis([-amplitude amplitude]);
title('3D Surface Gaussian Curvature Map');
colorbar;

[Leon Stan]

Thank you for helping me!

At some point I was thinking about this problem, but didn't know how to solve it. :)

[Mathieu NOE]

glad I could be of some help !

[Mathieu NOE]

hello again

do you mind accepting my answer ? tx !!

[Leon Stan]

Hello again, I'm new to the forum, so I did'nt know thats a thing :)

I accepted your answer!

[Mathieu NOE]

thanks !