-
Notifications
You must be signed in to change notification settings - Fork 0
/
Hessian3D.m
60 lines (52 loc) · 1.46 KB
/
Hessian3D.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
function [Dxx, Dyy, Dzz, Dxy, Dxz, Dyz] = Hessian3D(Volume,Sigma)
% This function Hessian3D filters the image with an Gaussian kernel
% followed by calculation of 2nd order gradients, which aprroximates the
% 2nd order derivatives of the image.
%
%
if nargin < 2, Sigma = 1; end
if(Sigma>0)
F=imgaussian(Volume,Sigma);
else
F=Volume;
end
% Create first and second order diferentiations
Dz=gradient3(F,'z');
Dzz=(gradient3(Dz,'z'));
clear Dz;
Dy=gradient3(F,'y');
Dyy=(gradient3(Dy,'y'));
Dyz=(gradient3(Dy,'z'));
clear Dy;
Dx=gradient3(F,'x');
Dxx=(gradient3(Dx,'x'));
Dxy=(gradient3(Dx,'y'));
Dxz=(gradient3(Dx,'z'));
clear Dx;
function D = gradient3(F,option)
% This function does the same as the default matlab "gradient" function
% but with one direction at the time, less cpu and less memory usage.
%
% Example:
%
% Fx = gradient3(F,'x');
[k,l,m] = size(F);
D = zeros(size(F),class(F));
switch lower(option)
case 'x'
% Take forward differences on left and right edges
D(1,:,:) = (F(2,:,:) - F(1,:,:));
D(k,:,:) = (F(k,:,:) - F(k-1,:,:));
% Take centered differences on interior points
D(2:k-1,:,:) = (F(3:k,:,:)-F(1:k-2,:,:))/2;
case 'y'
D(:,1,:) = (F(:,2,:) - F(:,1,:));
D(:,l,:) = (F(:,l,:) - F(:,l-1,:));
D(:,2:l-1,:) = (F(:,3:l,:)-F(:,1:l-2,:))/2;
case 'z'
D(:,:,1) = (F(:,:,2) - F(:,:,1));
D(:,:,m) = (F(:,:,m) - F(:,:,m-1));
D(:,:,2:m-1) = (F(:,:,3:m)-F(:,:,1:m-2))/2;
otherwise
disp('Unknown option')
end