How to apply directional gaussian filters to an image?

I have an image I(X,Y) and I wish to filter it using the difference of Gaussian filter for different directions. Since I do not know the direction of particular lines in the image, I want to implement a 12 directional filters each of them tuned to a specific orientation θi ∈ [−π/2, π/2], i = 1, . . . , 12. The output of the directional filter is then compared with the output of an omnidirectional filter. We will use Gaussian filters for this purpose. Considering both contributions, the filter impulse response is given by

hθ(x, y) = G1(x, y) − G2(x, y)

This is the difference of gaussian filter which I wish to convolve with my image.

   Ii(x, y) = hθi(x, y) ∗ I(x, y) for i=1 to 12

This is the code I have executed for difference of Gaussian filter.

My filter parameters are as given below: 
N = 12 filters,
σx1 = 40, σy1 = 40, σx2 = 3, σy2 = 0.5 
and the window size is 11x11

clc;
clear all;
close all;
hsize=[11, 11];
a=(imread('os.jpg'));
a1=rgb2gray(a);
figure();
imshow(a1);
h1=imgaussfilt(a1, [40, 40], 'filterSize', [11, 11]);
h2=imgaussfilt(a1, [3, 0.5], 'filterSize', [11,11]);
imshow(h2)
DoG=h1-h2;
imshow(DoG);

[Matteo Fadda]

how can I extend this example for all 12 directions? thank you

Answer 1

[Image Analyst]

Like it said, Gaussians are an omnidirectional filter. That's what it says: "The output of the directional filter is then compared with the output of an omnidirectional filter. We will use Gaussian filters for this purpose." It can be made non-rotationally symmetrix. But I don't know what the "directional" filter it mentions is.

Using gausfilt() or fspecial() will give you symmetric Gaussians, though you could resize them with imresize() though that just sizes along the x or y axes. If you want to rotate also, then call resize and then call imrotate().

[PaulLe]

Dear Image Analyst,

How can I extend this example for all 8 directions?

Thank you so much.

Answer 2

[Braiki Marwa]

Hello,

I want to apply the gaussian filter .I write this code but it's not working

for i=1:nb1_iteration

 Iblur1= imgaussfilt(im,0.5);
end

[Image Analyst]

Start a new question and say what's not working. What you're doing is to create the same blurry image nb1_iteration times. Iblur1 is the same every single time. That's what you did - is that what you want?

[Braiki Marwa]

I want to apply the process of filtering for different iterations and see the effect.

[Image Analyst]

OK, good luck.

Answer 3

[Gustavo Liñan]

I use this type of rotated filters many times when I create algorithms using the histogram of orientations. What I do, in these cases, is, First, I create the non-simetric filter (e.g. gaussian with \sigmaX != \sigmaY, or LoG...). Then I define the rotation vector (typically, Phi=0:pi/Step:pi) and for each rotation angle I create the rotated filter basically, I consider the filter an image, apply image rotation with the bicubic interpolation and 'loose' option. Finally, I take the filter out of its rotated image by cropping it to the correct size.