How to apply directional gaussian filters to an image?

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anastasia on 3 Mar 2017
Commented: PaulLe on 20 Jan 2020
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
clear all;
close all;
hsize=[11, 11];
h1=imgaussfilt(a1, [40, 40], 'filterSize', [11, 11]);
h2=imgaussfilt(a1, [3, 0.5], 'filterSize', [11,11]);
  1 Comment
Matteo Fadda
Matteo Fadda on 15 Apr 2018
how can I extend this example for all 12 directions? thank you

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Accepted Answer

Image Analyst
Image Analyst on 4 Mar 2017
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().
  1 Comment
PaulLe on 20 Jan 2020
Dear Image Analyst,
How can I extend this example for all 8 directions?
Thank you so much.

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More Answers (2)

Braiki Marwa
Braiki Marwa on 17 May 2017
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);

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Gustavo Liñan
Gustavo Liñan on 21 Nov 2017
Edited: Gustavo Liñan on 21 Nov 2017
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.

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