How to create 64 Gabor functions in each scale and orientation in the spatial and frequency domain

Question

Typically, the Gabor filter, as its name implies, is used to filter the image and extract everything that is oriented in the same filtering direction.

In this question you can see a more efficient code than in this Link

Suppose there are 16 filter scales in 4 orientations, so we get 64 gabor filters.

scales = [7: 2: 37], from 7x7 to 37x37 in two-pixel increments, so we have 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29, 31x31, 33x33 , 35x35 and 37x37.

directions = [0, pi / 4, pi / 2, 3pi / 4].

The Gabor filter equation in the spatial domain:

The Gabor filter equation in the frequency domain:

Answer 1

In the spatial domain:

function [fSiz,filters,c1OL,numSimpleFilters] = init_gabor(rot, RF_siz) image=imread('xxx.jpg'); image_gray=rgb2gray(image); image_gray=imresize(image_gray, [100 100]); image_double=double(image_gray); rot = [0 45 90 135]; % we have four orientations RF_siz = [7:2:37]; %we get 16 scales (7x7 to 37x37 in steps of two pixels) minFS = 7; % the minimum receptive field maxFS = 37; % the maximum receptive field sigma = 0.0036*RF_siz.^2 + 0.35*RF_siz + 0.18; %define the equation of effective width lambda = sigma/0.8; % it the equation of wavelength (lambda) G = 0.3; % spatial aspect ratio: 0.23 < gamma < 0.92 numFilterSizes = length(RF_siz); % we get 16 numSimpleFilters = length(rot); % we get 4 numFilters = numFilterSizes*numSimpleFilters; % we get 16x4 = 64 filters fSiz = zeros(numFilters,1); % It is a vector of size numFilters where each cell contains the size of the filter (7,7,7,7,9,9,9,9,11,11,11,11,......,37,37,37,37) filters = zeros(max(RF_siz)^2,numFilters); % Matrix of Gabor filters of size %max_fSiz x num_filters, where max_fSiz is the length of the largest filter and num_filters the total number of filters. Column j of filters matrix contains a n_jxn_j filter (reshaped as a column vector and padded with zeros). for k = 1:numFilterSizes for r = 1:numSimpleFilters theta = rot(r)*pi/180; % so we get 0, pi/4, pi/2, 3pi/4 filtSize = RF_siz(k); center = ceil(filtSize/2); filtSizeL = center-1; filtSizeR = filtSize-filtSizeL-1; sigmaq = sigma(k)^2; for i = -filtSizeL:filtSizeR for j = -filtSizeL:filtSizeR if ( sqrt(i^2+j^2)>filtSize/2 ) E = 0; else x = i*cos(theta) - j*sin(theta); y = i*sin(theta) + j*cos(theta); E = exp(-(x^2+G^2*y^2)/(2*sigmaq))*cos(2*pi*x/lambda(k)); end f(j+center,i+center) = E; end end f = f - mean(mean(f)); f = f ./ sqrt(sum(sum(f.^2))); p = numSimpleFilters*(k-1) + r; filters(1:filtSize^2,p)=reshape(f,filtSize^2,1); fSiz(p)=filtSize; end end % Rebuild all filters (of all sizes) nFilts = length(fSiz); for i = 1:nFilts sqfilter{i} = reshape(filters(1:(fSiz(i)^2),i),fSiz(i),fSiz(i)); %if you will use conv2 to convolve an image with this gabor, so you should also add the equation below. But if you will use imfilter instead of conv2, so do not add the equation below. sqfilter{i} = sqfilter{i}(end:-1:1,end:-1:1); %flip in order to use conv2 instead of imfilter (%bug_fix 6/28/2007); convv=imfilter(image_double, sqfilter{i}, 'same', 'conv'); figure; imagesc(convv); colormap(gray); end 

Answer 2

 phi = ij*pi/4; % ij = 0, 1, 2, 3 theta = 3; sigma = 0.65*theta; filterSize = 7; % 7:2:37 G = zeros(filterSize); for i=(0:filterSize-1)/filterSize for j=(0:filterSize-1)/filterSize xprime= j*cos(phi); yprime= i*sin(phi); K = exp(2*pi*theta*sqrt(-1)*(xprime+ yprime)); G(round((i+1)*filterSize),round((j+1)*filterSize)) =... exp(-(i^2+j^2)/(sigma^2))*K; end end 

Answer 3

Starting with version R2015b of the image processing package, you can create a Gabor filter bank using the gabor function in the image processing toolbar, and you can apply it to the image using imgaborfilt .

Answer 4

In the frequency domain:

 sigma_u=1/2*pi*sigmaq; sigma_v=1/2*pi*sigmaq; u0=2*pi*cos(theta)*lambda(k); v0=2*pi*sin(theta)*lambda(k); for u = -filtSizeL:filtSizeR for v = -filtSizeL:filtSizeR if ( sqrt(u^2+v^2)>filtSize/2 ) E = 0; else v_theta = u*cos(theta) - v*sin(theta); u_theta = u*sin(theta) + v*cos(theta); E=(1/2*pi*sigma_u*sigma_v)*((exp((-1/2)*(((u_theta-u0)^2/sigma_u^2))+((v_theta-v0)^2/sigma_v^2))) + (exp((-1/2)*(((u_theta+u0)^2/sigma_u^2))+((v_theta+v0)^2/sigma_v^2)))); end f(v+center,u+center) = E; end end