如何在空间和频域的每个尺度和方向上创建64个Gabor特征 [英] How to create 64 Gabor features at each scale and orientation in the spatial and frequency domain
问题描述
在这个问题中，你可以看到比这个链接
假设在4个方向上有16个过滤器的比例尺，所以我们得到64个gabor过滤器。 b = b
scale = [7：2：37]，7x7到37x37，以两个像素为单位，所以我们有7x7,9x9,11x11,13x13,15x15,17x17,19x19,21x21 ，23x23,25x25,27x27,29x29,31x31,33x33,35x35和37x37。 方向= [0，pi / 4，pi / 2，3pi / 4]。 空间域中Gabor滤波器的等式为： $ b $ Gabor滤波器在frequ ency域名是： 在空间领域： Normally, a Gabor filter, as its name suggests, is used to filter an image and extract everything that it is oriented in the same direction of the filtering. In this question, you can see more efficient code than written in this Link Assume 16 scales of Filters at 4 orientations, so we get 64 gabor filters. scales=[7:2:37], 7x7 to 37x37 in steps of two pixels, 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 equation of Gabor filter in the spatial domain is: The equation of Gabor filter in the frequency domain is:
In the spatial domain:
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函数[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]; ％我们有四个方向
RF_siz = [7：2：37]; ％我们得到16个尺度（7x7到37x37，以两个像素为单位）
minFS = 7;最小接收区域
maxFS = 37; ％最大感受野
sigma = 0.0036 * RF_siz。^ 2 + 0.35 * RF_siz + 0.18; ％定义有效宽度方程
lambda = sigma / 0.8; ％它的波长方程（λ）
G = 0.3; ％空间纵横比：0.23 < γ< 0.92
numFilterSizes = length（RF_siz）; ％我们得到16
numSimpleFilters = length（rot）; ％我们得到4
numFilters = numFilterSizes * numSimpleFilters; ％我们得到16x4 = 64个过滤器
fSiz = zeros（numFilters，1）; ％它是一个大小为numFilters的向量，其中每个单元格包含过滤器的大小（7,7,7,7,9,9,9,9,11,11,11,11，......，37 ，37,37,37）
filters =零（max（RF_siz）^ 2，numFilters）; ％大小为％max_fSiz x num_filters的Gabor滤波器的矩阵，其中max_fSiz是最大的滤波器的长度，num_filters是滤波器的总数。滤波器矩阵的第j列包含一个n_jxn_j滤波器（重新整形为列向量，并用零填充）。
$ b for k = 1：numFilterSizes
for r = 1：numSimpleFilters
theta = rot（r）* pi / 180 ; ％，所以我们得到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（θ） - j * sin（theta）;
y = i * sin（θ）+ j * cos（θ）;
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
重建所有大小的过滤器
nFilts = length（fSiz）; （fSiz（i）^ 2），i），fSiz（i），fSiz（i））;
for i = 1：nFilts
sqfilter {i} = reshape
％如果您将使用conv2来将图像与这个gabor进行卷积，那么您还应该添加下面的等式。但是，如果您将使用imfilter而不是conv2，那么请不要添加下面的公式。
sqfilter {i} = sqfilter {i}（结束：-1：1，结束：-1：1）; ％翻转为了使用conv2而不是imfilter（％bug_fix 6/28/2007）;
convv = imfilter（image_double，sqfilter {i}，'same'，'conv'）;
图;
imagesc（convv）;
colormap（gray）;
end
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
