# Complex image processing for loop vectorization

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Artur MKRTCHYAN on 19 May 2021
Commented: Artur MKRTCHYAN on 27 May 2021
Hello everyone, I am new to MatLab. I would like to reuse this code but I was wondering if there is a way to vectorize the double for loop ?
link to paper : Guided Image Filtering
function q = guidedfilter_color(I, p, r, eps)
% GUIDEDFILTER_COLOR O(1) time implementation of guided filter using a color image as the guidance.
%
% - guidance image: I (should be a color (RGB) image)
% - filtering input image: p (should be a gray-scale/single channel image)
% - local window radius: r
% - regularization parameter: eps
if ~(size(I,3) == 3)
error('The guidance image input should have 3 channels');
end
[hei, wid] = size(p);
if r<2*min(hei, wid), r = round(min(hei, wid)/4); end;
N = boxfilter(ones(hei, wid), r); % the size of each local patch; N=(2r+1)^2 except for boundary pixels.
mean_I = zeros(size(I));
for ii =1:size(I,3)
mean_I(:,:,ii) = boxfilter(I(:, :, ii), r) ./ N;
end
mean_p = boxfilter(p, r) ./ N;
mean_Ip = zeros(size(I));
for ii =1:size(I,3)
mean_Ip(:,:,ii) = boxfilter(I(:, :, ii).*p, r) ./ N;
end
% covariance of (I, p) in each local patch.
cov_Ip = zeros(size(I));
for ii =1:size(I,3)
cov_Ip(:,:,ii) = mean_Ip(:,:,ii) - mean_I(:,:,ii) .* mean_p;
end
% variance of I in each local patch: the matrix Sigma in Eqn (14).
% Note the variance in each local patch is a 3x3 symmetric matrix:
% rr, rg, rb
% Sigma = rg, gg, gb
% rb, gb, bb
var_I_rr = boxfilter(I(:, :, 1).*I(:, :, 1), r) ./ N - mean_I(:,:,1) .* mean_I(:,:,1);
var_I_rg = boxfilter(I(:, :, 1).*I(:, :, 2), r) ./ N - mean_I(:,:,1) .* mean_I(:,:,2);
var_I_gg = boxfilter(I(:, :, 2).*I(:, :, 2), r) ./ N - mean_I(:,:,2) .* mean_I(:,:,2);
var_I_rb = boxfilter(I(:, :, 1).*I(:, :, 3), r) ./ N - mean_I(:,:,1) .* mean_I(:,:,3);
var_I_gb = boxfilter(I(:, :, 2).*I(:, :, 3), r) ./ N - mean_I(:,:,2) .* mean_I(:,:,3);
var_I_bb = boxfilter(I(:, :, 3).*I(:, :, 3), r) ./ N - mean_I(:,:,3) .* mean_I(:,:,3);
a = zeros(hei, wid, 3);
for y=1:hei
for x=1:wid
Sigma = [var_I_rr(y, x), var_I_rg(y, x), var_I_rb(y, x);
var_I_rg(y, x), var_I_gg(y, x), var_I_gb(y, x);
var_I_rb(y, x), var_I_gb(y, x), var_I_bb(y, x)];
%Sigma = Sigma + eps * eye(3);
cov_Ip1 = [cov_Ip(y, x,1), cov_Ip(y, x,2), cov_Ip(y, x,3)];
a(y, x, :) = cov_Ip1 * inv(Sigma + eps * eye(3)); % Eqn. (14) in the paper;
end
end
b = mean_p - a(:, :, 1) .* mean_I(:,:,1) - a(:, :, 2) .* mean_I(:,:,2) - a(:, :, 3) .* mean_I(:,:,3); % Eqn. (15) in the paper;
q = (boxfilter(a(:, :, 1), r).* I(:, :, 1)...
+ boxfilter(a(:, :, 2), r).* I(:, :, 2)...
+ boxfilter(a(:, :, 3), r).* I(:, :, 3)...
+ boxfilter(b, r)) ./ N; % Eqn. (16) in the paper;
end
Artur MKRTCHYAN on 25 May 2021
Of course I've already used the profiler, and that's why I want to vectorize the double loop because that's exactly what takes more time. So I'm not asking to rewrite the code, I'm looking to see if it's possible to optimize only the double loop part.

Image Analyst on 21 May 2021
I would not reuse that code. I'd use the built-in imguidedfilter() function.
Artur MKRTCHYAN on 27 May 2021
It seems to me that this function has been created because the basic function is not adapted for RGB images. I'm not sure that's possible to make it this way.

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