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bdpca.m
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bdpca.m
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function varargout = bdpca(X, krows, kcols)
% [Y, X, Wrt, Wct] = bdpca(X, krows, kcols)
%
% This function implement the Bi-Directional Principal Component Analysis
% detail in :
%
% @inproceedings{zuo2005bi,
% title={Bi-directional PCA with assembled matrix distance metric},
% author={Zuo, Wangmeng and Wang, Kuanquan and Zhang, David},
% booktitle={IEEE International Conference on Image Processing 2005},
% volume={2},
% pages={II--958},
% year={2005},
% organization={IEEE}
% }
%Copyright 2017 Julien FLEURET University Laval CVSL-MIVIM
%
%Redistribution and use in source and binary forms, with or without modification,
% are permitted provided that the following conditions are met:
%
%1. Redistributions of source code must retain the above copyright notice,
% this list of conditions and the following disclaimer.
%
%2. Redistributions in binary form must reproduce the above copyright notice,
% this list of conditions and the following disclaimer in the documentation
% and/or other materials provided with the distribution.
%
%3. Neither the name of the copyright holder nor the names of its contributors
% may be used to endorse or promote products derived from this software without
% specific prior written permission.
%
%THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
% THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
% PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS
% BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY,
% OR CONSEQUENTIAL DAMAGES
% (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
% LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
% ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
% STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY
% WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
% DAMAGE.
if(nargin==1)
krows=9;
kcols = krows;
end
if(nargin==2)
kcols = krows;
end
if(~isa(X,'single') || ~isa(X,'double'))
X = single(X);
end
X = squeeze(X);
X = rescale(X);
if ndims(X) == 2
if size(X,1) < size(X,2)
X = X';
end
[rows, cols] = size(X);
X_ = mean(X);
X = X - X_;
Srt = (X' * X) ./ rows;
Sct = (X * X') ./ cols;
[Wrt,~] = eig(Srt);
[Wct,~] = eig(Sct);
Wrt = Wrt(:,1:kcols);
Wct = Wct(:,1:krows);
Wrt = sort(Wrt,'descend');
Wct = sort(Wct,'descend');
Y = Wct' * X * Wrt;
else
% X is a batch of image.
[rows, cols, frames] = size(X);
%%
% process the mean image.
% X_ = zeros(rows, cols);
%
% for i=1:frames
%
% X_ = X_ + X(:,:,i);
%
% end
%
% X_ = X_ / frames;
X_ = mean(X,3);
%%
% process the Scatter matrices.
Srt = zeros(cols, cols);
Sct = zeros(rows, rows);
if isa(class(X),"gpuArray")
for i=1:frames
A = X(:,:,i) - X_;
Ar = A'*A;
Ac = A*A';
Srt = Srt + Ar;
Sct = Sct + Ac;
end
else
parfor i=1:frames
A = X(:,:,i) - X_;
Ar = A'*A;
Ac = A*A';
Srt = Srt + Ar;
Sct = Sct + Ac;
end
end
Srt = Srt / (frames * rows);
Sct = Sct / (frames * cols);
%%
% process the eigenvectors of the Scatter matrices and keep on the krows, kcols
% largest eigenvalues.
[Wrt,~] = eig(Srt);
[Wct,~] = eig(Sct);
Wrt = Wrt(:,1:kcols);
Wct = Wct(:,1:krows);
Wrt = sort(Wrt,'descend');
Wct = sort(Wct,'descend');
Y = zeros(krows, kcols, frames);
%%
% process the features for every image of the batch.
if isa(class(X),"gpuArray")
for i=1:frames
Y(:,:,i) = Wct' * X(:,:,i) * Wrt;
end
else
parfor i=1:frames
Y(:,:,i) = Wct' * X(:,:,i) * Wrt;
end
end
end
outputs = {Y, X_, Wrt, Wct};
for i=1:nargout
varargout{i} = outputs{i};
end
end