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## Copyright (C) 2019 Avinoam Kalma <a.kalma@gmail.com>
##
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program. If not, see <https://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} integralImage (@var{img})
## @deftypefnx {Function File} {} integralImage (@var{img}, @var{orient})
## Calculate the integral image.
##
## @var{img} is the input image for integral image calculation. If it
## is an RGB image (or higher dimension), each 2D plane is treated
## separately.
##
## @var{orient} determines which integral image will be
## calculated. Its value must be the string @qcode{"upright"}
## (default) or @qcode{"rotated"}.
##
## The value of the integral image in the @qcode{"upright"}
## orientation, also called "summed-area table", at any poing (x, y)
## is the sum of all the pixels above and to the left of (x, y),
## inclusive, see [1].
##
## When using the @qcode{"rotated"} option, Rotated Summed Area Table
## (RSAT) is calculated. It is defined as the sum of the pixels of a
## 45 degrees rotated rectangle with the bottom most corner at (x,y):
##
## @example
## RSAT(x,y) = RSAT(x-1,y-1) + RSAT(x+1,y-1) - RSAT(x,y-2) + I(x,y) + I(x,y-1)
## @end example
##
## (see [2])
##
## References:
##
## [1] Viola, Paul; Jones, Michael (2001). @cite{"Robust Real-time
## Object Detection"}. Compaq Cambridge Research Laboratory (CRL)
## Technical Report, February 2001.
## @url{http://www.hpl.hp.com/techreports/Compaq-DEC/CRL-2001-1.pdf}
##
## [2] Lienhart, Kuranov and Pisarevsky (2002). @cite{"Empirical
## Analysis of Detection Cascades of Boosted Classifiers for Rapid
## Object Detection"}. Microprocessor Research Lab (MRL) Technical
## Report, May 2002.
## @url{http://www.multimedia-computing.de/mediawiki/images/5/52/MRL-TR-May02-revised-Dec02.pdf}
##
## @seealso{cumsum}
## @end deftypefn
function J = integralImage (I, orientation = "upright")
if (nargin < 1 || nargin > 2)
print_usage ();
endif
if (! isimage (I))
error ("integralImage: first argument should be an image");
endif
if (! strcmp (class (I), "double"))
I = double (I);
endif
orientation = lower (orientation);
if (strcmp (orientation, "upright"))
J = cumsum (cumsum (I, 2));
J = padarray (J, [1 1], "pre");
elseif (strcmp (orientation, "rotated"))
if (ndims (I) == 2)
J = integralImage_rotate_2D (I);
else
IR = reshape (I, size (I,1), size (I,2), []);
J = zeros (size (IR,1)+1, size (IR,2)+2, size (IR,3));
for i = 1:size (IR,3)
J(:,:,i) = integralImage_rotate_2D (IR(:,:,i));
endfor
s = size (I);
J = reshape (J, [size(J,1) size(J,2) s(3:end)]);
endif
else
error ("orientation should be \"upright\" (default) or \"rotated\"");
endif
endfunction
function J = integralImage_rotate_2D (I)
## FIXME: Can this part be more vectorized?
s = size (I);
s1 = s + [1,2];
J = zeros (s1);
J(2,2:s(2)+1) = I(1,:);
s21 = s(2)+1;
for y = 3:s1(1)
y1 = y-1;
J(y,1) = J(y1,2);
J(y,2:s21) = J(y1,1:s(2)) + J(y1,3:s1(2)) - J(y-2,2:s21) + I(y1,:) + I(y-2,:);
J(y,end) = J(y1,s21);
endfor
endfunction
%!test
%! assert (integralImage (10), [0 0; 0 10]);
%! assert (integralImage (10, "rotated"), [0 0 0; 0 10 0]);
%!test
%! J = integralImage (10);
%! assert (class(J), "double");
%! J = integralImage (uint8(10));
%! assert (class(J), "double");
%!test
%! I = [1, 2; 3, 4];
%! J = integralImage (I);
%! J1 = [0 0 0; 0 1 3; 0 4 10];
%! assert (J, J1)
%! J = integralImage (I, "rotated");
%! J1 = [0 0 0 0; 0 1 2 0; 1 6 7 2];
%! assert (J, J1)
%!test
%! I1 = [1, 2; 3, 4];
%! I2 = [5, 6; 7, 8];
%! I3 = [9, 10; 11, 12];
%! I = cat (3, I1, I2, I3);
%! J = integralImage (I);
%! J1 = [0 0 0; 0 1 3; 0 4 10];
%! J2 = [0 0 0; 0 5 11; 0 12 26];
%! J3 = [0 0 0; 0 9 19; 0 20 42];
%! J0 = cat (3, J1, J2, J3);
%! assert (J, J0)
%!test
%! I1 = [1, 2; 3, 4];
%! I2 = [5, 6; 7, 8];
%! I3 = [9, 10; 11, 12];
%! I = cat (3, I1, I2, I3);
%! J = integralImage (I, "rotated");
%! J1 = [0 0 0 0; 0 1 2 0; 1 6 7 2];
%! J2 = [0 0 0 0; 0 5 6 0; 5 18 19 6];
%! J3 = [0 0 0 0; 0 9 10 0; 9 30 31 10];
%! J0 = cat (3, J1, J2, J3);
%! assert (J, J0)
%!test
%! I = magic (5);
%! J = integralImage (I);
%! J_res = [0 0 0 0 0 0;
%! 0 17 41 42 50 65;
%! 0 40 69 77 99 130;
%! 0 44 79 100 142 195;
%! 0 54 101 141 204 260;
%! 0 65 130 195 260 325];
%! assert (J, J_res)
%!
%! J = integralImage (I, "rotated");
%! J_res_R = [0 0 0 0 0 0 0;
%! 0 17 24 1 8 15 0;
%! 17 64 47 40 38 39 15;
%! 64 74 91 104 105 76 39;
%! 74 105 149 188 183 130 76;
%! 105 170 232 272 236 195 130];
%! assert (J, J_res_R)
%!error
%! integralImage ();
%!error
%! integralImage (1, "xxx", 2);
%!error <integralImage: first argument should be an image>
%! integralImage ("abcd");
%!error <orientation should be "upright">
%! integralImage ([1 2; 3 4], "xxx");
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