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imrotate.m

## Copyright (C) 2004-2005 Justus H. Piater
##
## 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 2
## 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 <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {} imrotate(@var{imgPre}, @var{theta}, @var{method}, @var{bbox}, @var{extrapval})
## Rotation of a 2D matrix about its center.
##
## Input parameters:
##
##   @var{imgPre}   a gray-level image matrix
##
##   @var{theta}    the rotation angle in degrees counterclockwise
##
##   @var{method}
##     @itemize @w
##       @item "nearest" neighbor: fast, but produces aliasing effects.
##       @item "bilinear" interpolation: does anti-aliasing, but is slightly slower (default).
##       @item "bicubic" interpolation: does anti-aliasing, preserves edges better than bilinear interpolation, but gray levels may slightly overshoot at sharp edges. This is probably the best method for most purposes, but also the slowest.
##       @item "Fourier" uses Fourier interpolation, decomposing the rotation matrix into 3 shears. This method often results in different artifacts than homography-based methods.  Instead of slightly blurry edges, this method can result in ringing artifacts (little waves near high-contrast edges).  However, Fourier interpolation is better at maintaining the image information, so that unrotating will result in an image closer to the original than the other methods.
##     @end itemize
##
##   @var{bbox}
##     @itemize @w
##       @item "loose" grows the image to accommodate the rotated image (default).
##       @item "crop" rotates the image about its center, clipping any part of the image that is moved outside its boundaries.
##     @end itemize
##
##   @var{extrapval} sets the value used for extrapolation. The default value
##      is @code{NA} for images represented using doubles, and 0 otherwise.
##      This argument is ignored of Fourier interpolation is used.
##
## Output parameters:
##
##   @var{imgPost}  the rotated image matrix
##
##   @var{H}        the homography mapping original to rotated pixel
##                   coordinates. To map a coordinate vector c = [x;y] to its
##           rotated location, compute round((@var{H} * [c; 1])(1:2)).
##
##   @var{valid}    a binary matrix describing which pixels are valid,
##                  and which pixels are extrapolated. This output is
##                  not available if Fourier interpolation is used.
## @end deftypefn

## Author: Justus H. Piater  <Justus.Piater@ULg.ac.be>
## Created: 2004-10-18
## Version: 0.7

function [imgPost, H, valid] = imrotate(imgPre, thetaDeg, interp="bilinear", bbox="loose", extrapval=NA)
  ## Check input
  if (nargin < 2)
    error("imrotate: not enough input arguments");
  endif
  [imrows, imcols, imchannels, tmp] = size(imgPre);
  if (tmp != 1 || (imchannels != 1 && imchannels != 3))
    error("imrotate: first input argument must be an image");
  endif
  if (!isscalar(thetaDeg))
    error("imrotate: the angle must be given as a scalar");
  endif
  if (!any(strcmpi(interp, {"nearest", "linear", "bilinear", "cubic", "bicubic", "Fourier"})))
    error("imrotate: unsupported interpolation method");
  endif
  if (any(strcmpi(interp, {"bilinear", "bicubic"})))
    interp = interp(3:end); # Remove "bi"
  endif
  if (!any(strcmpi(bbox, {"loose", "crop"})))
    error("imrotate: bounding box must be either 'loose' or 'crop'");
  endif
  if (!isscalar(extrapval))
    error("imrotate: extrapolation value must be a scalar");
  endif

  ## Input checking done. Start working
  thetaDeg = mod(thetaDeg, 360); # some code below relies on positive angles
  theta = thetaDeg * pi/180;

  sizePre = size(imgPre);

  ## We think in x,y coordinates here (rather than row,column), except
  ## for size... variables that follow the usual size() convention. The
  ## coordinate system is aligned with the pixel centers.

  R = ;

  if (nargin >= 4 && strcmp(bbox, "crop"))
    sizePost = sizePre;
  else
    ## Compute new size by projecting zero-base image corner pixel
    ## coordinates through the rotation:
    corners = ;
    sizePost(2) = round(max(corners(:,1)) - min(corners(:,1))) + 1;
    sizePost(1) = round(max(corners(:,2)) - min(corners(:,2))) + 1;
    ## This size computation yields perfect results for 0-degree (mod
    ## 90) rotations and, together with the computation of the center of
    ## rotation below, yields an image whose corresponding region is
    ## identical to "crop". However, we may lose a boundary of a
    ## fractional pixel for general angles.
  endif

  ## Compute the center of rotation and the translational part of the
  ## homography:
  oPre  = ( + 1) / 2;
  oPost = ( + 1) / 2;
  T = oPost - R * oPre;       # translation part of the homography

  ## And here is the homography mapping old to new coordinates:
  H = ;

  ## Treat trivial rotations specially (multiples of 90 degrees):
  if (mod(thetaDeg, 90) == 0)
    nRot90 = mod(thetaDeg, 360) / 90;
    if (mod(thetaDeg, 180) == 0 || sizePre(1) == sizePre(2) ||
      strcmpi(bbox, "loose"))
      imgPost = rot90(imgPre, nRot90);
      return;
    elseif (mod(sizePre(1), 2) == mod(sizePre(2), 2))
      ## Here, bbox is "crop" and the rotation angle is +/- 90 degrees.
      ## This works only if the image dimensions are of equal parity.
      imgRot = rot90(imgPre, nRot90);
      imgPost = zeros(sizePre);
      hw = min(sizePre) / 2 - 0.5;
      imgPost   (round(oPost(2) - hw) : round(oPost(2) + hw),
             round(oPost(1) - hw) : round(oPost(1) + hw) ) = ...
        imgRot(round(oPost(1) - hw) : round(oPost(1) + hw),
             round(oPost(2) - hw) : round(oPost(2) + hw) );
      return;
    else
      ## Here, bbox is "crop", the rotation angle is +/- 90 degrees, and
      ## the image dimensions are of unequal parity. This case cannot
      ## correctly be handled by rot90() because the image square to be
      ## cropped does not align with the pixels - we must interpolate. A
      ## caller who wants to avoid this should ensure that the image
      ## dimensions are of equal parity.
    endif
  end

  ## Now the actual rotations happen
  if (strcmpi(interp, "Fourier"))
    if (isgray(imgPre))
      imgPost = imrotate_Fourier(imgPre, thetaDeg, interp, bbox);
    else # rgb image
      for i = 3:-1:1
        imgPost(:,:,i) = imrotate_Fourier(imgPre(:,:,i), thetaDeg, interp, bbox);
      endfor
    endif
    valid = NA;
  else
    [imgPost, valid] = imperspectivewarp(imgPre, H, interp, bbox, extrapval);
  endif
endfunction

%!test
%! ## Verify minimal loss across six rotations that add up to 360 +/- 1 deg.:
%! methods = { "nearest", "bilinear", "bicubic", "Fourier" };
%! angles     = ;
%! tolerances = /8;  # Fourier
%!
%! # This is peaks(50) without the dependency on the plot package
%! x = y = linspace(-3,3,50);
%! [X,Y] = meshgrid(x,y);
%! x = 3*(1-X).^2.*exp(-X.^2 - (Y+1).^2) \
%!      - 10*(X/5 - X.^3 - Y.^5).*exp(-X.^2-Y.^2) \
%!      - 1/3*exp(-(X+1).^2 - Y.^2);
%!
%! x -= min(x(:));            # Fourier does not handle neg. values well
%! x = x./max(x(:));
%! for m = 1:(length(methods))
%!   y = x;
%!   for i = 1:5
%!     y = imrotate(y, 60, methods{m}, "crop", 0);
%!   end
%!   for a = 1:(length(angles))
%!     assert(norm((x - imrotate(y, angles(a), methods{m}, "crop", 0))
%!                 (10:40, 10:40)) < tolerances(m,a));
%!   end
%! end


%!#test
%! ## Verify exactness of near-90 and 90-degree rotations:
%! X = rand(99);
%! for angle = 
%!   for da = 
%!     Y = imrotate(X,   angle + da , "nearest", :, 0);
%!     Z = imrotate(Y, -(angle + da), "nearest", :, 0);
%!     assert(norm(X - Z) == 0); # exact zero-sum rotation
%!     assert(norm(Y - imrotate(X, angle, "nearest", :, 0)) == 0); # near zero-sum
%!   end
%! end


%!#test
%! ## Verify preserved pixel density:
%! methods = { "nearest", "bilinear", "bicubic", "Fourier" };
%! ## This test does not seem to do justice to the Fourier method...:
%! tolerances = ;
%! range = 3:9:100;
%! for m = 1:(length(methods))
%!   t = [];
%!   for n = range
%!     t(end + 1) = sum(imrotate(eye(n), 20, methods{m}, :, 0)(:));
%!   end
%!   assert(t, range, tolerances(m));
%! end


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