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imshear.m

## Copyright (C) 2002 Jeff Orchard
##
## 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} {} imshear (@var{M}, @var{axis}, @var{alpha}, @var{bbox})
## Applies a shear to the image @var{M}.
##
## The argument @var{M} is either a matrix or an RGB image.
##
## @var{axis} is the axis along which the shear is to be applied, and can
## be either 'x' or 'y'.
## For example, to shear sideways is to shear along the 'x' axis. Choosing
## 'y' causes an up/down shearing.
##
## @var{alpha} is the slope of the shear. For an 'x' shear, it is the 
## horizontal shift (in pixels) applied to the pixel above the 
## center. For a 'y' shear, it is the vertical shift (in pixels)
## applied to the pixel just to the right of the center pixel.
##
## NOTE: @var{alpha} does NOT need to be an integer.
##
## @var{bbox} can be one of 'loose', 'crop' or 'wrap'.
## 'loose' allows the image to grow to accomodate the new transformed image.
## 'crop' keeps the same size as the original, clipping any part of the image
## that is moved outside the bounding box.
## 'wrap' keeps the same size as the original, but does not clip the part 
## of the image that is outside the bounding box. Instead, it wraps it back 
## into the image.
##
## If called with only 3 arguments, @var{bbox} is set to 'loose' by default.
## @end deftypefn

## Author: Jeff Orchard <jjo@sfu.ca>
## Created: June 2002

function g = imshear(m, axis, alpha, bbox, noshift)

      # The code below only does y-shearing. This is because of
      # the implementation of fft (operates on columns, but not rows).
      # So, transpose first for x-shearing.
      if ( strcmp(axis, "x")==1 )
            m = m';
      endif

      if ( nargin < 4 )
            bbox = "loose";
            noshift = 0;
      elseif ( nargin < 5 )
            noshift = 0;
      endif

      [ydim_orig xdim_orig] = size(m);
      if ( strcmp(bbox, "wrap") == 0 )
            ypad = ceil( (xdim_orig+1)/2 * abs(alpha) );
            m = impad(m, [0,0], [ypad,ypad]);
      endif

      [ydim_new xdim_new] = size(m);
      xcentre = ( xdim_new + 1 ) / 2;
      ycentre = ( ydim_new + 1 ) / 2;

      # This applies FFT to columns of m (x-axis remains a spatial axis).
      # Because the way that fft and fftshift are implemented, the origin
      # will move by 1/2 pixel, depending on the polarity of the image
      # dimensions.
      #
      # If dim is even (=2n), then the origin of the fft below is located
      # at the centre of pixel (n+1). ie. if dim=16, then centre is at 9.
      #
      # If dim is odd (=2n+1), then the origin of the fft below is located
      # at the centre of pixel (n). ie. if dim=15, then centre is at 8.
      if ( noshift==1 )
            M = fft(m);
      else
            #M = imtranslate(fft(imtranslate(m, -xcentre, ycentre, "wrap")), xcentre, -ycentre, "wrap");
            M = fftshift(fft(fftshift(m)));
      endif

      [ydim xdim] = size(m);
      x = zeros(ydim, xdim);

      # Find coords of the origin of the image.
      if ( noshift==1 )
            xc_coord = 1;
            yc_coord = 1;
            l = (1:ydim)' - yc_coord;
            r = (1:xdim) - xc_coord;
            if ( strcmp(bbox, "wrap")==1 )
                  l((ydim/2):ydim) = l((ydim/2):ydim) - ydim;
                  r((xdim/2):xdim) = r((xdim/2):xdim) - xdim;
            endif
      else
            xc_coord = (xdim+1)/2;
            yc_coord = (ydim+1)/2;
            l = (1:ydim)' - yc_coord;
            r = (1:xdim) - xc_coord;
      endif
      x = l * r;

      Ms = M.* exp(2*pi*I*alpha/ydim * x);

      if ( noshift==1 )
            g = abs(ifft(Ms));
      else
            #g = abs(imtranslate( ifft( imtranslate(Ms, -xcentre, ycentre, "wrap") ), xcentre, -ycentre, "wrap"));
            g = abs( fftshift(ifft(ifftshift(Ms))) );
      endif

      if ( strcmp(bbox, "crop")==1 )
            g = g(ypad+1:ydim_orig+ypad, :);
      endif

      # Un-transpose if x-shearing was wanted
      if ( strcmp(axis, "x")==1 )
            g = g';
      endif
endfunction

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