/tags/R2008-02-16/main/image/inst/imrotate.m
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Possible License(s): GPL-2.0, BSD-3-Clause, LGPL-2.1, GPL-3.0, LGPL-3.0
- ## 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 = [cos(theta) sin(theta); -sin(theta) cos(theta)];
- if (nargin >= 4 && strcmp(bbox, "crop"))
- sizePost = sizePre;
- else
- ## Compute new size by projecting zero-base image corner pixel
- ## coordinates through the rotation:
- corners = [0, 0;
- (R * [sizePre(2) - 1; 0 ])';
- (R * [sizePre(2) - 1; sizePre(1) - 1])';
- (R * [0 ; sizePre(1) - 1])' ];
- 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 = ([ sizePre(2); sizePre(1)] + 1) / 2;
- oPost = ([sizePost(2); sizePost(1)] + 1) / 2;
- T = oPost - R * oPre; # translation part of the homography
- ## And here is the homography mapping old to new coordinates:
- H = [[R; 0 0] [T; 1]];
- ## 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 = [ 59 60 61 ];
- %! tolerances = [ 7.4 8.5 8.6 # nearest
- %! 3.5 3.1 3.5 # bilinear
- %! 2.7 2.0 2.7 # bicubic
- %! 2.7 1.6 2.8 ]/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 = [90 180 270]
- %! for da = [-0.1 0.1]
- %! 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 = [ 4 2.2 2.0 209 ];
- %! 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