This file is indexed.

/usr/share/octave/packages/image-2.4.1/imrotate.m is in octave-image 2.4.1-1.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
## Copyright (C) 2002 Jeff Orchard <jorchard@cs.uwaterloo.ca>
## Copyright (C) 2004-2005 Justus H. Piater <Justus.Piater@ULg.ac.be>
##
## 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 <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {} imrotate (@var{imgPre}, @var{theta}, @var{method}, @var{bbox}, @var{extrapval})
## Rotate image about its center.
##
## Input parameters:
##
##   @var{imgPre}   a gray-level image matrix
##
##   @var{theta}    the rotation angle in degrees counterclockwise
##
## The optional argument @var{method} defines the interpolation method to be
## used.  All methods supported by @code{interp2} can be used.  In addition,
## Fourier interpolation by decomposing the rotation matrix into 3 shears can
## be used with the @code{fourier} method. By default, the @code{nearest} method
## is used.
##
## For @sc{matlab} compatibility, the methods @code{bicubic} (same as
## @code{cubic}), @code{bilinear} and @code{triangle} (both the same as
## @code{linear}) are also supported.
##
##   @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 0.  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

function [imgPost, H, valid] = imrotate (imgPre, thetaDeg, interp = "nearest", bbox = "loose", extrapval = 0)

  if (nargin < 2 || nargin > 5)
    print_usage ();
  elseif (! isimage (imgPre))
    error ("imrotate: IMGPRE must be a grayscale or RGB image.")
  elseif (! isscalar (thetaDeg))
    error("imrotate: THETA must be a scalar");
  elseif (! ischar (interp))
    error("imrotate: interpolation METHOD must be a character array");
  elseif (! isscalar (extrapval))
    error("imrotate: EXTRAPVAL must be a scalar");
  elseif (! ischar (bbox) || ! any (strcmpi (bbox, {"loose", "crop"})))
    error("imrotate: BBOX must be 'loose' or 'crop'");
  endif
  interp = interp_method (interp);

  ## 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 && strcmpi(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 = rotdim (imgPre, nRot90, [1 2]);
      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 = rotdim (imgPre, nRot90, [1 2]);
      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
  endif

  ## Now the actual rotations happen
  if (strcmpi (interp, "fourier"))
    in_class = class (imgPre);
    imgPre = im2double (imgPre);
    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;

    imgPost = imcast (imgPost, in_class);
  else
    [imgPost, valid] = imperspectivewarp(imgPre, H, interp, bbox, extrapval);
  endif
endfunction


function fs = imrotate_Fourier (f, theta, method, bbox)

    # Get original dimensions.
    [ydim_orig, xdim_orig] = size(f);

    # This finds the index coords of the centre of the image (indices are base-1)
    #   eg. if xdim_orig=8, then xcentre_orig=4.5 (half-way between 1 and 8)
    xcentre_orig = (xdim_orig+1) / 2;
    ycentre_orig = (ydim_orig+1) / 2;

    # Pre-process the angle ===========================================================
    # Whichever 90 degree multiple theta is closest to, that multiple of 90 will
    # be implemented by rot90. The remainder will be done by shears.

    # This ensures that 0 <= theta < 360.
    theta = rem( rem(theta,360) + 360, 360 );

    # This is a flag to keep track of 90-degree rotations.
    perp = 0;

    if ( theta>=0 && theta<=45 )
        phi = theta;
    elseif ( theta>45 && theta<=135 )
        phi = theta - 90;
        f = rotdim(f,1, [1 2]);
        perp = 1;
    elseif ( theta>135 && theta<=225 )
        phi = theta - 180;
        f = rotdim(f,2, [1 2]);
    elseif ( theta>225 && theta<=315 )
        phi = theta - 270;
        f = rotdim(f,3, [1 2]);
        perp = 1;
    else
        phi = theta;
    endif

    if ( phi == 0 )
        fs = f;
        if ( strcmp(bbox,"loose") == 1 )
            return;
        else
            xmax = xcentre_orig;
            ymax = ycentre_orig;
            if ( perp == 1 )
                xmax = max([xmax ycentre_orig]);
                ymax = max([ymax xcentre_orig]);
                [ydim xdim] = size(fs);
                xpad = ceil( xmax - (xdim+1)/2 );
                ypad = ceil( ymax - (ydim+1)/2 );
                fs = padarray (fs, [ypad xpad]);
            endif
            xcentre_new = (size(fs,2)+1) / 2;
            ycentre_new = (size(fs,1)+1) / 2;
        endif
    else

        # At this point, we can assume -45<theta<45 (degrees)
        phi = phi * pi / 180;
        theta = theta * pi / 180;
        R = [ cos(theta) -sin(theta) ; sin(theta) cos(theta) ];

        # Find max of each dimension... this will be expanded for "loose" and "crop"
        xmax = xcentre_orig;
        ymax = ycentre_orig;

        # If we don't want wrapping, we have to zeropad.
        # Cropping will be done later, if necessary.
        if ( strcmp(bbox, "wrap") == 0 )
            corners = ( [ xdim_orig xdim_orig -xdim_orig -xdim_orig ; ydim_orig -ydim_orig ydim_orig -ydim_orig ] + 1 )/ 2;
            rot_corners = R * corners;
            xmax = max([xmax rot_corners(1,:)]);
            ymax = max([ymax rot_corners(2,:)]);

            # If we are doing a 90-degree rotation first, we need to make sure our
            # image is large enough to hold the rot90 image as well.
            if ( perp == 1 )
                xmax = max([xmax ycentre_orig]);
                ymax = max([ymax xcentre_orig]);
            endif

            [ydim xdim] = size(f);
            xpad = ceil( xmax - xdim/2 );
            ypad = ceil( ymax - ydim/2 );
            %f = padarray (f, [ypad xpad]);
            xcentre_new = (size(f,2)+1) / 2;
            ycentre_new = (size(f,1)+1) / 2;
        endif

        S1 = S2 = eye (2);
        S1(1,2) = -tan(phi/2);
        S2(2,1) = sin(phi);

        f1 = imshear(f, 'x', S1(1,2), 'loose');
        f2 = imshear(f1, 'y', S2(2,1), 'loose');
        fs = real( imshear(f2, 'x', S1(1,2), 'loose') );
        %fs = f2;
        xcentre_new = (size(fs,2)+1) / 2;
        ycentre_new = (size(fs,1)+1) / 2;
    endif

    if ( strcmp(bbox, "crop") == 1 )

        # Crop to original dimensions
        x1 = ceil (xcentre_new - xdim_orig/2);
        y1 = ceil (ycentre_new - ydim_orig/2);
        fs = fs (y1:(y1+ydim_orig-1), x1:(x1+xdim_orig-1));

    elseif ( strcmp(bbox, "loose") == 1 )

        # Find tight bounds on size of rotated image
        # These should all be positive, or 0.
        xmax_loose = ceil( xcentre_new + max(rot_corners(1,:)) );
        xmin_loose = floor( xcentre_new - max(rot_corners(1,:)) );
        ymax_loose = ceil( ycentre_new + max(rot_corners(2,:)) );
        ymin_loose = floor( ycentre_new - max(rot_corners(2,:)) );

        fs = fs( (ymin_loose+1):(ymax_loose-1) , (xmin_loose+1):(xmax_loose-1) );

    endif

    ## Prevent overshooting
    if (strcmp(class(f), "double"))
      fs(fs>1) = 1;
      fs(fs<0) = 0;
    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

#%!xtest
#%! ## 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

%!test
%! a = reshape (1:18, [2 3 3]);
%!
%! a90(:,:,1) = [5 6; 3 4; 1 2];
%! a90(:,:,2) = a90(:,:,1) + 6;
%! a90(:,:,3) = a90(:,:,2) + 6;
%!
%! a180(:,:,1) = [6 4 2; 5 3 1];
%! a180(:,:,2) = a180(:,:,1) + 6;
%! a180(:,:,3) = a180(:,:,2) + 6;
%!
%! am90(:,:,1) = [2 1; 4 3; 6 5];
%! am90(:,:,2) = am90(:,:,1) + 6;
%! am90(:,:,3) = am90(:,:,2) + 6;
%!
%! assert (imrotate (a,    0), a);
%! assert (imrotate (a,   90), a90);
%! assert (imrotate (a,  -90), am90);
%! assert (imrotate (a,  180), a180);
%! assert (imrotate (a, -180), a180);
%! assert (imrotate (a,  270), am90);
%! assert (imrotate (a, -270), a90);
%! assert (imrotate (a,  360), a);