-
Notifications
You must be signed in to change notification settings - Fork 30
/
Copy pathCBM3D.m
640 lines (550 loc) · 27.9 KB
/
CBM3D.m
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
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
function [PSNR, yRGB_est] = CBM3D(yRGB, zRGB, sigma, profile, print_to_screen, colorspace)
%
% CBM3D is algorithm for attenuation of additive white Gaussian noise from
% color RGB images. This algorithm reproduces the results from the article:
%
% [1] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, "Color image
% denoising via sparse 3D collaborative filtering with grouping constraint in
% luminance-chrominance space," submitted to IEEE Int. Conf. Image Process.,
% January 2007, in review, preprint at http://www.cs.tut.fi/~foi/GCF-BM3D.
%
% FUNCTION INTERFACE:
%
% [PSNR, yRGB_est] = CBM3D(yRGB, zRGB, sigma, profile, print_to_screen, colorspace)
%
% ! The function can work without any of the input arguments,
% in which case, the internal default ones are used !
%
% BASIC USAGE EXAMPLES:
%
% Case 1) Using the default parameters (i.e., image name, sigma, etc.)
%
% [PSNR, yRGB_est] = CBM3D;
%
% Case 2) Using an external noisy image:
%
% % Read an RGB image and scale its intensities in range [0,1]
% yRGB = im2double(imread('image_House256rgb.png'));
% % Generate the same seed used in the experimental results of [1]
% randn('seed', 0);
% % Standard deviation of the noise --- corresponding to intensity
% % range [0,255], despite that the input was scaled in [0,1]
% sigma = 25;
% % Add the AWGN with zero mean and standard deviation 'sigma'
% zRGB = yRGB + (sigma/255)*randn(size(yRGB));
% % Denoise 'zRGB'. The denoised image is 'yRGB_est', and 'NA = 1'
% % because the true image was not provided
% [NA, yRGB_est] = CBM3D(1, zRGB, sigma);
% % Compute the putput PSNR
% PSNR = 10*log10(1/mean((yRGB(:)-yRGB_est(:)).^2))
% % show the noisy image 'zRGB' and the denoised 'yRGB_est'
% figure; imshow(min(max(zRGB,0),1));
% figure; imshow(min(max(yRGB_est,0),1));
%
% Case 3) If the original image yRGB is provided as the first input
% argument, then some additional information is printed (PSNRs,
% figures, etc.). That is, "[NA, yRGB_est] = BM3D(1, zRGB, sigma);" in the
% above code should be replaced with:
%
% [PSNR, yRGB_est] = CBM3D(yRGB, zRGB, sigma);
%
%
% INPUT ARGUMENTS (OPTIONAL):
% 1) yRGB (M x N x 3): Noise-free RGB image (needed for computing PSNR),
% replace with the scalar 1 if not available.
% 2) zRGB (M x N x 3): Noisy RGBimage (intensities in range [0,1] or [0,255])
% 3) sigma (double) : Std. dev. of the noise (corresponding to intensities
% in range [0,255] even if the range of zRGB is [0,1])
% 4) profile (char) : 'np' --> Normal Profile
% 'lc' --> Fast Profile
% 5) print_to_screen : 0 --> do not print output information (and do
% not plot figures)
% 1 --> print information and plot figures
% 6) colorspace (char): 'opp' --> use opponent colorspace
% 'yCbCr' --> use yCbCr colorspace
%
% OUTPUTS:
% 1) PSNR (double) : Output PSNR (dB), only if the original
% image is available, otherwise PSNR = 0
% 2) yRGB_est (M x N x 3): Final RGB estimate (in the range [0,1])
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Copyright (c) 2007-2011 Tampere University of Technology.
% All rights reserved.
% This work should only be used for nonprofit purposes.
%
% AUTHORS:
% Kostadin Dabov, email: dabov _at_ cs.tut.fi
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% In case, there is no input image (zRGB or yRGB), then use the filename
%%%% below to read an original image (might contain path also). Later,
%%%% artificial AWGN noise is added and this noisy image is processed
%%%% by the CBM3D.
%%%%
image_name = [
% 'kodim12.png'
'image_Lena512rgb.png'
% 'image_House256rgb.png'
% 'image_Peppers512rgb.png'
% 'image_Baboon512rgb.png'
% 'image_F16_512rgb.png'
];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Quality/complexity trade-off
%%%%
%%%% 'np' --> Normal Profile (balanced quality)
%%%% 'lc' --> Low Complexity Profile (fast, lower quality)
%%%%
%%%% 'high' --> High Profile (high quality, not documented in [1])
%%%%
%%%% 'vn' --> This profile is automatically enabled for high noise
%%%% when sigma > 40
%%%%
%%%% 'vn_old' --> This is the old 'vn' profile that was used in [1].
%%%% It gives inferior results than 'vn' in most cases.
%%%%
if (exist('profile') ~= 1)
profile = 'np'; %% default profile
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Specify the std. dev. of the corrupting noise
%%%%
if (exist('sigma') ~= 1),
sigma = 50; %% default standard deviation of the AWGN
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Colorspace in which we perform denoising. BM is applied to the first
%%%% component and the matching information is re-used for the other two.
%%%%
if (exist('colorspace') ~= 1),
colorspace = 'opp'; %%% (valid colorspaces are: 'yCbCr' and 'opp')
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Following are the parameters for the Normal Profile.
%%%%
%%%% Select transforms ('dct', 'dst', 'hadamard', or anything that is listed by 'help wfilters'):
transform_2D_HT_name = 'bior1.5'; %% transform used for the HT filt. of size N1 x N1
transform_2D_Wiener_name = 'dct'; %% transform used for the Wiener filt. of size N1_wiener x N1_wiener
transform_3rd_dim_name = 'haar'; %% transform used in the 3-rd dim, the same for HT and Wiener filt.
%%%% Hard-thresholding (HT) parameters:
N1 = 8; %% N1 x N1 is the block size used for the hard-thresholding (HT) filtering
Nstep = 3; %% sliding step to process every next reference block
N2 = 16; %% maximum number of similar blocks (maximum size of the 3rd dimension of a 3D array)
Ns = 39; %% length of the side of the search neighborhood for full-search block-matching (BM), must be odd
tau_match = 3000;%% threshold for the block-distance (d-distance)
lambda_thr2D = 0; %% threshold parameter for the coarse initial denoising used in the d-distance measure
lambda_thr3D = 2.7; %% threshold parameter for the hard-thresholding in 3D transform domain
beta = 2.0; %% parameter of the 2D Kaiser window used in the reconstruction
%%%% Wiener filtering parameters:
N1_wiener = 8;
Nstep_wiener = 3;
N2_wiener = 32;
Ns_wiener = 39;
tau_match_wiener = 400;
beta_wiener = 2.0;
%%%% Block-matching parameters:
stepFS = 1; %% step that forces to switch to full-search BM, "1" implies always full-search
smallLN = 'not used in np'; %% if stepFS > 1, then this specifies the size of the small local search neighb.
stepFSW = 1;
smallLNW = 'not used in np';
thrToIncStep = 8; %% used in the HT filtering to increase the sliding step in uniform regions
if strcmp(profile, 'lc') == 1,
Nstep = 6;
Ns = 25;
Nstep_wiener = 5;
N2_wiener = 16;
Ns_wiener = 25;
thrToIncStep = 3;
smallLN = 3;
stepFS = 6*Nstep;
smallLNW = 2;
stepFSW = 5*Nstep_wiener;
end
% Profile 'vn' was proposed in
% Y. Hou, C. Zhao, D. Yang, and Y. Cheng, 'Comment on "Image Denoising by Sparse 3D Transform-Domain
% Collaborative Filtering"', accepted for publication, IEEE Trans. on Image Processing, July, 2010.
% as a better alternative to that initially proposed in [1] (which is currently in profile 'vn_old')
if (strcmp(profile, 'vn') == 1) | (sigma > 40),
N2 = 32;
Nstep = 4;
N1_wiener = 11;
Nstep_wiener = 6;
lambda_thr3D = 2.8;
thrToIncStep = 3;
tau_match_wiener = 3500;
tau_match = 25000;
Ns_wiener = 39;
end
% The 'vn_old' profile corresponds to the original parameters for strong noise proposed in [1].
if (strcmp(profile, 'vn_old') == 1) & (sigma > 40),
transform_2D_HT_name = 'dct';
N1 = 12;
Nstep = 4;
N1_wiener = 11;
Nstep_wiener = 6;
lambda_thr3D = 2.8;
lambda_thr2D = 2.0;
thrToIncStep = 3;
tau_match_wiener = 3500;
tau_match = 5000;
Ns_wiener = 39;
end
decLevel = 0; %% dec. levels of the dyadic wavelet 2D transform for blocks (0 means full decomposition, higher values decrease the dec. number)
thr_mask = ones(N1); %% N1xN1 mask of threshold scaling coeff. --- by default there is no scaling, however the use of different thresholds for different wavelet decompoistion subbands can be done with this matrix
if strcmp(profile, 'high') == 1,
decLevel = 1;
Nstep = 2;
Nstep_wiener = 2;
lambda_thr3D = 2.5;
vMask = ones(N1,1); vMask((end/4+1):end/2)= 1.01; vMask((end/2+1):end) = 1.07; %% this allows to have different threhsolds for the finest and next-to-the-finest subbands
thr_mask = vMask * vMask';
beta = 2.5;
beta_wiener = 1.5;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Note: touch below this point only if you know what you are doing!
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Check whether to dump information to the screen or reamin silent
dump_output_information = 1;
if (exist('print_to_screen') == 1) & (print_to_screen == 0),
dump_output_information = 0;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Create transform matrices, etc.
%%%%
[Tfor, Tinv] = getTransfMatrix(N1, transform_2D_HT_name, decLevel); %% get (normalized) forward and inverse transform matrices
[TforW, TinvW] = getTransfMatrix(N1_wiener, transform_2D_Wiener_name); %% get (normalized) forward and inverse transform matrices
if (strcmp(transform_3rd_dim_name, 'haar') == 1) | (strcmp(transform_3rd_dim_name(end-2:end), '1.1') == 1),
%%% If Haar is used in the 3-rd dimension, then a fast internal transform is used, thus no need to generate transform
%%% matrices.
hadper_trans_single_den = {};
inverse_hadper_trans_single_den = {};
else
%%% Create transform matrices. The transforms are later applied by
%%% matrix-vector multiplication for the 1D case.
for hpow = 0:ceil(log2(max(N2,N2_wiener))),
h = 2^hpow;
[Tfor3rd, Tinv3rd] = getTransfMatrix(h, transform_3rd_dim_name, 0);
hadper_trans_single_den{h} = single(Tfor3rd);
inverse_hadper_trans_single_den{h} = single(Tinv3rd');
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% 2D Kaiser windows used in the aggregation of block-wise estimates
%%%%
if beta_wiener==2 & beta==2 & N1_wiener==8 & N1==8 % hardcode the window function so that the signal processing toolbox is not needed by default
Wwin2D = [ 0.1924 0.2989 0.3846 0.4325 0.4325 0.3846 0.2989 0.1924;
0.2989 0.4642 0.5974 0.6717 0.6717 0.5974 0.4642 0.2989;
0.3846 0.5974 0.7688 0.8644 0.8644 0.7688 0.5974 0.3846;
0.4325 0.6717 0.8644 0.9718 0.9718 0.8644 0.6717 0.4325;
0.4325 0.6717 0.8644 0.9718 0.9718 0.8644 0.6717 0.4325;
0.3846 0.5974 0.7688 0.8644 0.8644 0.7688 0.5974 0.3846;
0.2989 0.4642 0.5974 0.6717 0.6717 0.5974 0.4642 0.2989;
0.1924 0.2989 0.3846 0.4325 0.4325 0.3846 0.2989 0.1924];
Wwin2D_wiener = Wwin2D;
else
Wwin2D = kaiser(N1, beta) * kaiser(N1, beta)'; % Kaiser window used in the aggregation of the HT part
Wwin2D_wiener = kaiser(N1_wiener, beta_wiener) * kaiser(N1_wiener, beta_wiener)'; % Kaiser window used in the aggregation of the Wiener filt. part
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% If needed, read images, generate noise, or scale the images to the
%%%% [0,1] interval
%%%%
if (exist('yRGB') ~= 1) | (exist('zRGB') ~= 1)
yRGB = im2double(imread(image_name)); %% read a noise-free image
randn('seed', 0); %% generate seed
zRGB = yRGB + (sigma/255)*randn(size(yRGB)); %% create a noisy image
else % external images
image_name = 'External image';
% convert zRGB to double precision
zRGB = double(zRGB);
% convert yRGB to double precision
yRGB = double(yRGB);
% if zRGB's range is [0, 255], then convert to [0, 1]
if (max(zRGB(:)) > 10), % a naive check for intensity range
zRGB = zRGB / 255;
end
% if yRGB's range is [0, 255], then convert to [0, 1]
if (max(yRGB(:)) > 10), % a naive check for intensity range
yRGB = yRGB / 255;
end
end
if (size(zRGB,3) ~= 3) | (size(zRGB,4) ~= 1),
error('CBM3D accepts only input RGB images (i.e. matrices of size M x N x 3).');
end
% Check if the true image yRGB is a valid one; if not, then we cannot compute PSNR, etc.
yRGB_is_invalid_image = (length(size(zRGB)) ~= length(size(yRGB))) | (size(zRGB,1) ~= size(yRGB,1)) | (size(zRGB,2) ~= size(yRGB,2)) | (size(zRGB,3) ~= size(yRGB,3));
if (yRGB_is_invalid_image),
dump_output_information = 0;
end
[Xv, Xh, numSlices] = size(zRGB); %%% obtain image sizes
if numSlices ~= 3
fprintf('Error, an RGB color image is required!\n');
return;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Change colorspace, compute the l2-norms of the new color channels
%%%%
[zColSpace l2normLumChrom] = function_rgb2LumChrom(zRGB, colorspace);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Print image information to the screen
%%%%
if dump_output_information == 1,
fprintf(sprintf('Image: %s (%dx%dx%d), sigma: %.1f\n', image_name, Xv, Xh, numSlices, sigma));
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Step 1. Basic estimate by collaborative hard-thresholding and using
%%%% the grouping constraint on the chrominances.
%%%%
tic;
y_hat = bm3d_thr_color(zColSpace, hadper_trans_single_den, Nstep, N1, N2, lambda_thr2D,...
lambda_thr3D, tau_match*N1*N1/(255*255), (Ns-1)/2, sigma/255, thrToIncStep, single(Tfor), single(Tinv)', inverse_hadper_trans_single_den, single(thr_mask), 'unused arg', 'unused arg', l2normLumChrom, Wwin2D, smallLN, stepFS );
estimate_elapsed_time = toc;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Step 2. Final estimate by collaborative Wiener filtering and using
%%%% the grouping constraint on the chrominances.
%%%%
tic;
yRGB_est = bm3d_wiener_color(zColSpace, y_hat, hadper_trans_single_den, Nstep_wiener, N1_wiener, N2_wiener, ...
'unused_arg', tau_match_wiener*N1_wiener*N1_wiener/(255*255), (Ns_wiener-1)/2, sigma/255, 'unused arg', single(TforW), single(TinvW)', inverse_hadper_trans_single_den, 'unused arg', 'unused arg', l2normLumChrom, Wwin2D_wiener, smallLNW, stepFSW );
wiener_elapsed_time = toc;
yRGB_est = double(yRGB_est);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Convert back to RGB colorspace
%%%%
yRGB_est = function_LumChrom2rgb(yRGB_est, colorspace);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Calculate final estimate's PSNR and ISNR, print them, and show the
%%%% denoised image
%%%%
PSNR = 0; %% Remains 0 if the true image yRGB is not available
if (~yRGB_is_invalid_image), % then we assume yRGB is a valid image
PSNR = 10*log10(1/mean((yRGB(:)-yRGB_est(:)).^2));
end
if dump_output_information == 1,
fprintf(sprintf('FINAL ESTIMATE (total time: %.1f sec), PSNR: %.2f dB\n', ...
wiener_elapsed_time + estimate_elapsed_time, PSNR));
figure, imshow(min(max(zRGB,0),1)); title(sprintf('Noisy %s, PSNR: %.3f dB (sigma: %d)', ...
image_name(1:end-4), 10*log10(1/mean((yRGB(:)-zRGB(:)).^2)), sigma));
figure, imshow(min(max(yRGB_est,0),1)); title(sprintf('Denoised %s, PSNR: %.3f dB', ...
image_name(1:end-4), PSNR));
end
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Some auxiliary functions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Tforward, Tinverse] = getTransfMatrix (N, transform_type, dec_levels)
%
% Create forward and inverse transform matrices, which allow for perfect
% reconstruction. The forward transform matrix is normalized so that the
% l2-norm of each basis element is 1.
%
% [Tforward, Tinverse] = getTransfMatrix (N, transform_type, dec_levels)
%
% INPUTS:
%
% N --> Size of the transform (for wavelets, must be 2^K)
%
% transform_type --> 'dct', 'dst', 'hadamard', or anything that is
% listed by 'help wfilters' (bi-orthogonal wavelets)
% 'DCrand' -- an orthonormal transform with a DC and all
% the other basis elements of random nature
%
% dec_levels --> If a wavelet transform is generated, this is the
% desired decomposition level. Must be in the
% range [0, log2(N)-1], where "0" implies
% full decomposition.
%
% OUTPUTS:
%
% Tforward --> (N x N) Forward transform matrix
%
% Tinverse --> (N x N) Inverse transform matrix
%
if exist('dec_levels') ~= 1,
dec_levels = 0;
end
if N == 1,
Tforward = 1;
elseif strcmp(transform_type, 'hadamard') == 1,
Tforward = hadamard(N);
elseif (N == 8) & strcmp(transform_type, 'bior1.5')==1 % hardcoded transform so that the wavelet toolbox is not needed to generate it
Tforward = [ 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274;
0.219417649252501 0.449283757993216 0.449283757993216 0.219417649252501 -0.219417649252501 -0.449283757993216 -0.449283757993216 -0.219417649252501;
0.569359398342846 0.402347308162278 -0.402347308162278 -0.569359398342846 -0.083506045090284 0.083506045090284 -0.083506045090284 0.083506045090284;
-0.083506045090284 0.083506045090284 -0.083506045090284 0.083506045090284 0.569359398342846 0.402347308162278 -0.402347308162278 -0.569359398342846;
0.707106781186547 -0.707106781186547 0 0 0 0 0 0;
0 0 0.707106781186547 -0.707106781186547 0 0 0 0;
0 0 0 0 0.707106781186547 -0.707106781186547 0 0;
0 0 0 0 0 0 0.707106781186547 -0.707106781186547];
elseif (N == 8) & strcmp(transform_type, 'dct')==1 % hardcoded transform so that the signal processing toolbox is not needed to generate it
Tforward = [ 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274 0.353553390593274;
0.490392640201615 0.415734806151273 0.277785116509801 0.097545161008064 -0.097545161008064 -0.277785116509801 -0.415734806151273 -0.490392640201615;
0.461939766255643 0.191341716182545 -0.191341716182545 -0.461939766255643 -0.461939766255643 -0.191341716182545 0.191341716182545 0.461939766255643;
0.415734806151273 -0.097545161008064 -0.490392640201615 -0.277785116509801 0.277785116509801 0.490392640201615 0.097545161008064 -0.415734806151273;
0.353553390593274 -0.353553390593274 -0.353553390593274 0.353553390593274 0.353553390593274 -0.353553390593274 -0.353553390593274 0.353553390593274;
0.277785116509801 -0.490392640201615 0.097545161008064 0.415734806151273 -0.415734806151273 -0.097545161008064 0.490392640201615 -0.277785116509801;
0.191341716182545 -0.461939766255643 0.461939766255643 -0.191341716182545 -0.191341716182545 0.461939766255643 -0.461939766255643 0.191341716182545;
0.097545161008064 -0.277785116509801 0.415734806151273 -0.490392640201615 0.490392640201615 -0.415734806151273 0.277785116509801 -0.097545161008064];
elseif (N == 8) & strcmp(transform_type, 'dst')==1 % hardcoded transform so that the PDE toolbox is not needed to generate it
Tforward = [ 0.161229841765317 0.303012985114696 0.408248290463863 0.464242826880013 0.464242826880013 0.408248290463863 0.303012985114696 0.161229841765317;
0.303012985114696 0.464242826880013 0.408248290463863 0.161229841765317 -0.161229841765317 -0.408248290463863 -0.464242826880013 -0.303012985114696;
0.408248290463863 0.408248290463863 0 -0.408248290463863 -0.408248290463863 0 0.408248290463863 0.408248290463863;
0.464242826880013 0.161229841765317 -0.408248290463863 -0.303012985114696 0.303012985114696 0.408248290463863 -0.161229841765317 -0.464242826880013;
0.464242826880013 -0.161229841765317 -0.408248290463863 0.303012985114696 0.303012985114696 -0.408248290463863 -0.161229841765317 0.464242826880013;
0.408248290463863 -0.408248290463863 0 0.408248290463863 -0.408248290463863 0 0.408248290463863 -0.408248290463863;
0.303012985114696 -0.464242826880013 0.408248290463863 -0.161229841765317 -0.161229841765317 0.408248290463863 -0.464242826880013 0.303012985114696;
0.161229841765317 -0.303012985114696 0.408248290463863 -0.464242826880013 0.464242826880013 -0.408248290463863 0.303012985114696 -0.161229841765317];
elseif strcmp(transform_type, 'dct') == 1,
Tforward = dct(eye(N));
elseif strcmp(transform_type, 'dst') == 1,
Tforward = dst(eye(N));
elseif strcmp(transform_type, 'DCrand') == 1,
x = randn(N); x(1:end,1) = 1; [Q,R] = qr(x);
if (Q(1) < 0),
Q = -Q;
end;
Tforward = Q';
else %% a wavelet decomposition supported by 'wavedec'
%%% Set periodic boundary conditions, to preserve bi-orthogonality
dwtmode('per','nodisp');
Tforward = zeros(N,N);
for i = 1:N
Tforward(:,i)=wavedec(circshift([1 zeros(1,N-1)],[dec_levels i-1]), log2(N), transform_type); %% construct transform matrix
end
end
%%% Normalize the basis elements
Tforward = (Tforward' * diag(sqrt(1./sum(Tforward.^2,2))))';
%%% Compute the inverse transform matrix
Tinverse = inv(Tforward);
return;
function [y, A, l2normLumChrom]=function_rgb2LumChrom(xRGB, colormode)
% Forward color-space transformation ( inverse transformation is function_LumChrom2rgb.m )
%
% Alessandro Foi - Tampere University of Technology - 2005 - 2006 Public release v1.03 (March 2006)
% -----------------------------------------------------------------------------------------------------------------------------------------------
%
% SYNTAX:
%
% [y A l2normLumChrom] = function_rgb2LumChrom(xRGB, colormode);
%
% INPUTS:
% xRGB is RGB image with range [0 1]^3
%
% colormode = 'opp', 'yCbCr', 'pca', or a custom 3x3 matrix
%
% 'opp' Opponent color space ('opp' is equirange version)
% 'yCbCr' The standard yCbCr (e.g. for JPEG images)
% 'pca' Principal components (note that this transformation is renormalized to be equirange)
%
% OUTPUTS:
% y is color-transformed image (with range typically included in or equal to [0 1]^3, depending on the transformation matrix)
%
% l2normLumChrom (optional) l2-norm of the transformation (useful for noise std calculation)
% A transformation matrix (used necessarily if colormode='pca')
%
% NOTES: - If only two outputs are used, then the second output is l2normLumChrom, unless colormode='pca';
% - 'opp' is used by default if no colormode is specified.
%
%
% USAGE EXAMPLE FOR PCA TRANSFORMATION:
% %%%% -- forward color transformation --
% if colormode=='pca'
% [zLumChrom colormode] = function_rgb2LumChrom(zRGB,colormode); % 'colormode' is assigned a 3x3 transform matrix
% else
% zLumChrom = function_rgb2LumChrom(zRGB,colormode);
% end
%
% %%%% [ ... ] Some processing [ ... ]
%
% %%%% -- inverse color transformation --
% zRGB=function_LumChrom2rgb(zLumChrom,colormode);
%
if nargin==1
colormode='opp';
end
change_output=0;
if size(colormode)==[3 3]
A=colormode;
l2normLumChrom=sqrt(sum(A.^2,2));
else
if strcmp(colormode,'opp')
A=[1/3 1/3 1/3; 0.5 0 -0.5; 0.25 -0.5 0.25];
end
if strcmp(colormode,'yCbCr')
A=[0.299 0.587 0.114; -0.16873660714285 -0.33126339285715 0.5; 0.5 -0.4186875 -0.0813125];
end
if strcmp(colormode,'pca')
A=princomp(reshape(xRGB,[size(xRGB,1)*size(xRGB,2) 3]))';
A=A./repmat(sum(A.*(A>0),2)-sum(A.*(A<0),2),[1 3]); %% ranges are normalized to unitary length;
else
if nargout==2
change_output=1;
end
end
end
%%%% Make sure that each channel's intensity range is [0,1]
maxV = sum(A.*(A>0),2);
minV = sum(A.*(A<0),2);
yNormal = (reshape(xRGB,[size(xRGB,1)*size(xRGB,2) 3]) * A' - repmat(minV, [1 size(xRGB,1)*size(xRGB,2)])') * diag(1./(maxV-minV)); % put in range [0,1]
y = reshape(yNormal, [size(xRGB,1) size(xRGB,2) 3]);
%%%% The l2-norm of each of the 3 transform basis elements
l2normLumChrom = diag(1./(maxV-minV))*sqrt(sum(A.^2,2));
if change_output
A=l2normLumChrom;
end
return;
function yRGB=function_LumChrom2rgb(x,colormode)
% Inverse color-space transformation ( forward transformation is function_rgb2LumChrom.m )
%
% Alessandro Foi - Tampere University of Technology - 2005 - 2006 Public release v1.03 (March 2006)
% -----------------------------------------------------------------------------------------------------------------------------------------------
%
% SYNTAX:
%
% yRGB = function_LumChrom2rgb(x,colormode);
%
% INPUTS:
% x is color-transformed image (with range typically included in or equal to [0 1]^3, depending on the transformation matrix)
%
% colormode = 'opp', 'yCbCr', or a custom 3x3 matrix (e.g. provided by the forward transform when 'pca' is selected)
%
% 'opp' opponent color space ('opp' is equirange version)
% 'yCbCr' standard yCbCr (e.g. for JPEG images)
%
% OUTPUTS:
% x is RGB image (with range [0 1]^3)
%
%
% NOTE: 'opp' is used by default if no colormode is specified
%
if nargin==1
colormode='opp';
end
if size(colormode)==[3 3]
A=colormode;
B=inv(A);
else
if strcmp(colormode,'opp')
A =[1/3 1/3 1/3; 0.5 0 -0.5; 0.25 -0.5 0.25];
B =[1 1 2/3;1 0 -4/3;1 -1 2/3];
end
if strcmp(colormode,'yCbCr')
A=[0.299 0.587 0.114; -0.16873660714285 -0.33126339285715 0.5; 0.5 -0.4186875 -0.0813125];
B=inv(A);
end
end
%%%% Make sure that each channel's intensity range is [0,1]
maxV = sum(A.*(A>0),2);
minV = sum(A.*(A<0),2);
xNormal = reshape(x,[size(x,1)*size(x,2) 3]) * diag(maxV-minV) + repmat(minV, [1 size(x,1)*size(x,2)])'; % put in range [0,1]
yRGB = reshape(xNormal * B', [ size(x,1) size(x,2) 3]);
return;