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
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
|
/*
* Copyright (c) 2016, Alliance for Open Media. All rights reserved
*
* This source code is subject to the terms of the BSD 2 Clause License and
* the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
* was not distributed with this source code in the LICENSE file, you can
* obtain it at www.aomedia.org/license/software. If the Alliance for Open
* Media Patent License 1.0 was not distributed with this source code in the
* PATENTS file, you can obtain it at www.aomedia.org/license/patent.
*/
// Dense Inverse Search flow algorithm
// Paper: https://arxiv.org/abs/1603.03590
#include <assert.h>
#include <math.h>
#include "aom_dsp/aom_dsp_common.h"
#include "aom_dsp/flow_estimation/corner_detect.h"
#include "aom_dsp/flow_estimation/disflow.h"
#include "aom_dsp/flow_estimation/ransac.h"
#include "aom_dsp/pyramid.h"
#include "aom_mem/aom_mem.h"
#include "config/aom_dsp_rtcd.h"
// Amount to downsample the flow field by.
// eg. DOWNSAMPLE_SHIFT = 2 (DOWNSAMPLE_FACTOR == 4) means we calculate
// one flow point for each 4x4 pixel region of the frame
// Must be a power of 2
#define DOWNSAMPLE_SHIFT 3
#define DOWNSAMPLE_FACTOR (1 << DOWNSAMPLE_SHIFT)
// Filters used when upscaling the flow field from one pyramid level
// to another. See upscale_flow_component for details on kernel selection
#define FLOW_UPSCALE_TAPS 4
// Number of outermost flow field entries (on each edge) which can't be
// computed, because the patch they correspond to extends outside of the
// frame
// The border is (DISFLOW_PATCH_SIZE >> 1) pixels, which is
// (DISFLOW_PATCH_SIZE >> 1) >> DOWNSAMPLE_SHIFT many flow field entries
#define FLOW_BORDER_INNER ((DISFLOW_PATCH_SIZE >> 1) >> DOWNSAMPLE_SHIFT)
// Number of extra padding entries on each side of the flow field.
// These samples are added so that we do not need to apply clamping when
// interpolating or upsampling the flow field
#define FLOW_BORDER_OUTER (FLOW_UPSCALE_TAPS / 2)
// When downsampling the flow field, each flow field entry covers a square
// region of pixels in the image pyramid. This value is equal to the position
// of the center of that region, as an offset from the top/left edge.
//
// Note: Using ((DOWNSAMPLE_FACTOR - 1) / 2) is equivalent to the more
// natural expression ((DOWNSAMPLE_FACTOR / 2) - 1),
// unless DOWNSAMPLE_FACTOR == 1 (ie, no downsampling), in which case
// this gives the correct offset of 0 instead of -1.
#define UPSAMPLE_CENTER_OFFSET ((DOWNSAMPLE_FACTOR - 1) / 2)
static double flow_upscale_filter[2][FLOW_UPSCALE_TAPS] = {
// Cubic interpolation kernels for phase=0.75 and phase=0.25, respectively
{ -3 / 128., 29 / 128., 111 / 128., -9 / 128. },
{ -9 / 128., 111 / 128., 29 / 128., -3 / 128. }
};
static INLINE void get_cubic_kernel_dbl(double x, double kernel[4]) {
// Check that the fractional position is in range.
//
// Note: x is calculated from (eg.) `u_frac = u - floor(u)`.
// Mathematically, this implies that 0 <= x < 1. However, in practice it is
// possible to have x == 1 due to floating point rounding. This is fine,
// and we still interpolate correctly if we allow x = 1.
assert(0 <= x && x <= 1);
double x2 = x * x;
double x3 = x2 * x;
kernel[0] = -0.5 * x + x2 - 0.5 * x3;
kernel[1] = 1.0 - 2.5 * x2 + 1.5 * x3;
kernel[2] = 0.5 * x + 2.0 * x2 - 1.5 * x3;
kernel[3] = -0.5 * x2 + 0.5 * x3;
}
static INLINE void get_cubic_kernel_int(double x, int kernel[4]) {
double kernel_dbl[4];
get_cubic_kernel_dbl(x, kernel_dbl);
kernel[0] = (int)rint(kernel_dbl[0] * (1 << DISFLOW_INTERP_BITS));
kernel[1] = (int)rint(kernel_dbl[1] * (1 << DISFLOW_INTERP_BITS));
kernel[2] = (int)rint(kernel_dbl[2] * (1 << DISFLOW_INTERP_BITS));
kernel[3] = (int)rint(kernel_dbl[3] * (1 << DISFLOW_INTERP_BITS));
}
static INLINE double get_cubic_value_dbl(const double *p,
const double kernel[4]) {
return kernel[0] * p[0] + kernel[1] * p[1] + kernel[2] * p[2] +
kernel[3] * p[3];
}
static INLINE int get_cubic_value_int(const int *p, const int kernel[4]) {
return kernel[0] * p[0] + kernel[1] * p[1] + kernel[2] * p[2] +
kernel[3] * p[3];
}
static INLINE double bicubic_interp_one(const double *arr, int stride,
const double h_kernel[4],
const double v_kernel[4]) {
double tmp[1 * 4];
// Horizontal convolution
for (int i = -1; i < 3; ++i) {
tmp[i + 1] = get_cubic_value_dbl(&arr[i * stride - 1], h_kernel);
}
// Vertical convolution
return get_cubic_value_dbl(tmp, v_kernel);
}
static int determine_disflow_correspondence(const ImagePyramid *src_pyr,
const ImagePyramid *ref_pyr,
CornerList *corners,
const FlowField *flow,
Correspondence *correspondences) {
const int width = flow->width;
const int height = flow->height;
const int stride = flow->stride;
int num_correspondences = 0;
for (int i = 0; i < corners->num_corners; ++i) {
const int x0 = corners->corners[2 * i];
const int y0 = corners->corners[2 * i + 1];
// Offset points, to compensate for the fact that (say) a flow field entry
// at horizontal index i, is nominally associated with the pixel at
// horizontal coordinate (i << DOWNSAMPLE_FACTOR) + UPSAMPLE_CENTER_OFFSET
// This offset must be applied before we split the coordinate into integer
// and fractional parts, in order for the interpolation to be correct.
const int x = x0 - UPSAMPLE_CENTER_OFFSET;
const int y = y0 - UPSAMPLE_CENTER_OFFSET;
// Split the pixel coordinates into integer flow field coordinates and
// an offset for interpolation
const int flow_x = x >> DOWNSAMPLE_SHIFT;
const double flow_sub_x =
(x & (DOWNSAMPLE_FACTOR - 1)) / (double)DOWNSAMPLE_FACTOR;
const int flow_y = y >> DOWNSAMPLE_SHIFT;
const double flow_sub_y =
(y & (DOWNSAMPLE_FACTOR - 1)) / (double)DOWNSAMPLE_FACTOR;
// Exclude points which would sample from the outer border of the flow
// field, as this would give lower-quality results.
//
// Note: As we never read from the border region at pyramid level 0, we
// can skip filling it in. If the conditions here are removed, or any
// other logic is added which reads from this border region, then
// compute_flow_field() will need to be modified to call
// fill_flow_field_borders() at pyramid level 0 to set up the correct
// border data.
if (flow_x < 1 || (flow_x + 2) >= width) continue;
if (flow_y < 1 || (flow_y + 2) >= height) continue;
double h_kernel[4];
double v_kernel[4];
get_cubic_kernel_dbl(flow_sub_x, h_kernel);
get_cubic_kernel_dbl(flow_sub_y, v_kernel);
double flow_u = bicubic_interp_one(&flow->u[flow_y * stride + flow_x],
stride, h_kernel, v_kernel);
double flow_v = bicubic_interp_one(&flow->v[flow_y * stride + flow_x],
stride, h_kernel, v_kernel);
// Refine the interpolated flow vector one last time
const int patch_tl_x = x0 - DISFLOW_PATCH_CENTER;
const int patch_tl_y = y0 - DISFLOW_PATCH_CENTER;
aom_compute_flow_at_point(
src_pyr->layers[0].buffer, ref_pyr->layers[0].buffer, patch_tl_x,
patch_tl_y, src_pyr->layers[0].width, src_pyr->layers[0].height,
src_pyr->layers[0].stride, &flow_u, &flow_v);
// Use original points (without offsets) when filling in correspondence
// array
correspondences[num_correspondences].x = x0;
correspondences[num_correspondences].y = y0;
correspondences[num_correspondences].rx = x0 + flow_u;
correspondences[num_correspondences].ry = y0 + flow_v;
num_correspondences++;
}
return num_correspondences;
}
// Compare two regions of width x height pixels, one rooted at position
// (x, y) in src and the other at (x + u, y + v) in ref.
// This function returns the sum of squared pixel differences between
// the two regions.
static INLINE void compute_flow_vector(const uint8_t *src, const uint8_t *ref,
int width, int height, int stride, int x,
int y, double u, double v,
const int16_t *dx, const int16_t *dy,
int *b) {
memset(b, 0, 2 * sizeof(*b));
// Split offset into integer and fractional parts, and compute cubic
// interpolation kernels
const int u_int = (int)floor(u);
const int v_int = (int)floor(v);
const double u_frac = u - floor(u);
const double v_frac = v - floor(v);
int h_kernel[4];
int v_kernel[4];
get_cubic_kernel_int(u_frac, h_kernel);
get_cubic_kernel_int(v_frac, v_kernel);
// Storage for intermediate values between the two convolution directions
int tmp_[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 3)];
int *tmp = tmp_ + DISFLOW_PATCH_SIZE; // Offset by one row
// Clamp coordinates so that all pixels we fetch will remain within the
// allocated border region, but allow them to go far enough out that
// the border pixels' values do not change.
// Since we are calculating an 8x8 block, the bottom-right pixel
// in the block has coordinates (x0 + 7, y0 + 7). Then, the cubic
// interpolation has 4 taps, meaning that the output of pixel
// (x_w, y_w) depends on the pixels in the range
// ([x_w - 1, x_w + 2], [y_w - 1, y_w + 2]).
//
// Thus the most extreme coordinates which will be fetched are
// (x0 - 1, y0 - 1) and (x0 + 9, y0 + 9).
const int x0 = clamp(x + u_int, -9, width);
const int y0 = clamp(y + v_int, -9, height);
// Horizontal convolution
for (int i = -1; i < DISFLOW_PATCH_SIZE + 2; ++i) {
const int y_w = y0 + i;
for (int j = 0; j < DISFLOW_PATCH_SIZE; ++j) {
const int x_w = x0 + j;
int arr[4];
arr[0] = (int)ref[y_w * stride + (x_w - 1)];
arr[1] = (int)ref[y_w * stride + (x_w + 0)];
arr[2] = (int)ref[y_w * stride + (x_w + 1)];
arr[3] = (int)ref[y_w * stride + (x_w + 2)];
// Apply kernel and round, keeping 6 extra bits of precision.
//
// 6 is the maximum allowable number of extra bits which will avoid
// the intermediate values overflowing an int16_t. The most extreme
// intermediate value occurs when:
// * The input pixels are [0, 255, 255, 0]
// * u_frac = 0.5
// In this case, the un-scaled output is 255 * 1.125 = 286.875.
// As an integer with 6 fractional bits, that is 18360, which fits
// in an int16_t. But with 7 fractional bits it would be 36720,
// which is too large.
tmp[i * DISFLOW_PATCH_SIZE + j] = ROUND_POWER_OF_TWO(
get_cubic_value_int(arr, h_kernel), DISFLOW_INTERP_BITS - 6);
}
}
// Vertical convolution
for (int i = 0; i < DISFLOW_PATCH_SIZE; ++i) {
for (int j = 0; j < DISFLOW_PATCH_SIZE; ++j) {
const int *p = &tmp[i * DISFLOW_PATCH_SIZE + j];
const int arr[4] = { p[-DISFLOW_PATCH_SIZE], p[0], p[DISFLOW_PATCH_SIZE],
p[2 * DISFLOW_PATCH_SIZE] };
const int result = get_cubic_value_int(arr, v_kernel);
// Apply kernel and round.
// This time, we have to round off the 6 extra bits which were kept
// earlier, but we also want to keep DISFLOW_DERIV_SCALE_LOG2 extra bits
// of precision to match the scale of the dx and dy arrays.
const int round_bits = DISFLOW_INTERP_BITS + 6 - DISFLOW_DERIV_SCALE_LOG2;
const int warped = ROUND_POWER_OF_TWO(result, round_bits);
const int src_px = src[(x + j) + (y + i) * stride] << 3;
const int dt = warped - src_px;
b[0] += dx[i * DISFLOW_PATCH_SIZE + j] * dt;
b[1] += dy[i * DISFLOW_PATCH_SIZE + j] * dt;
}
}
}
static INLINE void sobel_filter(const uint8_t *src, int src_stride,
int16_t *dst, int dst_stride, int dir) {
int16_t tmp_[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 2)];
int16_t *tmp = tmp_ + DISFLOW_PATCH_SIZE;
// Sobel filter kernel
// This must have an overall scale factor equal to DISFLOW_DERIV_SCALE,
// in order to produce correctly scaled outputs.
// To work out the scale factor, we multiply two factors:
//
// * For the derivative filter (sobel_a), comparing our filter
// image[x - 1] - image[x + 1]
// to the standard form
// d/dx image[x] = image[x+1] - image[x]
// tells us that we're actually calculating -2 * d/dx image[2]
//
// * For the smoothing filter (sobel_b), all coefficients are positive
// so the scale factor is just the sum of the coefficients
//
// Thus we need to make sure that DISFLOW_DERIV_SCALE = 2 * sum(sobel_b)
// (and take care of the - sign from sobel_a elsewhere)
static const int16_t sobel_a[3] = { 1, 0, -1 };
static const int16_t sobel_b[3] = { 1, 2, 1 };
const int taps = 3;
// horizontal filter
const int16_t *h_kernel = dir ? sobel_a : sobel_b;
for (int y = -1; y < DISFLOW_PATCH_SIZE + 1; ++y) {
for (int x = 0; x < DISFLOW_PATCH_SIZE; ++x) {
int sum = 0;
for (int k = 0; k < taps; ++k) {
sum += h_kernel[k] * src[y * src_stride + (x + k - 1)];
}
tmp[y * DISFLOW_PATCH_SIZE + x] = sum;
}
}
// vertical filter
const int16_t *v_kernel = dir ? sobel_b : sobel_a;
for (int y = 0; y < DISFLOW_PATCH_SIZE; ++y) {
for (int x = 0; x < DISFLOW_PATCH_SIZE; ++x) {
int sum = 0;
for (int k = 0; k < taps; ++k) {
sum += v_kernel[k] * tmp[(y + k - 1) * DISFLOW_PATCH_SIZE + x];
}
dst[y * dst_stride + x] = sum;
}
}
}
// Computes the components of the system of equations used to solve for
// a flow vector.
//
// The flow equations are a least-squares system, derived as follows:
//
// For each pixel in the patch, we calculate the current error `dt`,
// and the x and y gradients `dx` and `dy` of the source patch.
// This means that, to first order, the squared error for this pixel is
//
// (dt + u * dx + v * dy)^2
//
// where (u, v) are the incremental changes to the flow vector.
//
// We then want to find the values of u and v which minimize the sum
// of the squared error across all pixels. Conveniently, this fits exactly
// into the form of a least squares problem, with one equation
//
// u * dx + v * dy = -dt
//
// for each pixel.
//
// Summing across all pixels in a square window of size DISFLOW_PATCH_SIZE,
// and absorbing the - sign elsewhere, this results in the least squares system
//
// M = |sum(dx * dx) sum(dx * dy)|
// |sum(dx * dy) sum(dy * dy)|
//
// b = |sum(dx * dt)|
// |sum(dy * dt)|
static INLINE void compute_flow_matrix(const int16_t *dx, int dx_stride,
const int16_t *dy, int dy_stride,
double *M) {
int tmp[4] = { 0 };
for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
for (int j = 0; j < DISFLOW_PATCH_SIZE; j++) {
tmp[0] += dx[i * dx_stride + j] * dx[i * dx_stride + j];
tmp[1] += dx[i * dx_stride + j] * dy[i * dy_stride + j];
// Don't compute tmp[2], as it should be equal to tmp[1]
tmp[3] += dy[i * dy_stride + j] * dy[i * dy_stride + j];
}
}
// Apply regularization
// We follow the standard regularization method of adding `k * I` before
// inverting. This ensures that the matrix will be invertible.
//
// Setting the regularization strength k to 1 seems to work well here, as
// typical values coming from the other equations are very large (1e5 to
// 1e6, with an upper limit of around 6e7, at the time of writing).
// It also preserves the property that all matrix values are whole numbers,
// which is convenient for integerized SIMD implementation.
tmp[0] += 1;
tmp[3] += 1;
tmp[2] = tmp[1];
M[0] = (double)tmp[0];
M[1] = (double)tmp[1];
M[2] = (double)tmp[2];
M[3] = (double)tmp[3];
}
// Try to invert the matrix M
// Note: Due to the nature of how a least-squares matrix is constructed, all of
// the eigenvalues will be >= 0, and therefore det M >= 0 as well.
// The regularization term `+ k * I` further ensures that det M >= k^2.
// As mentioned in compute_flow_matrix(), here we use k = 1, so det M >= 1.
// So we don't have to worry about non-invertible matrices here.
static INLINE void invert_2x2(const double *M, double *M_inv) {
double det = (M[0] * M[3]) - (M[1] * M[2]);
assert(det >= 1);
const double det_inv = 1 / det;
M_inv[0] = M[3] * det_inv;
M_inv[1] = -M[1] * det_inv;
M_inv[2] = -M[2] * det_inv;
M_inv[3] = M[0] * det_inv;
}
void aom_compute_flow_at_point_c(const uint8_t *src, const uint8_t *ref, int x,
int y, int width, int height, int stride,
double *u, double *v) {
double M[4];
double M_inv[4];
int b[2];
int16_t dx[DISFLOW_PATCH_SIZE * DISFLOW_PATCH_SIZE];
int16_t dy[DISFLOW_PATCH_SIZE * DISFLOW_PATCH_SIZE];
// Compute gradients within this patch
const uint8_t *src_patch = &src[y * stride + x];
sobel_filter(src_patch, stride, dx, DISFLOW_PATCH_SIZE, 1);
sobel_filter(src_patch, stride, dy, DISFLOW_PATCH_SIZE, 0);
compute_flow_matrix(dx, DISFLOW_PATCH_SIZE, dy, DISFLOW_PATCH_SIZE, M);
invert_2x2(M, M_inv);
for (int itr = 0; itr < DISFLOW_MAX_ITR; itr++) {
compute_flow_vector(src, ref, width, height, stride, x, y, *u, *v, dx, dy,
b);
// Solve flow equations to find a better estimate for the flow vector
// at this point
const double step_u = M_inv[0] * b[0] + M_inv[1] * b[1];
const double step_v = M_inv[2] * b[0] + M_inv[3] * b[1];
*u += fclamp(step_u * DISFLOW_STEP_SIZE, -2, 2);
*v += fclamp(step_v * DISFLOW_STEP_SIZE, -2, 2);
if (fabs(step_u) + fabs(step_v) < DISFLOW_STEP_SIZE_THRESOLD) {
// Stop iteration when we're close to convergence
break;
}
}
}
static void fill_flow_field_borders(double *flow, int width, int height,
int stride) {
// Calculate the bounds of the rectangle which was filled in by
// compute_flow_field() before calling this function.
// These indices are inclusive on both ends.
const int left_index = FLOW_BORDER_INNER;
const int right_index = (width - FLOW_BORDER_INNER - 1);
const int top_index = FLOW_BORDER_INNER;
const int bottom_index = (height - FLOW_BORDER_INNER - 1);
// Left area
for (int i = top_index; i <= bottom_index; i += 1) {
double *row = flow + i * stride;
const double left = row[left_index];
for (int j = -FLOW_BORDER_OUTER; j < left_index; j++) {
row[j] = left;
}
}
// Right area
for (int i = top_index; i <= bottom_index; i += 1) {
double *row = flow + i * stride;
const double right = row[right_index];
for (int j = right_index + 1; j < width + FLOW_BORDER_OUTER; j++) {
row[j] = right;
}
}
// Top area
const double *top_row = flow + top_index * stride - FLOW_BORDER_OUTER;
for (int i = -FLOW_BORDER_OUTER; i < top_index; i++) {
double *row = flow + i * stride - FLOW_BORDER_OUTER;
size_t length = width + 2 * FLOW_BORDER_OUTER;
memcpy(row, top_row, length * sizeof(*row));
}
// Bottom area
const double *bottom_row = flow + bottom_index * stride - FLOW_BORDER_OUTER;
for (int i = bottom_index + 1; i < height + FLOW_BORDER_OUTER; i++) {
double *row = flow + i * stride - FLOW_BORDER_OUTER;
size_t length = width + 2 * FLOW_BORDER_OUTER;
memcpy(row, bottom_row, length * sizeof(*row));
}
}
// Upscale one component of the flow field, from a size of
// cur_width x cur_height to a size of (2*cur_width) x (2*cur_height), storing
// the result back into the same buffer. This function also scales the flow
// vector by 2, so that when we move to the next pyramid level down, the implied
// motion vector is the same.
//
// The temporary buffer tmpbuf must be large enough to hold an intermediate
// array of size stride * cur_height, *plus* FLOW_BORDER_OUTER rows above and
// below. In other words, indices from -FLOW_BORDER_OUTER * stride to
// (cur_height + FLOW_BORDER_OUTER) * stride - 1 must be valid.
//
// Note that the same stride is used for u before and after upscaling
// and for the temporary buffer, for simplicity.
//
// A note on phasing:
//
// The flow fields at two adjacent pyramid levels are offset from each other,
// and we need to account for this in the construction of the interpolation
// kernels.
//
// Consider an 8x8 pixel patch at pyramid level n. This is split into four
// patches at pyramid level n-1. Bringing these patches back up to pyramid level
// n, each sub-patch covers 4x4 pixels, and between them they cover the same
// 8x8 region.
//
// Therefore, at pyramid level n, two adjacent patches look like this:
//
// + - - - - - - - + - - - - - - - +
// | | |
// | x x | x x |
// | | |
// | # | # |
// | | |
// | x x | x x |
// | | |
// + - - - - - - - + - - - - - - - +
//
// where # marks the center of a patch at pyramid level n (the input to this
// function), and x marks the center of a patch at pyramid level n-1 (the output
// of this function).
//
// By counting pixels (marked by +, -, and |), we can see that the flow vectors
// at pyramid level n-1 are offset relative to the flow vectors at pyramid
// level n, by 1/4 of the larger (input) patch size. Therefore, our
// interpolation kernels need to have phases of 0.25 and 0.75.
//
// In addition, in order to handle the frame edges correctly, we need to
// generate one output vector to the left and one to the right of each input
// vector, even though these must be interpolated using different source points.
static void upscale_flow_component(double *flow, int cur_width, int cur_height,
int stride, double *tmpbuf) {
const int half_len = FLOW_UPSCALE_TAPS / 2;
// Check that the outer border is large enough to avoid needing to clamp
// the source locations
assert(half_len <= FLOW_BORDER_OUTER);
// Horizontal upscale and multiply by 2
for (int i = 0; i < cur_height; i++) {
for (int j = 0; j < cur_width; j++) {
double left = 0;
for (int k = -half_len; k < half_len; k++) {
left +=
flow[i * stride + (j + k)] * flow_upscale_filter[0][k + half_len];
}
tmpbuf[i * stride + (2 * j + 0)] = 2.0 * left;
// Right output pixel is 0.25 units to the right of the input pixel
double right = 0;
for (int k = -(half_len - 1); k < (half_len + 1); k++) {
right += flow[i * stride + (j + k)] *
flow_upscale_filter[1][k + (half_len - 1)];
}
tmpbuf[i * stride + (2 * j + 1)] = 2.0 * right;
}
}
// Fill in top and bottom borders of tmpbuf
const double *top_row = &tmpbuf[0];
for (int i = -FLOW_BORDER_OUTER; i < 0; i++) {
double *row = &tmpbuf[i * stride];
memcpy(row, top_row, 2 * cur_width * sizeof(*row));
}
const double *bottom_row = &tmpbuf[(cur_height - 1) * stride];
for (int i = cur_height; i < cur_height + FLOW_BORDER_OUTER; i++) {
double *row = &tmpbuf[i * stride];
memcpy(row, bottom_row, 2 * cur_width * sizeof(*row));
}
// Vertical upscale
int upscaled_width = cur_width * 2;
for (int i = 0; i < cur_height; i++) {
for (int j = 0; j < upscaled_width; j++) {
double top = 0;
for (int k = -half_len; k < half_len; k++) {
top +=
tmpbuf[(i + k) * stride + j] * flow_upscale_filter[0][k + half_len];
}
flow[(2 * i) * stride + j] = top;
double bottom = 0;
for (int k = -(half_len - 1); k < (half_len + 1); k++) {
bottom += tmpbuf[(i + k) * stride + j] *
flow_upscale_filter[1][k + (half_len - 1)];
}
flow[(2 * i + 1) * stride + j] = bottom;
}
}
}
// make sure flow_u and flow_v start at 0
static bool compute_flow_field(const ImagePyramid *src_pyr,
const ImagePyramid *ref_pyr, FlowField *flow) {
bool mem_status = true;
assert(src_pyr->n_levels == ref_pyr->n_levels);
double *flow_u = flow->u;
double *flow_v = flow->v;
double *tmpbuf0;
double *tmpbuf;
if (src_pyr->n_levels < 2) {
// tmpbuf not needed
tmpbuf0 = NULL;
tmpbuf = NULL;
} else {
// This line must match the calculation of cur_flow_height below
const int layer1_height = src_pyr->layers[1].height >> DOWNSAMPLE_SHIFT;
const size_t tmpbuf_size =
(layer1_height + 2 * FLOW_BORDER_OUTER) * flow->stride;
tmpbuf0 = aom_malloc(tmpbuf_size * sizeof(*tmpbuf0));
if (!tmpbuf0) {
mem_status = false;
goto free_tmpbuf;
}
tmpbuf = tmpbuf0 + FLOW_BORDER_OUTER * flow->stride;
}
// Compute flow field from coarsest to finest level of the pyramid
//
// Note: We stop after refining pyramid level 1 and interpolating it to
// generate an initial flow field at level 0. We do *not* refine the dense
// flow field at level 0. Instead, we wait until we have generated
// correspondences by interpolating this flow field, and then refine the
// correspondences themselves. This is both faster and gives better output
// compared to refining the flow field at level 0 and then interpolating.
for (int level = src_pyr->n_levels - 1; level >= 1; --level) {
const PyramidLayer *cur_layer = &src_pyr->layers[level];
const int cur_width = cur_layer->width;
const int cur_height = cur_layer->height;
const int cur_stride = cur_layer->stride;
const uint8_t *src_buffer = cur_layer->buffer;
const uint8_t *ref_buffer = ref_pyr->layers[level].buffer;
const int cur_flow_width = cur_width >> DOWNSAMPLE_SHIFT;
const int cur_flow_height = cur_height >> DOWNSAMPLE_SHIFT;
const int cur_flow_stride = flow->stride;
for (int i = FLOW_BORDER_INNER; i < cur_flow_height - FLOW_BORDER_INNER;
i += 1) {
for (int j = FLOW_BORDER_INNER; j < cur_flow_width - FLOW_BORDER_INNER;
j += 1) {
const int flow_field_idx = i * cur_flow_stride + j;
// Calculate the position of a patch of size DISFLOW_PATCH_SIZE pixels,
// which is centered on the region covered by this flow field entry
const int patch_center_x =
(j << DOWNSAMPLE_SHIFT) + UPSAMPLE_CENTER_OFFSET; // In pixels
const int patch_center_y =
(i << DOWNSAMPLE_SHIFT) + UPSAMPLE_CENTER_OFFSET; // In pixels
const int patch_tl_x = patch_center_x - DISFLOW_PATCH_CENTER;
const int patch_tl_y = patch_center_y - DISFLOW_PATCH_CENTER;
assert(patch_tl_x >= 0);
assert(patch_tl_y >= 0);
aom_compute_flow_at_point(src_buffer, ref_buffer, patch_tl_x,
patch_tl_y, cur_width, cur_height, cur_stride,
&flow_u[flow_field_idx],
&flow_v[flow_field_idx]);
}
}
// Fill in the areas which we haven't explicitly computed, with copies
// of the outermost values which we did compute
fill_flow_field_borders(flow_u, cur_flow_width, cur_flow_height,
cur_flow_stride);
fill_flow_field_borders(flow_v, cur_flow_width, cur_flow_height,
cur_flow_stride);
if (level > 0) {
const int upscale_flow_width = cur_flow_width << 1;
const int upscale_flow_height = cur_flow_height << 1;
const int upscale_stride = flow->stride;
upscale_flow_component(flow_u, cur_flow_width, cur_flow_height,
cur_flow_stride, tmpbuf);
upscale_flow_component(flow_v, cur_flow_width, cur_flow_height,
cur_flow_stride, tmpbuf);
// If we didn't fill in the rightmost column or bottommost row during
// upsampling (in order to keep the ratio to exactly 2), fill them
// in here by copying the next closest column/row
const PyramidLayer *next_layer = &src_pyr->layers[level - 1];
const int next_flow_width = next_layer->width >> DOWNSAMPLE_SHIFT;
const int next_flow_height = next_layer->height >> DOWNSAMPLE_SHIFT;
// Rightmost column
if (next_flow_width > upscale_flow_width) {
assert(next_flow_width == upscale_flow_width + 1);
for (int i = 0; i < upscale_flow_height; i++) {
const int index = i * upscale_stride + upscale_flow_width;
flow_u[index] = flow_u[index - 1];
flow_v[index] = flow_v[index - 1];
}
}
// Bottommost row
if (next_flow_height > upscale_flow_height) {
assert(next_flow_height == upscale_flow_height + 1);
for (int j = 0; j < next_flow_width; j++) {
const int index = upscale_flow_height * upscale_stride + j;
flow_u[index] = flow_u[index - upscale_stride];
flow_v[index] = flow_v[index - upscale_stride];
}
}
}
}
free_tmpbuf:
aom_free(tmpbuf0);
return mem_status;
}
static FlowField *alloc_flow_field(int frame_width, int frame_height) {
FlowField *flow = (FlowField *)aom_malloc(sizeof(FlowField));
if (flow == NULL) return NULL;
// Calculate the size of the bottom (largest) layer of the flow pyramid
flow->width = frame_width >> DOWNSAMPLE_SHIFT;
flow->height = frame_height >> DOWNSAMPLE_SHIFT;
flow->stride = flow->width + 2 * FLOW_BORDER_OUTER;
const size_t flow_size =
flow->stride * (size_t)(flow->height + 2 * FLOW_BORDER_OUTER);
flow->buf0 = aom_calloc(2 * flow_size, sizeof(*flow->buf0));
if (!flow->buf0) {
aom_free(flow);
return NULL;
}
flow->u = flow->buf0 + FLOW_BORDER_OUTER * flow->stride + FLOW_BORDER_OUTER;
flow->v = flow->u + flow_size;
return flow;
}
static void free_flow_field(FlowField *flow) {
aom_free(flow->buf0);
aom_free(flow);
}
// Compute flow field between `src` and `ref`, and then use that flow to
// compute a global motion model relating the two frames.
//
// Following the convention in flow_estimation.h, the flow vectors are computed
// at fixed points in `src` and point to the corresponding locations in `ref`,
// regardless of the temporal ordering of the frames.
bool av1_compute_global_motion_disflow(TransformationType type,
YV12_BUFFER_CONFIG *src,
YV12_BUFFER_CONFIG *ref, int bit_depth,
MotionModel *motion_models,
int num_motion_models,
bool *mem_alloc_failed) {
// Precompute information we will need about each frame
ImagePyramid *src_pyramid = src->y_pyramid;
CornerList *src_corners = src->corners;
ImagePyramid *ref_pyramid = ref->y_pyramid;
if (!aom_compute_pyramid(src, bit_depth, src_pyramid)) {
*mem_alloc_failed = true;
return false;
}
if (!av1_compute_corner_list(src_pyramid, src_corners)) {
*mem_alloc_failed = true;
return false;
}
if (!aom_compute_pyramid(ref, bit_depth, ref_pyramid)) {
*mem_alloc_failed = true;
return false;
}
const int src_width = src_pyramid->layers[0].width;
const int src_height = src_pyramid->layers[0].height;
assert(ref_pyramid->layers[0].width == src_width);
assert(ref_pyramid->layers[0].height == src_height);
FlowField *flow = alloc_flow_field(src_width, src_height);
if (!flow) {
*mem_alloc_failed = true;
return false;
}
if (!compute_flow_field(src_pyramid, ref_pyramid, flow)) {
*mem_alloc_failed = true;
free_flow_field(flow);
return false;
}
// find correspondences between the two images using the flow field
Correspondence *correspondences =
aom_malloc(src_corners->num_corners * sizeof(*correspondences));
if (!correspondences) {
*mem_alloc_failed = true;
free_flow_field(flow);
return false;
}
const int num_correspondences = determine_disflow_correspondence(
src_pyramid, ref_pyramid, src_corners, flow, correspondences);
bool result = ransac(correspondences, num_correspondences, type,
motion_models, num_motion_models, mem_alloc_failed);
aom_free(correspondences);
free_flow_field(flow);
return result;
}
|