warped_motion.c 41 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
/*
 *  Copyright (c) 2015 The WebM project authors. All Rights Reserved.
 *
 *  Use of this source code is governed by a BSD-style license
 *  that can be found in the LICENSE file in the root of the source
 *  tree. An additional intellectual property rights grant can be
 *  found  in the file PATENTS.  All contributing project authors may
 *  be found in the AUTHORS file in the root of the source tree.
 */

#include <stdio.h>
#include <stdlib.h>
#include <memory.h>
#include <math.h>
#include <assert.h>

17
#include "av1/common/warped_motion.h"
18

19
20
#define ERRORADV_CLAMP  128

21
static ProjectPointsFunc get_project_points_type(TransformationType type) {
22
  switch (type) {
23
24
25
26
    case HOMOGRAPHY: return project_points_homography;
    case AFFINE: return project_points_affine;
    case ROTZOOM: return project_points_rotzoom;
    case TRANSLATION: return project_points_translation;
clang-format's avatar
clang-format committed
27
    default: assert(0); return NULL;
28
29
30
  }
}

31
void project_points_translation(int32_t *mat, int *points, int *proj,
32
33
34
                                const int n, const int stride_points,
                                const int stride_proj, const int subsampling_x,
                                const int subsampling_y) {
35
36
37
38
  int i;
  for (i = 0; i < n; ++i) {
    const int x = *(points++), y = *(points++);
    if (subsampling_x)
39
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
40
          ((x * (1 << (WARPEDMODEL_PREC_BITS + 1))) + mat[0]),
41
          WARPEDDIFF_PREC_BITS + 1);
42
    else
43
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
44
          ((x * (1 << WARPEDMODEL_PREC_BITS)) + mat[0]), WARPEDDIFF_PREC_BITS);
45
    if (subsampling_y)
46
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
47
          ((y * (1 << (WARPEDMODEL_PREC_BITS + 1))) + mat[1]),
48
          WARPEDDIFF_PREC_BITS + 1);
49
    else
50
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
51
          ((y * (1 << WARPEDMODEL_PREC_BITS))) + mat[1], WARPEDDIFF_PREC_BITS);
52
53
54
55
56
    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

57
void project_points_rotzoom(int32_t *mat, int *points, int *proj, const int n,
58
59
                            const int stride_points, const int stride_proj,
                            const int subsampling_x, const int subsampling_y) {
60
61
62
63
  int i;
  for (i = 0; i < n; ++i) {
    const int x = *(points++), y = *(points++);
    if (subsampling_x)
64
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
65
66
          mat[2] * 2 * x + mat[3] * 2 * y + mat[0] +
              (mat[2] + mat[3] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
67
68
          WARPEDDIFF_PREC_BITS + 1);
    else
69
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[2] * x + mat[3] * y + mat[0],
70
                                            WARPEDDIFF_PREC_BITS);
71
    if (subsampling_y)
72
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
73
74
          -mat[3] * 2 * x + mat[2] * 2 * y + mat[1] +
              (-mat[3] + mat[2] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
75
76
          WARPEDDIFF_PREC_BITS + 1);
    else
77
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(-mat[3] * x + mat[2] * y + mat[1],
78
                                            WARPEDDIFF_PREC_BITS);
79
80
81
82
83
    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

84
void project_points_affine(int32_t *mat, int *points, int *proj, const int n,
85
86
                           const int stride_points, const int stride_proj,
                           const int subsampling_x, const int subsampling_y) {
87
88
89
90
  int i;
  for (i = 0; i < n; ++i) {
    const int x = *(points++), y = *(points++);
    if (subsampling_x)
91
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
92
93
          mat[2] * 2 * x + mat[3] * 2 * y + mat[0] +
              (mat[2] + mat[3] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
94
95
          WARPEDDIFF_PREC_BITS + 1);
    else
96
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[2] * x + mat[3] * y + mat[0],
97
                                            WARPEDDIFF_PREC_BITS);
98
    if (subsampling_y)
99
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
100
          mat[4] * 2 * x + mat[5] * 2 * y + mat[1] +
Sarah Parker's avatar
Sarah Parker committed
101
              (mat[4] + mat[5] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
102
103
          WARPEDDIFF_PREC_BITS + 1);
    else
104
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[4] * x + mat[5] * y + mat[1],
105
                                            WARPEDDIFF_PREC_BITS);
106
107
108
109
110
    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

111
void project_points_homography(int32_t *mat, int *points, int *proj,
112
113
114
                               const int n, const int stride_points,
                               const int stride_proj, const int subsampling_x,
                               const int subsampling_y) {
115
  int i;
116
117
  int64_t x, y, Z;
  int64_t xp, yp;
118
119
120
121
122
  for (i = 0; i < n; ++i) {
    x = *(points++), y = *(points++);
    x = (subsampling_x ? 4 * x + 1 : 2 * x);
    y = (subsampling_y ? 4 * y + 1 : 2 * y);

123
124
    Z = (mat[6] * x + mat[7] * y + (1 << (WARPEDMODEL_ROW3HOMO_PREC_BITS + 1)));
    xp = (mat[2] * x + mat[3] * y + 2 * mat[0]) *
125
126
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));
127
    yp = (mat[4] * x + mat[5] * y + 2 * mat[1]) *
128
129
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));
130
131
132
133

    xp = xp > 0 ? (xp + Z / 2) / Z : (xp - Z / 2) / Z;
    yp = yp > 0 ? (yp + Z / 2) / Z : (yp - Z / 2) / Z;

clang-format's avatar
clang-format committed
134
135
    if (subsampling_x) xp = (xp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2;
    if (subsampling_y) yp = (yp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2;
136
137
138
139
140
141
142
143
144
    *(proj++) = xp;
    *(proj++) = yp;

    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

static const int16_t
clang-format's avatar
clang-format committed
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
    filter_ntap[WARPEDPIXEL_PREC_SHIFTS][WARPEDPIXEL_FILTER_TAPS] = {
      { 0, 0, 128, 0, 0, 0 },      { 0, -1, 128, 2, -1, 0 },
      { 1, -3, 127, 4, -1, 0 },    { 1, -4, 126, 6, -2, 1 },
      { 1, -5, 126, 8, -3, 1 },    { 1, -6, 125, 11, -4, 1 },
      { 1, -7, 124, 13, -4, 1 },   { 2, -8, 123, 15, -5, 1 },
      { 2, -9, 122, 18, -6, 1 },   { 2, -10, 121, 20, -6, 1 },
      { 2, -11, 120, 22, -7, 2 },  { 2, -12, 119, 25, -8, 2 },
      { 3, -13, 117, 27, -8, 2 },  { 3, -13, 116, 29, -9, 2 },
      { 3, -14, 114, 32, -10, 3 }, { 3, -15, 113, 35, -10, 2 },
      { 3, -15, 111, 37, -11, 3 }, { 3, -16, 109, 40, -11, 3 },
      { 3, -16, 108, 42, -12, 3 }, { 4, -17, 106, 45, -13, 3 },
      { 4, -17, 104, 47, -13, 3 }, { 4, -17, 102, 50, -14, 3 },
      { 4, -17, 100, 52, -14, 3 }, { 4, -18, 98, 55, -15, 4 },
      { 4, -18, 96, 58, -15, 3 },  { 4, -18, 94, 60, -16, 4 },
      { 4, -18, 91, 63, -16, 4 },  { 4, -18, 89, 65, -16, 4 },
      { 4, -18, 87, 68, -17, 4 },  { 4, -18, 85, 70, -17, 4 },
      { 4, -18, 82, 73, -17, 4 },  { 4, -18, 80, 75, -17, 4 },
      { 4, -18, 78, 78, -18, 4 },  { 4, -17, 75, 80, -18, 4 },
      { 4, -17, 73, 82, -18, 4 },  { 4, -17, 70, 85, -18, 4 },
      { 4, -17, 68, 87, -18, 4 },  { 4, -16, 65, 89, -18, 4 },
      { 4, -16, 63, 91, -18, 4 },  { 4, -16, 60, 94, -18, 4 },
      { 3, -15, 58, 96, -18, 4 },  { 4, -15, 55, 98, -18, 4 },
      { 3, -14, 52, 100, -17, 4 }, { 3, -14, 50, 102, -17, 4 },
      { 3, -13, 47, 104, -17, 4 }, { 3, -13, 45, 106, -17, 4 },
      { 3, -12, 42, 108, -16, 3 }, { 3, -11, 40, 109, -16, 3 },
      { 3, -11, 37, 111, -15, 3 }, { 2, -10, 35, 113, -15, 3 },
      { 3, -10, 32, 114, -14, 3 }, { 2, -9, 29, 116, -13, 3 },
      { 2, -8, 27, 117, -13, 3 },  { 2, -8, 25, 119, -12, 2 },
      { 2, -7, 22, 120, -11, 2 },  { 1, -6, 20, 121, -10, 2 },
      { 1, -6, 18, 122, -9, 2 },   { 1, -5, 15, 123, -8, 2 },
      { 1, -4, 13, 124, -7, 1 },   { 1, -4, 11, 125, -6, 1 },
      { 1, -3, 8, 126, -5, 1 },    { 1, -2, 6, 126, -4, 1 },
      { 0, -1, 4, 127, -3, 1 },    { 0, -1, 2, 128, -1, 0 },
    };
179
180
181
182
183
184
185
186
187
188
189

static int32_t do_ntap_filter(int32_t *p, int x) {
  int i;
  int32_t sum = 0;
  for (i = 0; i < WARPEDPIXEL_FILTER_TAPS; ++i) {
    sum += p[i - WARPEDPIXEL_FILTER_TAPS / 2 + 1] * filter_ntap[x][i];
  }
  return sum;
}

static int32_t do_cubic_filter(int32_t *p, int x) {
clang-format's avatar
clang-format committed
190
  if (x == 0) {
191
    return p[0] * (1 << WARPEDPIXEL_FILTER_BITS);
192
  } else if (x == (1 << WARPEDPIXEL_PREC_BITS)) {
193
    return p[1] * (1 << WARPEDPIXEL_FILTER_BITS);
194
  } else {
195
    const int64_t v1 = (int64_t)x * x * x * (3 * (p[0] - p[1]) + p[2] - p[-1]);
196
197
198
    const int64_t v2 = x * x * (2 * p[-1] - 5 * p[0] + 4 * p[1] - p[2]);
    const int64_t v3 = x * (p[1] - p[-1]);
    const int64_t v4 = 2 * p[0];
199
    return (int32_t)ROUND_POWER_OF_TWO_SIGNED(
200
201
202
        (v4 * (1 << (3 * WARPEDPIXEL_PREC_BITS))) +
            (v3 * (1 << (2 * WARPEDPIXEL_PREC_BITS))) +
            (v2 * (1 << WARPEDPIXEL_PREC_BITS)) + v1,
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
        3 * WARPEDPIXEL_PREC_BITS + 1 - WARPEDPIXEL_FILTER_BITS);
  }
}

static INLINE void get_subcolumn(int taps, uint8_t *ref, int32_t *col,
                                 int stride, int x, int y_start) {
  int i;
  for (i = 0; i < taps; ++i) {
    col[i] = ref[(i + y_start) * stride + x];
  }
}

static uint8_t bi_ntap_filter(uint8_t *ref, int x, int y, int stride) {
  int32_t val, arr[WARPEDPIXEL_FILTER_TAPS];
  int k;
clang-format's avatar
clang-format committed
218
219
  int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  int j = (int)y >> WARPEDPIXEL_PREC_BITS;
220
221
222
223
224
225
  for (k = 0; k < WARPEDPIXEL_FILTER_TAPS; ++k) {
    int32_t arr_temp[WARPEDPIXEL_FILTER_TAPS];
    get_subcolumn(WARPEDPIXEL_FILTER_TAPS, ref, arr_temp, stride,
                  i + k + 1 - WARPEDPIXEL_FILTER_TAPS / 2,
                  j + 1 - WARPEDPIXEL_FILTER_TAPS / 2);
    arr[k] = do_ntap_filter(arr_temp + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
226
                            y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
227
228
  }
  val = do_ntap_filter(arr + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
229
                       x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
230
231
232
233
234
235
236
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
  return (uint8_t)clip_pixel(val);
}

static uint8_t bi_cubic_filter(uint8_t *ref, int x, int y, int stride) {
  int32_t val, arr[4];
  int k;
clang-format's avatar
clang-format committed
237
238
  int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  int j = (int)y >> WARPEDPIXEL_PREC_BITS;
239
240
  for (k = 0; k < 4; ++k) {
    int32_t arr_temp[4];
clang-format's avatar
clang-format committed
241
    get_subcolumn(4, ref, arr_temp, stride, i + k - 1, j - 1);
242
243
    arr[k] =
        do_cubic_filter(arr_temp + 1, y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
244
  }
245
  val = do_cubic_filter(arr + 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
246
247
248
249
250
251
252
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
  return (uint8_t)clip_pixel(val);
}

static uint8_t bi_linear_filter(uint8_t *ref, int x, int y, int stride) {
  const int ix = x >> WARPEDPIXEL_PREC_BITS;
  const int iy = y >> WARPEDPIXEL_PREC_BITS;
253
254
  const int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  const int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
255
256
257
  int32_t val;
  val = ROUND_POWER_OF_TWO_SIGNED(
      ref[iy * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sy) *
clang-format's avatar
clang-format committed
258
259
260
261
              (WARPEDPIXEL_PREC_SHIFTS - sx) +
          ref[iy * stride + ix + 1] * (WARPEDPIXEL_PREC_SHIFTS - sy) * sx +
          ref[(iy + 1) * stride + ix] * sy * (WARPEDPIXEL_PREC_SHIFTS - sx) +
          ref[(iy + 1) * stride + ix + 1] * sy * sx,
262
263
264
265
      WARPEDPIXEL_PREC_BITS * 2);
  return (uint8_t)clip_pixel(val);
}

clang-format's avatar
clang-format committed
266
267
static uint8_t warp_interpolate(uint8_t *ref, int x, int y, int width,
                                int height, int stride) {
268
269
  int ix = x >> WARPEDPIXEL_PREC_BITS;
  int iy = y >> WARPEDPIXEL_PREC_BITS;
270
271
  int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
272
273
  int32_t v;

clang-format's avatar
clang-format committed
274
275
  if (ix < 0 && iy < 0)
    return ref[0];
276
277
278
279
280
281
282
283
284
  else if (ix < 0 && iy > height - 1)
    return ref[(height - 1) * stride];
  else if (ix > width - 1 && iy < 0)
    return ref[width - 1];
  else if (ix > width - 1 && iy > height - 1)
    return ref[(height - 1) * stride + (width - 1)];
  else if (ix < 0) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[iy * stride] * (WARPEDPIXEL_PREC_SHIFTS - sy) +
clang-format's avatar
clang-format committed
285
            ref[(iy + 1) * stride] * sy,
286
287
288
289
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel(v);
  } else if (iy < 0) {
    v = ROUND_POWER_OF_TWO_SIGNED(
clang-format's avatar
clang-format committed
290
        ref[ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) + ref[ix + 1] * sx,
291
292
293
294
295
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel(v);
  } else if (ix > width - 1) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[iy * stride + width - 1] * (WARPEDPIXEL_PREC_SHIFTS - sy) +
clang-format's avatar
clang-format committed
296
            ref[(iy + 1) * stride + width - 1] * sy,
297
298
299
300
301
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel(v);
  } else if (iy > height - 1) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[(height - 1) * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) +
clang-format's avatar
clang-format committed
302
            ref[(height - 1) * stride + ix + 1] * sx,
303
304
305
306
307
308
309
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel(v);
  } else if (ix >= WARPEDPIXEL_FILTER_TAPS / 2 - 1 &&
             iy >= WARPEDPIXEL_FILTER_TAPS / 2 - 1 &&
             ix < width - WARPEDPIXEL_FILTER_TAPS / 2 &&
             iy < height - WARPEDPIXEL_FILTER_TAPS / 2) {
    return bi_ntap_filter(ref, x, y, stride);
clang-format's avatar
clang-format committed
310
  } else if (ix >= 1 && iy >= 1 && ix < width - 2 && iy < height - 2) {
311
312
313
314
315
316
    return bi_cubic_filter(ref, x, y, stride);
  } else {
    return bi_linear_filter(ref, x, y, stride);
  }
}

Yaowu Xu's avatar
Yaowu Xu committed
317
#if CONFIG_AOM_HIGHBITDEPTH
318
319
320
321
322
323
324
325
static INLINE void highbd_get_subcolumn(int taps, uint16_t *ref, int32_t *col,
                                        int stride, int x, int y_start) {
  int i;
  for (i = 0; i < taps; ++i) {
    col[i] = ref[(i + y_start) * stride + x];
  }
}

clang-format's avatar
clang-format committed
326
static uint16_t highbd_bi_ntap_filter(uint16_t *ref, int x, int y, int stride,
327
328
329
                                      int bd) {
  int32_t val, arr[WARPEDPIXEL_FILTER_TAPS];
  int k;
clang-format's avatar
clang-format committed
330
331
  int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  int j = (int)y >> WARPEDPIXEL_PREC_BITS;
332
333
334
335
336
337
  for (k = 0; k < WARPEDPIXEL_FILTER_TAPS; ++k) {
    int32_t arr_temp[WARPEDPIXEL_FILTER_TAPS];
    highbd_get_subcolumn(WARPEDPIXEL_FILTER_TAPS, ref, arr_temp, stride,
                         i + k + 1 - WARPEDPIXEL_FILTER_TAPS / 2,
                         j + 1 - WARPEDPIXEL_FILTER_TAPS / 2);
    arr[k] = do_ntap_filter(arr_temp + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
338
                            y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
339
340
  }
  val = do_ntap_filter(arr + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
341
                       x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
342
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
343
  return (uint16_t)clip_pixel_highbd(val, bd);
344
345
}

clang-format's avatar
clang-format committed
346
static uint16_t highbd_bi_cubic_filter(uint16_t *ref, int x, int y, int stride,
347
348
349
                                       int bd) {
  int32_t val, arr[4];
  int k;
clang-format's avatar
clang-format committed
350
351
  int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  int j = (int)y >> WARPEDPIXEL_PREC_BITS;
352
353
  for (k = 0; k < 4; ++k) {
    int32_t arr_temp[4];
clang-format's avatar
clang-format committed
354
    highbd_get_subcolumn(4, ref, arr_temp, stride, i + k - 1, j - 1);
355
356
    arr[k] =
        do_cubic_filter(arr_temp + 1, y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
357
  }
358
  val = do_cubic_filter(arr + 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
359
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
360
  return (uint16_t)clip_pixel_highbd(val, bd);
361
362
}

clang-format's avatar
clang-format committed
363
static uint16_t highbd_bi_linear_filter(uint16_t *ref, int x, int y, int stride,
364
365
366
                                        int bd) {
  const int ix = x >> WARPEDPIXEL_PREC_BITS;
  const int iy = y >> WARPEDPIXEL_PREC_BITS;
367
368
  const int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  const int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
369
370
371
  int32_t val;
  val = ROUND_POWER_OF_TWO_SIGNED(
      ref[iy * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sy) *
clang-format's avatar
clang-format committed
372
373
374
375
              (WARPEDPIXEL_PREC_SHIFTS - sx) +
          ref[iy * stride + ix + 1] * (WARPEDPIXEL_PREC_SHIFTS - sy) * sx +
          ref[(iy + 1) * stride + ix] * sy * (WARPEDPIXEL_PREC_SHIFTS - sx) +
          ref[(iy + 1) * stride + ix + 1] * sy * sx,
376
      WARPEDPIXEL_PREC_BITS * 2);
377
  return (uint16_t)clip_pixel_highbd(val, bd);
378
379
}

clang-format's avatar
clang-format committed
380
381
static uint16_t highbd_warp_interpolate(uint16_t *ref, int x, int y, int width,
                                        int height, int stride, int bd) {
382
383
  int ix = x >> WARPEDPIXEL_PREC_BITS;
  int iy = y >> WARPEDPIXEL_PREC_BITS;
384
385
  int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
386
387
  int32_t v;

clang-format's avatar
clang-format committed
388
389
  if (ix < 0 && iy < 0)
    return ref[0];
390
391
392
393
394
395
396
397
398
  else if (ix < 0 && iy > height - 1)
    return ref[(height - 1) * stride];
  else if (ix > width - 1 && iy < 0)
    return ref[width - 1];
  else if (ix > width - 1 && iy > height - 1)
    return ref[(height - 1) * stride + (width - 1)];
  else if (ix < 0) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[iy * stride] * (WARPEDPIXEL_PREC_SHIFTS - sy) +
clang-format's avatar
clang-format committed
399
            ref[(iy + 1) * stride] * sy,
400
        WARPEDPIXEL_PREC_BITS);
401
    return clip_pixel_highbd(v, bd);
402
403
  } else if (iy < 0) {
    v = ROUND_POWER_OF_TWO_SIGNED(
clang-format's avatar
clang-format committed
404
        ref[ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) + ref[ix + 1] * sx,
405
        WARPEDPIXEL_PREC_BITS);
406
    return clip_pixel_highbd(v, bd);
407
408
409
  } else if (ix > width - 1) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[iy * stride + width - 1] * (WARPEDPIXEL_PREC_SHIFTS - sy) +
clang-format's avatar
clang-format committed
410
            ref[(iy + 1) * stride + width - 1] * sy,
411
        WARPEDPIXEL_PREC_BITS);
412
    return clip_pixel_highbd(v, bd);
413
414
415
  } else if (iy > height - 1) {
    v = ROUND_POWER_OF_TWO_SIGNED(
        ref[(height - 1) * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) +
clang-format's avatar
clang-format committed
416
            ref[(height - 1) * stride + ix + 1] * sx,
417
        WARPEDPIXEL_PREC_BITS);
418
    return clip_pixel_highbd(v, bd);
419
420
421
422
423
  } else if (ix >= WARPEDPIXEL_FILTER_TAPS / 2 - 1 &&
             iy >= WARPEDPIXEL_FILTER_TAPS / 2 - 1 &&
             ix < width - WARPEDPIXEL_FILTER_TAPS / 2 &&
             iy < height - WARPEDPIXEL_FILTER_TAPS / 2) {
    return highbd_bi_ntap_filter(ref, x, y, stride, bd);
clang-format's avatar
clang-format committed
424
  } else if (ix >= 1 && iy >= 1 && ix < width - 2 && iy < height - 2) {
425
426
427
428
429
430
    return highbd_bi_cubic_filter(ref, x, y, stride, bd);
  } else {
    return highbd_bi_linear_filter(ref, x, y, stride, bd);
  }
}

431
432
433
434
435
436
437
static double highbd_warp_erroradv(WarpedMotionParams *wm, uint8_t *ref8,
                                   int width, int height, int stride,
                                   uint8_t *dst8, int p_col, int p_row,
                                   int p_width, int p_height, int p_stride,
                                   int subsampling_x, int subsampling_y,
                                   int x_scale, int y_scale, int bd) {
  int i, j;
438
  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
439
440
441
  uint16_t *dst = CONVERT_TO_SHORTPTR(dst8);
  uint16_t *ref = CONVERT_TO_SHORTPTR(ref8);
  int gm_err = 0, no_gm_err = 0;
442
  int64_t gm_sumerr = 0, no_gm_sumerr = 0;
443
444
445
446
447
  for (i = p_row; i < p_row + p_height; ++i) {
    for (j = p_col; j < p_col + p_width; ++j) {
      int in[2], out[2];
      in[0] = j;
      in[1] = i;
448
      projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
449
450
451
452
453
454
455
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      gm_err = dst[(j - p_col) + (i - p_row) * p_stride] -
               highbd_warp_interpolate(ref, out[0], out[1], width, height,
                                       stride, bd);
      no_gm_err = dst[(j - p_col) + (i - p_row) * p_stride] -
                  ref[(j - p_col) + (i - p_row) * stride];
456
457
458
459
      gm_err = abs(gm_err);
      no_gm_err = abs(no_gm_err);
      gm_sumerr += (int64_t)AOMMIN(gm_err, ERRORADV_CLAMP << (bd - 8));
      no_gm_sumerr += (int64_t)AOMMIN(no_gm_err, ERRORADV_CLAMP << (bd - 8));
460
461
462
463
464
    }
  }
  return (double)gm_sumerr / no_gm_sumerr;
}

clang-format's avatar
clang-format committed
465
466
467
468
469
static void highbd_warp_plane(WarpedMotionParams *wm, uint8_t *ref8, int width,
                              int height, int stride, uint8_t *pred8, int p_col,
                              int p_row, int p_width, int p_height,
                              int p_stride, int subsampling_x,
                              int subsampling_y, int x_scale, int y_scale,
470
                              int bd, int ref_frm) {
471
  int i, j;
472
  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
473
474
  uint16_t *pred = CONVERT_TO_SHORTPTR(pred8);
  uint16_t *ref = CONVERT_TO_SHORTPTR(ref8);
475
  if (projectpoints == NULL) return;
476
477
478
  for (i = p_row; i < p_row + p_height; ++i) {
    for (j = p_col; j < p_col + p_width; ++j) {
      int in[2], out[2];
479
480
      in[0] = j;
      in[1] = i;
481
      projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
482
483
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
484
485
486
487
488
489
490
491
492
      if (ref_frm)
        pred[(j - p_col) + (i - p_row) * p_stride] = ROUND_POWER_OF_TWO(
            pred[(j - p_col) + (i - p_row) * p_stride] +
                highbd_warp_interpolate(ref, out[0], out[1], width, height,
                                        stride, bd),
            1);
      else
        pred[(j - p_col) + (i - p_row) * p_stride] = highbd_warp_interpolate(
            ref, out[0], out[1], width, height, stride, bd);
493
494
495
    }
  }
}
Yaowu Xu's avatar
Yaowu Xu committed
496
#endif  // CONFIG_AOM_HIGHBITDEPTH
497

498
499
500
501
502
503
504
505
static double warp_erroradv(WarpedMotionParams *wm, uint8_t *ref, int width,
                            int height, int stride, uint8_t *dst, int p_col,
                            int p_row, int p_width, int p_height, int p_stride,
                            int subsampling_x, int subsampling_y, int x_scale,
                            int y_scale) {
  int gm_err = 0, no_gm_err = 0;
  int gm_sumerr = 0, no_gm_sumerr = 0;
  int i, j;
506
  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
507
508
509
510
511
  for (i = p_row; i < p_row + p_height; ++i) {
    for (j = p_col; j < p_col + p_width; ++j) {
      int in[2], out[2];
      in[0] = j;
      in[1] = i;
512
      projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
513
514
515
516
517
518
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
      gm_err = dst[(j - p_col) + (i - p_row) * p_stride] -
               warp_interpolate(ref, out[0], out[1], width, height, stride);
      no_gm_err = dst[(j - p_col) + (i - p_row) * p_stride] -
                  ref[(j - p_col) + (i - p_row) * stride];
519
520
521
522
      gm_err = abs(gm_err);
      no_gm_err = abs(no_gm_err);
      gm_sumerr += AOMMIN(gm_err, ERRORADV_CLAMP);
      no_gm_sumerr += AOMMIN(no_gm_err, ERRORADV_CLAMP);
523
524
525
526
527
528
529
530
531
    }
  }
  return (double)gm_sumerr / no_gm_sumerr;
}

static void warp_plane(WarpedMotionParams *wm, uint8_t *ref, int width,
                       int height, int stride, uint8_t *pred, int p_col,
                       int p_row, int p_width, int p_height, int p_stride,
                       int subsampling_x, int subsampling_y, int x_scale,
532
                       int y_scale, int ref_frm) {
533
  int i, j;
534
  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
535
536
537
538
539
540
  if (projectpoints == NULL) return;
  for (i = p_row; i < p_row + p_height; ++i) {
    for (j = p_col; j < p_col + p_width; ++j) {
      int in[2], out[2];
      in[0] = j;
      in[1] = i;
541
      projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
542
543
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
544
545
546
547
548
549
550
551
      if (ref_frm)
        pred[(j - p_col) + (i - p_row) * p_stride] = ROUND_POWER_OF_TWO(
            pred[(j - p_col) + (i - p_row) * p_stride] +
                warp_interpolate(ref, out[0], out[1], width, height, stride),
            1);
      else
        pred[(j - p_col) + (i - p_row) * p_stride] =
            warp_interpolate(ref, out[0], out[1], width, height, stride);
552
553
554
555
    }
  }
}

Yaowu Xu's avatar
Yaowu Xu committed
556
557
558
559
560
561
562
563
564
double av1_warp_erroradv(WarpedMotionParams *wm,
#if CONFIG_AOM_HIGHBITDEPTH
                         int use_hbd, int bd,
#endif  // CONFIG_AOM_HIGHBITDEPTH
                         uint8_t *ref, int width, int height, int stride,
                         uint8_t *dst, int p_col, int p_row, int p_width,
                         int p_height, int p_stride, int subsampling_x,
                         int subsampling_y, int x_scale, int y_scale) {
#if CONFIG_AOM_HIGHBITDEPTH
565
566
567
568
  if (use_hbd)
    return highbd_warp_erroradv(
        wm, ref, width, height, stride, dst, p_col, p_row, p_width, p_height,
        p_stride, subsampling_x, subsampling_y, x_scale, y_scale, bd);
Yaowu Xu's avatar
Yaowu Xu committed
569
#endif  // CONFIG_AOM_HIGHBITDEPTH
570
571
572
  return warp_erroradv(wm, ref, width, height, stride, dst, p_col, p_row,
                       p_width, p_height, p_stride, subsampling_x,
                       subsampling_y, x_scale, y_scale);
573
574
}

Yaowu Xu's avatar
Yaowu Xu committed
575
576
577
578
579
580
581
void av1_warp_plane(WarpedMotionParams *wm,
#if CONFIG_AOM_HIGHBITDEPTH
                    int use_hbd, int bd,
#endif  // CONFIG_AOM_HIGHBITDEPTH
                    uint8_t *ref, int width, int height, int stride,
                    uint8_t *pred, int p_col, int p_row, int p_width,
                    int p_height, int p_stride, int subsampling_x,
582
                    int subsampling_y, int x_scale, int y_scale, int ref_frm) {
Yaowu Xu's avatar
Yaowu Xu committed
583
#if CONFIG_AOM_HIGHBITDEPTH
584
  if (use_hbd)
clang-format's avatar
clang-format committed
585
586
    highbd_warp_plane(wm, ref, width, height, stride, pred, p_col, p_row,
                      p_width, p_height, p_stride, subsampling_x, subsampling_y,
587
                      x_scale, y_scale, bd, ref_frm);
588
  else
Yaowu Xu's avatar
Yaowu Xu committed
589
#endif  // CONFIG_AOM_HIGHBITDEPTH
clang-format's avatar
clang-format committed
590
591
    warp_plane(wm, ref, width, height, stride, pred, p_col, p_row, p_width,
               p_height, p_stride, subsampling_x, subsampling_y, x_scale,
592
               y_scale, ref_frm);
593
}
594

Yaowu Xu's avatar
Yaowu Xu committed
595
596
void av1_integerize_model(const double *model, TransformationType wmtype,
                          WarpedMotionParams *wm) {
597
598
599
600
  wm->wmtype = wmtype;
  switch (wmtype) {
    case HOMOGRAPHY:
      assert(fabs(model[8] - 1.0) < 1e-12);
601
602
603
604
      wm->wmmat[6] =
          (int32_t)lrint(model[6] * (1 << WARPEDMODEL_ROW3HOMO_PREC_BITS));
      wm->wmmat[7] =
          (int32_t)lrint(model[7] * (1 << WARPEDMODEL_ROW3HOMO_PREC_BITS));
605
606
    /* fallthrough intended */
    case AFFINE:
607
608
      wm->wmmat[4] = (int32_t)lrint(model[4] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[5] = (int32_t)lrint(model[5] * (1 << WARPEDMODEL_PREC_BITS));
609
610
    /* fallthrough intended */
    case ROTZOOM:
611
612
      wm->wmmat[2] = (int32_t)lrint(model[2] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[3] = (int32_t)lrint(model[3] * (1 << WARPEDMODEL_PREC_BITS));
613
614
    /* fallthrough intended */
    case TRANSLATION:
615
616
      wm->wmmat[0] = (int32_t)lrint(model[0] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[1] = (int32_t)lrint(model[1] * (1 << WARPEDMODEL_PREC_BITS));
617
618
619
620
      break;
    default: assert(0 && "Invalid TransformationType");
  }
}
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

///////////////////////////////////////////////////////////////////////////////
// svdcmp
// Adopted from Numerical Recipes in C

static const double TINY_NEAR_ZERO = 1.0E-12;

static INLINE double sign(double a, double b) {
  return ((b) >= 0 ? fabs(a) : -fabs(a));
}

static INLINE double pythag(double a, double b) {
  double ct;
  const double absa = fabs(a);
  const double absb = fabs(b);

  if (absa > absb) {
    ct = absb / absa;
    return absa * sqrt(1.0 + ct * ct);
  } else {
    ct = absa / absb;
    return (absb == 0) ? 0 : absb * sqrt(1.0 + ct * ct);
  }
}

static void multiply_mat(const double *m1, const double *m2, double *res,
                         const int m1_rows, const int inner_dim,
                         const int m2_cols) {
  double sum;

  int row, col, inner;
  for (row = 0; row < m1_rows; ++row) {
    for (col = 0; col < m2_cols; ++col) {
      sum = 0;
      for (inner = 0; inner < inner_dim; ++inner)
        sum += m1[row * inner_dim + inner] * m2[inner * m2_cols + col];
      *(res++) = sum;
    }
  }
}

static int svdcmp(double **u, int m, int n, double w[], double **v) {
  const int max_its = 30;
  int flag, i, its, j, jj, k, l, nm;
  double anorm, c, f, g, h, s, scale, x, y, z;
  double *rv1 = (double *)aom_malloc(sizeof(*rv1) * (n + 1));
  g = scale = anorm = 0.0;
  for (i = 0; i < n; i++) {
    l = i + 1;
    rv1[i] = scale * g;
    g = s = scale = 0.0;
    if (i < m) {
      for (k = i; k < m; k++) scale += fabs(u[k][i]);
674
      if (scale != 0.) {
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
        for (k = i; k < m; k++) {
          u[k][i] /= scale;
          s += u[k][i] * u[k][i];
        }
        f = u[i][i];
        g = -sign(sqrt(s), f);
        h = f * g - s;
        u[i][i] = f - g;
        for (j = l; j < n; j++) {
          for (s = 0.0, k = i; k < m; k++) s += u[k][i] * u[k][j];
          f = s / h;
          for (k = i; k < m; k++) u[k][j] += f * u[k][i];
        }
        for (k = i; k < m; k++) u[k][i] *= scale;
      }
    }
    w[i] = scale * g;
    g = s = scale = 0.0;
    if (i < m && i != n - 1) {
      for (k = l; k < n; k++) scale += fabs(u[i][k]);
695
      if (scale != 0.) {
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
        for (k = l; k < n; k++) {
          u[i][k] /= scale;
          s += u[i][k] * u[i][k];
        }
        f = u[i][l];
        g = -sign(sqrt(s), f);
        h = f * g - s;
        u[i][l] = f - g;
        for (k = l; k < n; k++) rv1[k] = u[i][k] / h;
        for (j = l; j < m; j++) {
          for (s = 0.0, k = l; k < n; k++) s += u[j][k] * u[i][k];
          for (k = l; k < n; k++) u[j][k] += s * rv1[k];
        }
        for (k = l; k < n; k++) u[i][k] *= scale;
      }
    }
    anorm = fmax(anorm, (fabs(w[i]) + fabs(rv1[i])));
  }

  for (i = n - 1; i >= 0; i--) {
    if (i < n - 1) {
717
      if (g != 0.) {
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
        for (j = l; j < n; j++) v[j][i] = (u[i][j] / u[i][l]) / g;
        for (j = l; j < n; j++) {
          for (s = 0.0, k = l; k < n; k++) s += u[i][k] * v[k][j];
          for (k = l; k < n; k++) v[k][j] += s * v[k][i];
        }
      }
      for (j = l; j < n; j++) v[i][j] = v[j][i] = 0.0;
    }
    v[i][i] = 1.0;
    g = rv1[i];
    l = i;
  }
  for (i = AOMMIN(m, n) - 1; i >= 0; i--) {
    l = i + 1;
    g = w[i];
    for (j = l; j < n; j++) u[i][j] = 0.0;
734
    if (g != 0.) {
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
      g = 1.0 / g;
      for (j = l; j < n; j++) {
        for (s = 0.0, k = l; k < m; k++) s += u[k][i] * u[k][j];
        f = (s / u[i][i]) * g;
        for (k = i; k < m; k++) u[k][j] += f * u[k][i];
      }
      for (j = i; j < m; j++) u[j][i] *= g;
    } else {
      for (j = i; j < m; j++) u[j][i] = 0.0;
    }
    ++u[i][i];
  }
  for (k = n - 1; k >= 0; k--) {
    for (its = 0; its < max_its; its++) {
      flag = 1;
      for (l = k; l >= 0; l--) {
        nm = l - 1;
        if ((double)(fabs(rv1[l]) + anorm) == anorm || nm < 0) {
          flag = 0;
          break;
        }
        if ((double)(fabs(w[nm]) + anorm) == anorm) break;
      }
      if (flag) {
        c = 0.0;
        s = 1.0;
        for (i = l; i <= k; i++) {
          f = s * rv1[i];
          rv1[i] = c * rv1[i];
          if ((double)(fabs(f) + anorm) == anorm) break;
          g = w[i];
          h = pythag(f, g);
          w[i] = h;
          h = 1.0 / h;
          c = g * h;
          s = -f * h;
          for (j = 0; j < m; j++) {
            y = u[j][nm];
            z = u[j][i];
            u[j][nm] = y * c + z * s;
            u[j][i] = z * c - y * s;
          }
        }
      }
      z = w[k];
      if (l == k) {
        if (z < 0.0) {
          w[k] = -z;
          for (j = 0; j < n; j++) v[j][k] = -v[j][k];
        }
        break;
      }
      if (its == max_its - 1) {
788
        aom_free(rv1);
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
        return 1;
      }
      assert(k > 0);
      x = w[l];
      nm = k - 1;
      y = w[nm];
      g = rv1[nm];
      h = rv1[k];
      f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y);
      g = pythag(f, 1.0);
      f = ((x - z) * (x + z) + h * ((y / (f + sign(g, f))) - h)) / x;
      c = s = 1.0;
      for (j = l; j <= nm; j++) {
        i = j + 1;
        g = rv1[i];
        y = w[i];
        h = s * g;
        g = c * g;
        z = pythag(f, h);
        rv1[j] = z;
        c = f / z;
        s = h / z;
        f = x * c + g * s;
        g = g * c - x * s;
        h = y * s;
        y *= c;
        for (jj = 0; jj < n; jj++) {
          x = v[jj][j];
          z = v[jj][i];
          v[jj][j] = x * c + z * s;
          v[jj][i] = z * c - x * s;
        }
        z = pythag(f, h);
        w[j] = z;
823
        if (z != 0.) {
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
          z = 1.0 / z;
          c = f * z;
          s = h * z;
        }
        f = c * g + s * y;
        x = c * y - s * g;
        for (jj = 0; jj < m; jj++) {
          y = u[jj][j];
          z = u[jj][i];
          u[jj][j] = y * c + z * s;
          u[jj][i] = z * c - y * s;
        }
      }
      rv1[l] = 0.0;
      rv1[k] = f;
      w[k] = x;
    }
  }
  aom_free(rv1);
  return 0;
}

static int SVD(double *U, double *W, double *V, double *matx, int M, int N) {
  // Assumes allocation for U is MxN
  double **nrU = (double **)aom_malloc((M) * sizeof(*nrU));
  double **nrV = (double **)aom_malloc((N) * sizeof(*nrV));
  int problem, i;

  problem = !(nrU && nrV);
  if (!problem) {
    for (i = 0; i < M; i++) {
      nrU[i] = &U[i * N];
    }
    for (i = 0; i < N; i++) {
      nrV[i] = &V[i * N];
    }
  } else {
    if (nrU) aom_free(nrU);
    if (nrV) aom_free(nrV);
    return 1;
  }

  /* copy from given matx into nrU */
  for (i = 0; i < M; i++) {
    memcpy(&(nrU[i][0]), matx + N * i, N * sizeof(*matx));
  }

  /* HERE IT IS: do SVD */
  if (svdcmp(nrU, M, N, W, nrV)) {
    aom_free(nrU);
    aom_free(nrV);
    return 1;
  }

  /* aom_free Numerical Recipes arrays */
  aom_free(nrU);
  aom_free(nrV);

  return 0;
}

int pseudo_inverse(double *inv, double *matx, const int M, const int N) {
  double ans;
  int i, j, k;
  double *const U = (double *)aom_malloc(M * N * sizeof(*matx));
  double *const W = (double *)aom_malloc(N * sizeof(*matx));
  double *const V = (double *)aom_malloc(N * N * sizeof(*matx));

  if (!(U && W && V)) {
    return 1;
  }
  if (SVD(U, W, V, matx, M, N)) {
896
897
898
    aom_free(U);
    aom_free(W);
    aom_free(V);
899
900
901
902
    return 1;
  }
  for (i = 0; i < N; i++) {
    if (fabs(W[i]) < TINY_NEAR_ZERO) {
903
904
905
      aom_free(U);
      aom_free(W);
      aom_free(V);
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
      return 1;
    }
  }

  for (i = 0; i < N; i++) {
    for (j = 0; j < M; j++) {
      ans = 0;
      for (k = 0; k < N; k++) {
        ans += V[k + N * i] * U[k + N * j] / W[k];
      }
      inv[j + M * i] = ans;
    }
  }
  aom_free(U);
  aom_free(W);
  aom_free(V);
  return 0;
}

static void normalize_homography(double *pts, int n, double *T) {
  double *p = pts;
  double mean[2] = { 0, 0 };
  double msqe = 0;
  double scale;
  int i;
  for (i = 0; i < n; ++i, p += 2) {
    mean[0] += p[0];
    mean[1] += p[1];
  }
  mean[0] /= n;
  mean[1] /= n;
  for (p = pts, i = 0; i < n; ++i, p += 2) {
    p[0] -= mean[0];
    p[1] -= mean[1];
    msqe += sqrt(p[0] * p[0] + p[1] * p[1]);
  }
  msqe /= n;
  scale = sqrt(2) / msqe;
  T[0] = scale;
  T[1] = 0;
  T[2] = -scale * mean[0];
  T[3] = 0;
  T[4] = scale;
  T[5] = -scale * mean[1];
  T[6] = 0;
  T[7] = 0;
  T[8] = 1;
  for (p = pts, i = 0; i < n; ++i, p += 2) {
    p[0] *= scale;
    p[1] *= scale;
  }
}

static void invnormalize_mat(double *T, double *iT) {
  double is = 1.0 / T[0];
  double m0 = -T[2] * is;
  double m1 = -T[5] * is;
  iT[0] = is;
  iT[1] = 0;
  iT[2] = m0;
  iT[3] = 0;
  iT[4] = is;
  iT[5] = m1;
  iT[6] = 0;
  iT[7] = 0;
  iT[8] = 1;
}

static void denormalize_homography(double *params, double *T1, double *T2) {
  double iT2[9];
  double params2[9];
  invnormalize_mat(T2, iT2);
  multiply_mat(params, T1, params2, 3, 3, 3);
  multiply_mat(iT2, params2, params, 3, 3, 3);
}

982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
static void denormalize_homography_reorder(double *params, double *T1,
                                           double *T2) {
  double params_denorm[MAX_PARAMDIM];
  memcpy(params_denorm, params, sizeof(*params) * 8);
  params_denorm[8] = 1.0;
  denormalize_homography(params_denorm, T1, T2);
  params[0] = params_denorm[2];
  params[1] = params_denorm[5];
  params[2] = params_denorm[0];
  params[3] = params_denorm[1];
  params[4] = params_denorm[3];
  params[5] = params_denorm[4];
  params[6] = params_denorm[6];
  params[7] = params_denorm[7];
}

static void denormalize_affine_reorder(double *params, double *T1, double *T2) {
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
  double params_denorm[MAX_PARAMDIM];
  params_denorm[0] = params[0];
  params_denorm[1] = params[1];
  params_denorm[2] = params[4];
  params_denorm[3] = params[2];
  params_denorm[4] = params[3];
  params_denorm[5] = params[5];
  params_denorm[6] = params_denorm[7] = 0;
  params_denorm[8] = 1;
  denormalize_homography(params_denorm, T1, T2);
1009
1010
1011
1012
  params[0] = params_denorm[2];
  params[1] = params_denorm[5];
  params[2] = params_denorm[0];
  params[3] = params_denorm[1];
1013
1014
  params[4] = params_denorm[3];
  params[5] = params_denorm[4];
1015
  params[6] = params[7] = 0;
1016
1017
}

1018
1019
static void denormalize_rotzoom_reorder(double *params, double *T1,
                                        double *T2) {
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
  double params_denorm[MAX_PARAMDIM];
  params_denorm[0] = params[0];
  params_denorm[1] = params[1];
  params_denorm[2] = params[2];
  params_denorm[3] = -params[1];
  params_denorm[4] = params[0];
  params_denorm[5] = params[3];
  params_denorm[6] = params_denorm[7] = 0;
  params_denorm[8] = 1;
  denormalize_homography(params_denorm, T1, T2);
1030
1031
1032
1033
1034
1035
1036
  params[0] = params_denorm[2];
  params[1] = params_denorm[5];
  params[2] = params_denorm[0];
  params[3] = params_denorm[1];
  params[4] = -params[3];
  params[5] = params[2];
  params[6] = params[7] = 0;
1037
1038
}

1039
1040
static void denormalize_translation_reorder(double *params, double *T1,
                                            double *T2) {
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
  double params_denorm[MAX_PARAMDIM];
  params_denorm[0] = 1;
  params_denorm[1] = 0;
  params_denorm[2] = params[0];
  params_denorm[3] = 0;
  params_denorm[4] = 1;
  params_denorm[5] = params[1];
  params_denorm[6] = params_denorm[7] = 0;
  params_denorm[8] = 1;
  denormalize_homography(params_denorm, T1, T2);
1051
1052
1053
1054
1055
  params[0] = params_denorm[2];
  params[1] = params_denorm[5];
  params[2] = params[5] = 1;
  params[3] = params[4] = 0;
  params[6] = params[7] = 0;
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
}

int find_translation(const int np, double *pts1, double *pts2, double *mat) {
  int i;
  double sx, sy, dx, dy;
  double sumx, sumy;

  double T1[9], T2[9];
  normalize_homography(pts1, np, T1);
  normalize_homography(pts2, np, T2);

  sumx = 0;
  sumy = 0;
  for (i = 0; i < np; ++i) {
    dx = *(pts2++);
    dy = *(pts2++);
    sx = *(pts1++);
    sy = *(pts1++);

    sumx += dx - sx;
    sumy += dy - sy;
  }
  mat[0] = sumx / np;
  mat[1] = sumy / np;
1080
  denormalize_translation_reorder(mat, T1, T2);
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
  return 0;
}

int find_rotzoom(const int np, double *pts1, double *pts2, double *mat) {
  const int np2 = np * 2;
  double *a = (double *)aom_malloc(sizeof(*a) * np2 * 9);
  double *b = a + np2 * 4;
  double *temp = b + np2;
  int i;
  double sx, sy, dx, dy;

  double T1[9], T2[9];
  normalize_homography(pts1, np, T1);
  normalize_homography(pts2, np, T2);

  for (i = 0; i < np; ++i) {
    dx = *(pts2++);
    dy = *(pts2++);
    sx = *(pts1++);
    sy = *(pts1++);

    a[i * 2 * 4 + 0] = sx;
    a[i * 2 * 4 + 1] = sy;
    a[i * 2 * 4 + 2] = 1;
    a[i * 2 * 4 + 3] = 0;
    a[(i * 2 + 1) * 4 + 0] = sy;
    a[(i * 2 + 1) * 4 + 1] = -sx;
    a[(i * 2 + 1) * 4 + 2] = 0;
    a[(i * 2 + 1) * 4 + 3] = 1;

    b[2 * i] = dx;
    b[2 * i + 1] = dy;
  }
  if (pseudo_inverse(temp, a, np2, 4)) {
    aom_free(a);
    return 1;
  }
  multiply_mat(temp, b, mat, 4, np2, 1);
1119
  denormalize_rotzoom_reorder(mat, T1, T2);
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
  aom_free(a);
  return 0;
}

int find_affine(const int np, double *pts1, double *pts2, double *mat) {
  const int np2 = np * 2;
  double *a = (double *)aom_malloc(sizeof(*a) * np2 * 13);
  double *b = a + np2 * 6;
  double *temp = b + np2;
  int i;
  double sx, sy, dx, dy;

  double T1[9], T2[9];
  normalize_homography(pts1, np, T1);
  normalize_homography(pts2, np, T2);

  for (i = 0; i < np; ++i) {
    dx = *(pts2++);
    dy = *(pts2++);
    sx = *(pts1++);
    sy = *(pts1++);

    a[i * 2 * 6 + 0] = sx;
    a[i * 2 * 6 + 1] = sy;
    a[i * 2 * 6 + 2] = 0;
    a[i * 2 * 6 + 3] = 0;
    a[i * 2 * 6 + 4] = 1;
    a[i * 2 * 6 + 5] = 0;
    a[(i * 2 + 1) * 6 + 0] = 0;
    a[(i * 2 + 1) * 6 + 1] = 0;
    a[(i * 2 + 1) * 6 + 2] = sx;
    a[(i * 2 + 1) * 6 + 3] = sy;
    a[(i * 2 + 1) * 6 + 4] = 0;
    a[(i * 2 + 1) * 6 + 5] = 1;

    b[2 * i] = dx;
    b[2 * i + 1] = dy;
  }
  if (pseudo_inverse(temp, a, np2, 6)) {
    aom_free(a);
    return 1;
  }
  multiply_mat(temp, b, mat, 6, np2, 1);
1163
  denormalize_affine_reorder(mat, T1, T2);
1164
1165
1166
1167
1168
1169
1170
1171
1172
  aom_free(a);
  return 0;
}

int find_homography(const int np, double *pts1, double *pts2, double *mat) {
  // Implemented from Peter Kovesi's normalized implementation
  const int np3 = np * 3;
  double *a = (double *)aom_malloc(sizeof(*a) * np3 * 18);
  double *U = a + np3 * 9;
1173
  double S[9], V[9 * 9], H[9];
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
  int i, mini;
  double sx, sy, dx, dy;
  double T1[9], T2[9];

  normalize_homography(pts1, np, T1);
  normalize_homography(pts2, np, T2);

  for (i = 0; i < np; ++i) {
    dx = *(pts2++);
    dy = *(pts2++);
    sx = *(pts1++);
    sy = *(pts1++);

    a[i * 3 * 9 + 0] = a[i * 3 * 9 + 1] = a[i * 3 * 9 + 2] = 0;
    a[i * 3 * 9 + 3] = -sx;
    a[i * 3 * 9 + 4] = -sy;
    a[i * 3 * 9 + 5] = -1;
    a[i * 3 * 9 + 6] = dy * sx;
    a[i * 3 * 9 + 7] = dy * sy;
    a[i * 3 * 9 + 8] = dy;

    a[(i * 3 + 1) * 9 + 0] = sx;
    a[(i * 3 + 1) * 9 + 1] = sy;
    a[(i * 3 + 1) * 9 + 2] = 1;
    a[(i * 3 + 1) * 9 + 3] = a[(i * 3 + 1) * 9 + 4] = a[(i * 3 + 1) * 9 + 5] =
        0;
    a[(i * 3 + 1) * 9 + 6] = -dx * sx;
    a[(i * 3 + 1) * 9 + 7] = -dx * sy;
    a[(i * 3 + 1) * 9 + 8] = -dx;

    a[(i * 3 + 2) * 9 + 0] = -dy * sx;
    a[(i * 3 + 2) * 9 + 1] = -dy * sy;
    a[(i * 3 + 2) * 9 + 2] = -dy;
    a[(i * 3 + 2) * 9 + 3] = dx * sx;
    a[(i * 3 + 2) * 9 + 4] = dx * sy;
    a[(i * 3 + 2) * 9 + 5] = dx;
    a[(i * 3 + 2) * 9 + 6] = a[(i * 3 + 2) * 9 + 7] = a[(i * 3 + 2) * 9 + 8] =
        0;
  }

  if (SVD(U, S, V, a, np3, 9)) {
    aom_free(a);
    return 1;
  } else {
    double minS = 1e12;
    mini = -1;
    for (i = 0; i < 9; ++i) {
      if (S[i] < minS) {
        minS = S[i];
        mini = i;
      }
    }
  }

1228
1229
  for (i = 0; i < 9; i++) H[i] = V[i * 9 + mini];
  denormalize_homography_reorder(H, T1, T2);
1230
  aom_free(a);
1231
  if (H[8] == 0.0) {
1232
    return 1;
1233
1234
1235
1236
  } else {
    // normalize
    double f = 1.0 / H[8];
    for (i = 0; i < 8; i++) mat[i] = f * H[i];
1237
1238
1239
  }
  return 0;
}