warped_motion.c 40.8 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
static ProjectPointsFunc get_project_points_type(TransformationType type) {
20
  switch (type) {
21 22 23 24
    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
25
    default: assert(0); return NULL;
26 27 28
  }
}

29
void project_points_translation(int32_t *mat, int *points, int *proj,
30 31 32
                                const int n, const int stride_points,
                                const int stride_proj, const int subsampling_x,
                                const int subsampling_y) {
33 34 35 36
  int i;
  for (i = 0; i < n; ++i) {
    const int x = *(points++), y = *(points++);
    if (subsampling_x)
37
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
38
          ((x * (1 << (WARPEDMODEL_PREC_BITS + 1))) + mat[0]),
39
          WARPEDDIFF_PREC_BITS + 1);
40
    else
41
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
42
          ((x * (1 << WARPEDMODEL_PREC_BITS)) + mat[0]), WARPEDDIFF_PREC_BITS);
43
    if (subsampling_y)
44
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
45
          ((y * (1 << (WARPEDMODEL_PREC_BITS + 1))) + mat[1]),
46
          WARPEDDIFF_PREC_BITS + 1);
47
    else
48
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
49
          ((y * (1 << WARPEDMODEL_PREC_BITS))) + mat[1], WARPEDDIFF_PREC_BITS);
50 51 52 53 54
    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

55
void project_points_rotzoom(int32_t *mat, int *points, int *proj, const int n,
56 57
                            const int stride_points, const int stride_proj,
                            const int subsampling_x, const int subsampling_y) {
58 59 60 61
  int i;
  for (i = 0; i < n; ++i) {
    const int x = *(points++), y = *(points++);
    if (subsampling_x)
62
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
63 64
          mat[2] * 2 * x + mat[3] * 2 * y + mat[0] +
              (mat[2] + mat[3] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
65 66
          WARPEDDIFF_PREC_BITS + 1);
    else
67
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[2] * x + mat[3] * y + mat[0],
68
                                            WARPEDDIFF_PREC_BITS);
69
    if (subsampling_y)
70
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
71 72
          -mat[3] * 2 * x + mat[2] * 2 * y + mat[1] +
              (-mat[3] + mat[2] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
73 74
          WARPEDDIFF_PREC_BITS + 1);
    else
75
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(-mat[3] * x + mat[2] * y + mat[1],
76
                                            WARPEDDIFF_PREC_BITS);
77 78 79 80 81
    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

82
void project_points_affine(int32_t *mat, int *points, int *proj, const int n,
83 84
                           const int stride_points, const int stride_proj,
                           const int subsampling_x, const int subsampling_y) {
85 86 87 88
  int i;
  for (i = 0; i < n; ++i) {
    const int x = *(points++), y = *(points++);
    if (subsampling_x)
89
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
90 91
          mat[2] * 2 * x + mat[3] * 2 * y + mat[0] +
              (mat[2] + mat[3] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
92 93
          WARPEDDIFF_PREC_BITS + 1);
    else
94
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[2] * x + mat[3] * y + mat[0],
95
                                            WARPEDDIFF_PREC_BITS);
96
    if (subsampling_y)
97
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(
98
          mat[4] * 2 * x + mat[5] * 2 * y + mat[1] +
Sarah Parker's avatar
Sarah Parker committed
99
              (mat[4] + mat[5] - (1 << WARPEDMODEL_PREC_BITS)) / 2,
100 101
          WARPEDDIFF_PREC_BITS + 1);
    else
102
      *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[4] * x + mat[5] * y + mat[1],
103
                                            WARPEDDIFF_PREC_BITS);
104 105 106 107 108
    points += stride_points - 2;
    proj += stride_proj - 2;
  }
}

109
void project_points_homography(int32_t *mat, int *points, int *proj,
110 111 112
                               const int n, const int stride_points,
                               const int stride_proj, const int subsampling_x,
                               const int subsampling_y) {
113
  int i;
114 115
  int64_t x, y, Z;
  int64_t xp, yp;
116 117 118 119 120
  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);

121 122
    Z = (mat[6] * x + mat[7] * y + (1 << (WARPEDMODEL_ROW3HOMO_PREC_BITS + 1)));
    xp = (mat[2] * x + mat[3] * y + 2 * mat[0]) *
123 124
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));
125
    yp = (mat[4] * x + mat[5] * y + 2 * mat[1]) *
126 127
         (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS -
                WARPEDMODEL_PREC_BITS));
128 129 130 131

    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
132 133
    if (subsampling_x) xp = (xp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2;
    if (subsampling_y) yp = (yp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2;
134 135 136 137 138 139 140 141 142
    *(proj++) = xp;
    *(proj++) = yp;

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

static const int16_t
clang-format's avatar
clang-format committed
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
    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 },
    };
177 178 179 180 181 182 183 184 185 186 187

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
188
  if (x == 0) {
189
    return p[0] * (1 << WARPEDPIXEL_FILTER_BITS);
190
  } else if (x == (1 << WARPEDPIXEL_PREC_BITS)) {
191
    return p[1] * (1 << WARPEDPIXEL_FILTER_BITS);
192
  } else {
193
    const int64_t v1 = (int64_t)x * x * x * (3 * (p[0] - p[1]) + p[2] - p[-1]);
194 195 196
    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];
197
    return (int32_t)ROUND_POWER_OF_TWO_SIGNED(
198 199 200
        (v4 * (1 << (3 * WARPEDPIXEL_PREC_BITS))) +
            (v3 * (1 << (2 * WARPEDPIXEL_PREC_BITS))) +
            (v2 * (1 << WARPEDPIXEL_PREC_BITS)) + v1,
201 202 203 204 205 206 207 208 209 210 211 212 213 214 215
        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
216 217
  int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  int j = (int)y >> WARPEDPIXEL_PREC_BITS;
218 219 220 221 222 223
  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,
224
                            y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
225 226
  }
  val = do_ntap_filter(arr + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
227
                       x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
228 229 230 231 232 233 234
  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
235 236
  int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  int j = (int)y >> WARPEDPIXEL_PREC_BITS;
237 238
  for (k = 0; k < 4; ++k) {
    int32_t arr_temp[4];
clang-format's avatar
clang-format committed
239
    get_subcolumn(4, ref, arr_temp, stride, i + k - 1, j - 1);
240 241
    arr[k] =
        do_cubic_filter(arr_temp + 1, y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
242
  }
243
  val = do_cubic_filter(arr + 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
244 245 246 247 248 249 250
  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;
251 252
  const int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  const int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
253 254 255
  int32_t val;
  val = ROUND_POWER_OF_TWO_SIGNED(
      ref[iy * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sy) *
clang-format's avatar
clang-format committed
256 257 258 259
              (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,
260 261 262 263
      WARPEDPIXEL_PREC_BITS * 2);
  return (uint8_t)clip_pixel(val);
}

clang-format's avatar
clang-format committed
264 265
static uint8_t warp_interpolate(uint8_t *ref, int x, int y, int width,
                                int height, int stride) {
266 267
  int ix = x >> WARPEDPIXEL_PREC_BITS;
  int iy = y >> WARPEDPIXEL_PREC_BITS;
268 269
  int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
270 271
  int32_t v;

clang-format's avatar
clang-format committed
272 273
  if (ix < 0 && iy < 0)
    return ref[0];
274 275 276 277 278 279 280 281 282
  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
283
            ref[(iy + 1) * stride] * sy,
284 285 286 287
        WARPEDPIXEL_PREC_BITS);
    return clip_pixel(v);
  } else if (iy < 0) {
    v = ROUND_POWER_OF_TWO_SIGNED(
clang-format's avatar
clang-format committed
288
        ref[ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) + ref[ix + 1] * sx,
289 290 291 292 293
        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
294
            ref[(iy + 1) * stride + width - 1] * sy,
295 296 297 298 299
        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
300
            ref[(height - 1) * stride + ix + 1] * sx,
301 302 303 304 305 306 307
        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
308
  } else if (ix >= 1 && iy >= 1 && ix < width - 2 && iy < height - 2) {
309 310 311 312 313 314
    return bi_cubic_filter(ref, x, y, stride);
  } else {
    return bi_linear_filter(ref, x, y, stride);
  }
}

Yaowu Xu's avatar
Yaowu Xu committed
315
#if CONFIG_AOM_HIGHBITDEPTH
316 317 318 319 320 321 322 323
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
324
static uint16_t highbd_bi_ntap_filter(uint16_t *ref, int x, int y, int stride,
325 326 327
                                      int bd) {
  int32_t val, arr[WARPEDPIXEL_FILTER_TAPS];
  int k;
clang-format's avatar
clang-format committed
328 329
  int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  int j = (int)y >> WARPEDPIXEL_PREC_BITS;
330 331 332 333 334 335
  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,
336
                            y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
337 338
  }
  val = do_ntap_filter(arr + WARPEDPIXEL_FILTER_TAPS / 2 - 1,
339
                       x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
340
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
341
  return (uint16_t)clip_pixel_highbd(val, bd);
342 343
}

clang-format's avatar
clang-format committed
344
static uint16_t highbd_bi_cubic_filter(uint16_t *ref, int x, int y, int stride,
345 346 347
                                       int bd) {
  int32_t val, arr[4];
  int k;
clang-format's avatar
clang-format committed
348 349
  int i = (int)x >> WARPEDPIXEL_PREC_BITS;
  int j = (int)y >> WARPEDPIXEL_PREC_BITS;
350 351
  for (k = 0; k < 4; ++k) {
    int32_t arr_temp[4];
clang-format's avatar
clang-format committed
352
    highbd_get_subcolumn(4, ref, arr_temp, stride, i + k - 1, j - 1);
353 354
    arr[k] =
        do_cubic_filter(arr_temp + 1, y - (j * (1 << WARPEDPIXEL_PREC_BITS)));
355
  }
356
  val = do_cubic_filter(arr + 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS)));
357
  val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2);
358
  return (uint16_t)clip_pixel_highbd(val, bd);
359 360
}

clang-format's avatar
clang-format committed
361
static uint16_t highbd_bi_linear_filter(uint16_t *ref, int x, int y, int stride,
362 363 364
                                        int bd) {
  const int ix = x >> WARPEDPIXEL_PREC_BITS;
  const int iy = y >> WARPEDPIXEL_PREC_BITS;
365 366
  const int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  const int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
367 368 369
  int32_t val;
  val = ROUND_POWER_OF_TWO_SIGNED(
      ref[iy * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sy) *
clang-format's avatar
clang-format committed
370 371 372 373
              (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,
374
      WARPEDPIXEL_PREC_BITS * 2);
375
  return (uint16_t)clip_pixel_highbd(val, bd);
376 377
}

clang-format's avatar
clang-format committed
378 379
static uint16_t highbd_warp_interpolate(uint16_t *ref, int x, int y, int width,
                                        int height, int stride, int bd) {
380 381
  int ix = x >> WARPEDPIXEL_PREC_BITS;
  int iy = y >> WARPEDPIXEL_PREC_BITS;
382 383
  int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS));
  int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS));
384 385
  int32_t v;

clang-format's avatar
clang-format committed
386 387
  if (ix < 0 && iy < 0)
    return ref[0];
388 389 390 391 392 393 394 395 396
  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
397
            ref[(iy + 1) * stride] * sy,
398
        WARPEDPIXEL_PREC_BITS);
399
    return clip_pixel_highbd(v, bd);
400 401
  } else if (iy < 0) {
    v = ROUND_POWER_OF_TWO_SIGNED(
clang-format's avatar
clang-format committed
402
        ref[ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) + ref[ix + 1] * sx,
403
        WARPEDPIXEL_PREC_BITS);
404
    return clip_pixel_highbd(v, bd);
405 406 407
  } 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
408
            ref[(iy + 1) * stride + width - 1] * sy,
409
        WARPEDPIXEL_PREC_BITS);
410
    return clip_pixel_highbd(v, bd);
411 412 413
  } 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
414
            ref[(height - 1) * stride + ix + 1] * sx,
415
        WARPEDPIXEL_PREC_BITS);
416
    return clip_pixel_highbd(v, bd);
417 418 419 420 421
  } 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
422
  } else if (ix >= 1 && iy >= 1 && ix < width - 2 && iy < height - 2) {
423 424 425 426 427 428
    return highbd_bi_cubic_filter(ref, x, y, stride, bd);
  } else {
    return highbd_bi_linear_filter(ref, x, y, stride, bd);
  }
}

429 430 431 432 433 434 435
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;
436
  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
437 438 439
  uint16_t *dst = CONVERT_TO_SHORTPTR(dst8);
  uint16_t *ref = CONVERT_TO_SHORTPTR(ref8);
  int gm_err = 0, no_gm_err = 0;
440
  int64_t gm_sumerr = 0, no_gm_sumerr = 0;
441 442 443 444 445
  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;
446
      projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
447 448 449 450 451 452 453
      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];
454 455
      gm_sumerr += (int64_t)gm_err * gm_err;
      no_gm_sumerr += (int64_t)no_gm_err * no_gm_err;
456 457 458 459 460
    }
  }
  return (double)gm_sumerr / no_gm_sumerr;
}

clang-format's avatar
clang-format committed
461 462 463 464 465
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,
466
                              int bd, int ref_frm) {
467
  int i, j;
468
  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
469 470
  uint16_t *pred = CONVERT_TO_SHORTPTR(pred8);
  uint16_t *ref = CONVERT_TO_SHORTPTR(ref8);
471
  if (projectpoints == NULL) return;
472 473 474
  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];
475 476
      in[0] = j;
      in[1] = i;
477
      projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
478 479
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
480 481 482 483 484 485 486 487 488
      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);
489 490 491
    }
  }
}
Yaowu Xu's avatar
Yaowu Xu committed
492
#endif  // CONFIG_AOM_HIGHBITDEPTH
493

494 495 496 497 498 499 500 501
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;
502
  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
503 504 505 506 507
  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;
508
      projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
509 510 511 512 513 514
      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];
515 516
      gm_sumerr += abs(gm_err);
      no_gm_sumerr += abs(no_gm_err);
517 518 519 520 521 522 523 524 525
    }
  }
  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,
526
                       int y_scale, int ref_frm) {
527
  int i, j;
528
  ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype);
529 530 531 532 533 534
  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;
535
      projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y);
536 537
      out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4);
      out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4);
538 539 540 541 542 543 544 545
      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);
546 547 548 549
    }
  }
}

Yaowu Xu's avatar
Yaowu Xu committed
550 551 552 553 554 555 556 557 558
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
559 560 561 562
  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
563
#endif  // CONFIG_AOM_HIGHBITDEPTH
564 565 566
  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);
567 568
}

Yaowu Xu's avatar
Yaowu Xu committed
569 570 571 572 573 574 575
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,
576
                    int subsampling_y, int x_scale, int y_scale, int ref_frm) {
Yaowu Xu's avatar
Yaowu Xu committed
577
#if CONFIG_AOM_HIGHBITDEPTH
578
  if (use_hbd)
clang-format's avatar
clang-format committed
579 580
    highbd_warp_plane(wm, ref, width, height, stride, pred, p_col, p_row,
                      p_width, p_height, p_stride, subsampling_x, subsampling_y,
581
                      x_scale, y_scale, bd, ref_frm);
582
  else
Yaowu Xu's avatar
Yaowu Xu committed
583
#endif  // CONFIG_AOM_HIGHBITDEPTH
clang-format's avatar
clang-format committed
584 585
    warp_plane(wm, ref, width, height, stride, pred, p_col, p_row, p_width,
               p_height, p_stride, subsampling_x, subsampling_y, x_scale,
586
               y_scale, ref_frm);
587
}
588

Yaowu Xu's avatar
Yaowu Xu committed
589 590
void av1_integerize_model(const double *model, TransformationType wmtype,
                          WarpedMotionParams *wm) {
591 592 593 594
  wm->wmtype = wmtype;
  switch (wmtype) {
    case HOMOGRAPHY:
      assert(fabs(model[8] - 1.0) < 1e-12);
595 596 597 598
      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));
599 600
    /* fallthrough intended */
    case AFFINE:
601 602
      wm->wmmat[4] = (int32_t)lrint(model[4] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[5] = (int32_t)lrint(model[5] * (1 << WARPEDMODEL_PREC_BITS));
603 604
    /* fallthrough intended */
    case ROTZOOM:
605 606
      wm->wmmat[2] = (int32_t)lrint(model[2] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[3] = (int32_t)lrint(model[3] * (1 << WARPEDMODEL_PREC_BITS));
607 608
    /* fallthrough intended */
    case TRANSLATION:
609 610
      wm->wmmat[0] = (int32_t)lrint(model[0] * (1 << WARPEDMODEL_PREC_BITS));
      wm->wmmat[1] = (int32_t)lrint(model[1] * (1 << WARPEDMODEL_PREC_BITS));
611 612 613 614
      break;
    default: assert(0 && "Invalid TransformationType");
  }
}
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

///////////////////////////////////////////////////////////////////////////////
// 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]);
668
      if (scale != 0.) {
669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688
        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]);
689
      if (scale != 0.) {
690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710
        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) {
711
      if (g != 0.) {
712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727
        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;
728
    if (g != 0.) {
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
      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) {
782
        aom_free(rv1);
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
        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;
817
        if (z != 0.) {
818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889
          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)) {
890 891 892
    aom_free(U);
    aom_free(W);
    aom_free(V);
893 894 895 896
    return 1;
  }
  for (i = 0; i < N; i++) {
    if (fabs(W[i]) < TINY_NEAR_ZERO) {
897 898 899
      aom_free(U);
      aom_free(W);
      aom_free(V);
900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975
      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);
}

976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992
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) {
993 994 995 996 997 998 999 1000 1001 1002
  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);
1003 1004 1005 1006
  params[0] = params_denorm[2];
  params[1] = params_denorm[5];
  params[2] = params_denorm[0];
  params[3] = params_denorm[1];
1007 1008
  params[4] = params_denorm[3];
  params[5] = params_denorm[4];
1009
  params[6] = params[7] = 0;
1010 1011
}

1012 1013
static void denormalize_rotzoom_reorder(double *params, double *T1,
                                        double *T2) {
1014 1015 1016 1017 1018 1019 1020 1021 1022 1023
  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