/* * 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 #include #include #include #include #include "av1/common/warped_motion.h" static ProjectPointsFunc get_project_points_type(TransformationType type) { switch (type) { case HOMOGRAPHY: return project_points_homography; case AFFINE: return project_points_affine; case ROTZOOM: return project_points_rotzoom; case TRANSLATION: return project_points_translation; default: assert(0); return NULL; } } void project_points_translation(int32_t *mat, int *points, int *proj, const int n, const int stride_points, const int stride_proj, const int subsampling_x, const int subsampling_y) { int i; for (i = 0; i < n; ++i) { const int x = *(points++), y = *(points++); if (subsampling_x) *(proj++) = ROUND_POWER_OF_TWO_SIGNED( ((x * (1 << (WARPEDMODEL_PREC_BITS + 1))) + mat[1]), WARPEDDIFF_PREC_BITS + 1); else *(proj++) = ROUND_POWER_OF_TWO_SIGNED( ((x * (1 << WARPEDMODEL_PREC_BITS)) + mat[1]), WARPEDDIFF_PREC_BITS); if (subsampling_y) *(proj++) = ROUND_POWER_OF_TWO_SIGNED( ((y * (1 << (WARPEDMODEL_PREC_BITS + 1))) + mat[0]), WARPEDDIFF_PREC_BITS + 1); else *(proj++) = ROUND_POWER_OF_TWO_SIGNED( ((y * (1 << WARPEDMODEL_PREC_BITS))) + mat[0], WARPEDDIFF_PREC_BITS); points += stride_points - 2; proj += stride_proj - 2; } } void project_points_rotzoom(int32_t *mat, int *points, int *proj, const int n, const int stride_points, const int stride_proj, const int subsampling_x, const int subsampling_y) { int i; for (i = 0; i < n; ++i) { const int x = *(points++), y = *(points++); if (subsampling_x) *(proj++) = ROUND_POWER_OF_TWO_SIGNED( mat[3] * 2 * x + mat[2] * 2 * y + mat[1] + (mat[3] + mat[2] - (1 << WARPEDMODEL_PREC_BITS)) / 2, WARPEDDIFF_PREC_BITS + 1); else *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[3] * x + mat[2] * y + mat[1], WARPEDDIFF_PREC_BITS); if (subsampling_y) *(proj++) = ROUND_POWER_OF_TWO_SIGNED( -mat[2] * 2 * x + mat[3] * 2 * y + mat[0] + (-mat[2] + mat[3] - (1 << WARPEDMODEL_PREC_BITS)) / 2, WARPEDDIFF_PREC_BITS + 1); else *(proj++) = ROUND_POWER_OF_TWO_SIGNED(-mat[2] * x + mat[3] * y + mat[0], WARPEDDIFF_PREC_BITS); points += stride_points - 2; proj += stride_proj - 2; } } void project_points_affine(int32_t *mat, int *points, int *proj, const int n, const int stride_points, const int stride_proj, const int subsampling_x, const int subsampling_y) { int i; for (i = 0; i < n; ++i) { const int x = *(points++), y = *(points++); if (subsampling_x) *(proj++) = ROUND_POWER_OF_TWO_SIGNED( mat[3] * 2 * x + mat[2] * 2 * y + mat[1] + (mat[3] + mat[2] - (1 << WARPEDMODEL_PREC_BITS)) / 2, WARPEDDIFF_PREC_BITS + 1); else *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[3] * x + mat[2] * y + mat[1], WARPEDDIFF_PREC_BITS); if (subsampling_y) *(proj++) = ROUND_POWER_OF_TWO_SIGNED( mat[4] * 2 * x + mat[5] * 2 * y + mat[0] + (mat[4] + mat[5] - (1 << WARPEDMODEL_PREC_BITS)) / 2, WARPEDDIFF_PREC_BITS + 1); else *(proj++) = ROUND_POWER_OF_TWO_SIGNED(mat[4] * x + mat[5] * y + mat[0], WARPEDDIFF_PREC_BITS); points += stride_points - 2; proj += stride_proj - 2; } } void project_points_homography(int32_t *mat, int *points, int *proj, const int n, const int stride_points, const int stride_proj, const int subsampling_x, const int subsampling_y) { int i; int64_t x, y, Z; int64_t xp, yp; 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); Z = (mat[7] * x + mat[6] * y + (1 << (WARPEDMODEL_ROW3HOMO_PREC_BITS + 1))); xp = (mat[1] * x + mat[0] * y + 2 * mat[3]) * (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS - WARPEDMODEL_PREC_BITS)); yp = (mat[2] * x + mat[5] * y + 2 * mat[4]) * (1 << (WARPEDPIXEL_PREC_BITS + WARPEDMODEL_ROW3HOMO_PREC_BITS - WARPEDMODEL_PREC_BITS)); xp = xp > 0 ? (xp + Z / 2) / Z : (xp - Z / 2) / Z; yp = yp > 0 ? (yp + Z / 2) / Z : (yp - Z / 2) / Z; if (subsampling_x) xp = (xp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2; if (subsampling_y) yp = (yp - (1 << (WARPEDPIXEL_PREC_BITS - 1))) / 2; *(proj++) = xp; *(proj++) = yp; points += stride_points - 2; proj += stride_proj - 2; } } static const int16_t 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 }, }; 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) { if (x == 0) { return p[0] * (1 << WARPEDPIXEL_FILTER_BITS); } else if (x == (1 << WARPEDPIXEL_PREC_BITS)) { return p[1] * (1 << WARPEDPIXEL_FILTER_BITS); } else { const int64_t v1 = (int64_t)x * x * x * (3 * (p[0] - p[1]) + p[2] - p[-1]); 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]; return (int32_t)ROUND_POWER_OF_TWO_SIGNED( (v4 * (1 << (3 * WARPEDPIXEL_PREC_BITS))) + (v3 * (1 << (2 * WARPEDPIXEL_PREC_BITS))) + (v2 * (1 << WARPEDPIXEL_PREC_BITS)) + v1, 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; int i = (int)x >> WARPEDPIXEL_PREC_BITS; int j = (int)y >> WARPEDPIXEL_PREC_BITS; 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, y - (j * (1 << WARPEDPIXEL_PREC_BITS))); } val = do_ntap_filter(arr + WARPEDPIXEL_FILTER_TAPS / 2 - 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS))); 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; int i = (int)x >> WARPEDPIXEL_PREC_BITS; int j = (int)y >> WARPEDPIXEL_PREC_BITS; for (k = 0; k < 4; ++k) { int32_t arr_temp[4]; get_subcolumn(4, ref, arr_temp, stride, i + k - 1, j - 1); arr[k] = do_cubic_filter(arr_temp + 1, y - (j * (1 << WARPEDPIXEL_PREC_BITS))); } val = do_cubic_filter(arr + 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS))); 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; const int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS)); const int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS)); int32_t val; val = ROUND_POWER_OF_TWO_SIGNED( ref[iy * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sy) * (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, WARPEDPIXEL_PREC_BITS * 2); return (uint8_t)clip_pixel(val); } static uint8_t warp_interpolate(uint8_t *ref, int x, int y, int width, int height, int stride) { int ix = x >> WARPEDPIXEL_PREC_BITS; int iy = y >> WARPEDPIXEL_PREC_BITS; int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS)); int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS)); int32_t v; if (ix < 0 && iy < 0) return ref[0]; 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) + ref[(iy + 1) * stride] * sy, WARPEDPIXEL_PREC_BITS); return clip_pixel(v); } else if (iy < 0) { v = ROUND_POWER_OF_TWO_SIGNED( ref[ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) + ref[ix + 1] * sx, 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) + ref[(iy + 1) * stride + width - 1] * sy, 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) + ref[(height - 1) * stride + ix + 1] * sx, 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); } else if (ix >= 1 && iy >= 1 && ix < width - 2 && iy < height - 2) { return bi_cubic_filter(ref, x, y, stride); } else { return bi_linear_filter(ref, x, y, stride); } } #if CONFIG_AOM_HIGHBITDEPTH 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]; } } static uint16_t highbd_bi_ntap_filter(uint16_t *ref, int x, int y, int stride, int bd) { int32_t val, arr[WARPEDPIXEL_FILTER_TAPS]; int k; int i = (int)x >> WARPEDPIXEL_PREC_BITS; int j = (int)y >> WARPEDPIXEL_PREC_BITS; 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, y - (j * (1 << WARPEDPIXEL_PREC_BITS))); } val = do_ntap_filter(arr + WARPEDPIXEL_FILTER_TAPS / 2 - 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS))); val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2); return (uint16_t)clip_pixel_highbd(val, bd); } static uint16_t highbd_bi_cubic_filter(uint16_t *ref, int x, int y, int stride, int bd) { int32_t val, arr[4]; int k; int i = (int)x >> WARPEDPIXEL_PREC_BITS; int j = (int)y >> WARPEDPIXEL_PREC_BITS; for (k = 0; k < 4; ++k) { int32_t arr_temp[4]; highbd_get_subcolumn(4, ref, arr_temp, stride, i + k - 1, j - 1); arr[k] = do_cubic_filter(arr_temp + 1, y - (j * (1 << WARPEDPIXEL_PREC_BITS))); } val = do_cubic_filter(arr + 1, x - (i * (1 << WARPEDPIXEL_PREC_BITS))); val = ROUND_POWER_OF_TWO_SIGNED(val, WARPEDPIXEL_FILTER_BITS * 2); return (uint16_t)clip_pixel_highbd(val, bd); } static uint16_t highbd_bi_linear_filter(uint16_t *ref, int x, int y, int stride, int bd) { const int ix = x >> WARPEDPIXEL_PREC_BITS; const int iy = y >> WARPEDPIXEL_PREC_BITS; const int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS)); const int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS)); int32_t val; val = ROUND_POWER_OF_TWO_SIGNED( ref[iy * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sy) * (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, WARPEDPIXEL_PREC_BITS * 2); return (uint16_t)clip_pixel_highbd(val, bd); } static uint16_t highbd_warp_interpolate(uint16_t *ref, int x, int y, int width, int height, int stride, int bd) { int ix = x >> WARPEDPIXEL_PREC_BITS; int iy = y >> WARPEDPIXEL_PREC_BITS; int sx = x - (ix * (1 << WARPEDPIXEL_PREC_BITS)); int sy = y - (iy * (1 << WARPEDPIXEL_PREC_BITS)); int32_t v; if (ix < 0 && iy < 0) return ref[0]; 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) + ref[(iy + 1) * stride] * sy, WARPEDPIXEL_PREC_BITS); return clip_pixel_highbd(v, bd); } else if (iy < 0) { v = ROUND_POWER_OF_TWO_SIGNED( ref[ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) + ref[ix + 1] * sx, WARPEDPIXEL_PREC_BITS); return clip_pixel_highbd(v, bd); } else if (ix > width - 1) { v = ROUND_POWER_OF_TWO_SIGNED( ref[iy * stride + width - 1] * (WARPEDPIXEL_PREC_SHIFTS - sy) + ref[(iy + 1) * stride + width - 1] * sy, WARPEDPIXEL_PREC_BITS); return clip_pixel_highbd(v, bd); } else if (iy > height - 1) { v = ROUND_POWER_OF_TWO_SIGNED( ref[(height - 1) * stride + ix] * (WARPEDPIXEL_PREC_SHIFTS - sx) + ref[(height - 1) * stride + ix + 1] * sx, WARPEDPIXEL_PREC_BITS); return clip_pixel_highbd(v, bd); } 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); } else if (ix >= 1 && iy >= 1 && ix < width - 2 && iy < height - 2) { return highbd_bi_cubic_filter(ref, x, y, stride, bd); } else { return highbd_bi_linear_filter(ref, x, y, stride, bd); } } 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; ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype); uint16_t *dst = CONVERT_TO_SHORTPTR(dst8); uint16_t *ref = CONVERT_TO_SHORTPTR(ref8); int gm_err = 0, no_gm_err = 0; int64_t gm_sumerr = 0, no_gm_sumerr = 0; 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; projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y); 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]; gm_sumerr += (int64_t)gm_err * gm_err; no_gm_sumerr += (int64_t)no_gm_err * no_gm_err; } } return (double)gm_sumerr / no_gm_sumerr; } 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, int bd, int ref_frm) { int i, j; ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype); uint16_t *pred = CONVERT_TO_SHORTPTR(pred8); uint16_t *ref = CONVERT_TO_SHORTPTR(ref8); 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; projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y); out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4); out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4); 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); } } } #endif // CONFIG_AOM_HIGHBITDEPTH 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; ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype); 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; projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y); 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]; gm_sumerr += gm_err * gm_err; no_gm_sumerr += no_gm_err * no_gm_err; } } 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, int y_scale, int ref_frm) { int i, j; ProjectPointsFunc projectpoints = get_project_points_type(wm->wmtype); 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; projectpoints(wm->wmmat, in, out, 1, 2, 2, subsampling_x, subsampling_y); out[0] = ROUND_POWER_OF_TWO_SIGNED(out[0] * x_scale, 4); out[1] = ROUND_POWER_OF_TWO_SIGNED(out[1] * y_scale, 4); 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); } } } 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 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); #endif // CONFIG_AOM_HIGHBITDEPTH 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); } 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, int subsampling_y, int x_scale, int y_scale, int ref_frm) { #if CONFIG_AOM_HIGHBITDEPTH if (use_hbd) highbd_warp_plane(wm, ref, width, height, stride, pred, p_col, p_row, p_width, p_height, p_stride, subsampling_x, subsampling_y, x_scale, y_scale, bd, ref_frm); else #endif // CONFIG_AOM_HIGHBITDEPTH warp_plane(wm, ref, width, height, stride, pred, p_col, p_row, p_width, p_height, p_stride, subsampling_x, subsampling_y, x_scale, y_scale, ref_frm); } void av1_integerize_model(const double *model, TransformationType wmtype, WarpedMotionParams *wm) { wm->wmtype = wmtype; switch (wmtype) { case HOMOGRAPHY: assert(fabs(model[8] - 1.0) < 1e-12); 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)); /* fallthrough intended */ case AFFINE: wm->wmmat[4] = (int32_t)lrint(model[4] * (1 << WARPEDMODEL_PREC_BITS)); wm->wmmat[5] = (int32_t)lrint(model[5] * (1 << WARPEDMODEL_PREC_BITS)); /* fallthrough intended */ case ROTZOOM: wm->wmmat[2] = (int32_t)lrint(model[2] * (1 << WARPEDMODEL_PREC_BITS)); wm->wmmat[3] = (int32_t)lrint(model[3] * (1 << WARPEDMODEL_PREC_BITS)); /* fallthrough intended */ case TRANSLATION: wm->wmmat[0] = (int32_t)lrint(model[0] * (1 << WARPEDMODEL_PREC_BITS)); wm->wmmat[1] = (int32_t)lrint(model[1] * (1 << WARPEDMODEL_PREC_BITS)); break; default: assert(0 && "Invalid TransformationType"); } } /////////////////////////////////////////////////////////////////////////////// // 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]); if (scale != 0.) { 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]); if (scale != 0.) { 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) { if (g != 0.) { 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; if (g != 0.) { 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) { 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; if (z != 0.) { 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)) { return 1; } for (i = 0; i < N; i++) { if (fabs(W[i]) < TINY_NEAR_ZERO) { 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) { // Assume the points are 2d coordinates with scale = 1 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); } static void denormalize_affine(double *params, double *T1, double *T2) { 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); params[0] = params_denorm[5]; params[1] = params_denorm[2]; params[2] = params_denorm[1]; params[3] = params_denorm[0]; params[4] = params_denorm[3]; params[5] = params_denorm[4]; } static void denormalize_rotzoom(double *params, double *T1, double *T2) { 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); params[0] = params_denorm[5]; params[1] = params_denorm[2]; params[2] = params_denorm[1]; params[3] = params_denorm[0]; } static void denormalize_translation(double *params, double *T1, double *T2) { 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); params[0] = params_denorm[5]; params[1] = params_denorm[2]; } 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; denormalize_translation(mat, T1, T2); 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); denormalize_rotzoom(mat, T1, T2); 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); denormalize_affine(mat, T1, T2); 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; double S[9], V[9 * 9]; 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; } } } for (i = 0; i < 9; i++) mat[i] = V[i * 9 + mini]; denormalize_homography(mat, T1, T2); aom_free(a); if (mat[8] == 0.0) { return 1; } return 0; }