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aom/av1/common/warped_motion.c

1234 строки
41 KiB
C
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/*
* 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>
#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(int16_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(int16_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(int16_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(int16_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_4tap[WARPEDPIXEL_PREC_SHIFTS][4] = {
{ 0, 128, 0, 0 }, { -1, 127, 2, 0 }, { -2, 127, 4, -1 },
{ -3, 126, 6, -1 }, { -3, 125, 8, -2 }, { -4, 124, 11, -3 },
{ -5, 123, 13, -3 }, { -5, 121, 15, -3 }, { -6, 120, 18, -4 },
{ -7, 119, 20, -4 }, { -7, 118, 22, -5 }, { -8, 116, 25, -5 },
{ -8, 115, 27, -6 }, { -9, 113, 30, -6 }, { -9, 112, 32, -7 },
{ -9, 110, 34, -7 }, { -10, 108, 37, -7 }, { -10, 107, 39, -8 },
{ -10, 105, 41, -8 }, { -11, 103, 44, -8 }, { -11, 101, 47, -9 },
{ -11, 99, 49, -9 }, { -11, 97, 51, -9 }, { -11, 95, 54, -10 },
{ -11, 93, 56, -10 }, { -12, 91, 59, -10 }, { -12, 89, 61, -10 },
{ -12, 87, 64, -11 }, { -12, 85, 66, -11 }, { -12, 82, 69, -11 },
{ -12, 80, 71, -11 }, { -12, 78, 73, -11 }, { -11, 75, 75, -11 },
{ -11, 73, 78, -12 }, { -11, 71, 80, -12 }, { -11, 69, 82, -12 },
{ -11, 66, 85, -12 }, { -11, 64, 87, -12 }, { -10, 61, 89, -12 },
{ -10, 59, 91, -12 }, { -10, 56, 93, -11 }, { -10, 54, 95, -11 },
{ -9, 51, 97, -11 }, { -9, 49, 99, -11 }, { -9, 47, 101, -11 },
{ -8, 44, 103, -11 }, { -8, 41, 105, -10 }, { -8, 39, 107, -10 },
{ -7, 37, 108, -10 }, { -7, 34, 110, -9 }, { -7, 32, 112, -9 },
{ -6, 30, 113, -9 }, { -6, 27, 115, -8 }, { -5, 25, 116, -8 },
{ -5, 22, 118, -7 }, { -4, 20, 119, -7 }, { -4, 18, 120, -6 },
{ -3, 15, 121, -5 }, { -3, 13, 123, -5 }, { -3, 11, 124, -4 },
{ -2, 8, 125, -3 }, { -1, 6, 126, -3 }, { -1, 4, 127, -2 },
{ 0, 2, 127, -1 },
};
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];
} else if (x == (1 << WARPEDPIXEL_PREC_BITS)) {
return p[1];
} else {
const int64_t v1 = 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((int16_t *)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((int16_t *)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((int16_t *)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((int16_t *)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[3].as_mv.row =
(int16_t)lrint(model[6] * (1 << WARPEDMODEL_ROW3HOMO_PREC_BITS));
wm->wmmat[3].as_mv.col =
(int16_t)lrint(model[7] * (1 << WARPEDMODEL_ROW3HOMO_PREC_BITS));
/* fallthrough intended */
case AFFINE:
wm->wmmat[2].as_mv.row =
(int16_t)lrint(model[4] * (1 << WARPEDMODEL_PREC_BITS));
wm->wmmat[2].as_mv.col =
(int16_t)lrint(model[5] * (1 << WARPEDMODEL_PREC_BITS));
/* fallthrough intended */
case ROTZOOM:
wm->wmmat[1].as_mv.row =
(int16_t)lrint(model[2] * (1 << WARPEDMODEL_PREC_BITS));
wm->wmmat[1].as_mv.col =
(int16_t)lrint(model[3] * (1 << WARPEDMODEL_PREC_BITS));
/* fallthrough intended */
case TRANSLATION:
wm->wmmat[0].as_mv.row =
(int16_t)lrint(model[0] * (1 << WARPEDMODEL_PREC_BITS));
wm->wmmat[0].as_mv.col =
(int16_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) {
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) {
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) {
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) {
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) {
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;
}
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