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/*
* Copyright (c) 2022, Alliance for Open Media. All rights reserved
*
* This source code is subject to the terms of the BSD 3-Clause Clear License
* and the Alliance for Open Media Patent License 1.0. If the BSD 3-Clause Clear
* License was not distributed with this source code in the LICENSE file, you
* can obtain it at aomedia.org/license/software-license/bsd-3-c-c/. If the
* Alliance for Open Media Patent License 1.0 was not distributed with this
* source code in the PATENTS file, you can obtain it at
* aomedia.org/license/patent-license/.
*/
#include <assert.h>
#include <math.h>
#include <smmintrin.h>
#include "aom_dsp/aom_dsp_common.h"
#include "aom_dsp/flow_estimation/disflow.h"
#include "aom_dsp/x86/synonyms.h"
#include "config/aom_dsp_rtcd.h"
// Internal cross-check against C code
// If you set this to 1 and compile in debug mode, then the outputs of the two
// convolution stages will be checked against the plain C version of the code,
// and an assertion will be fired if the results differ.
#define CHECK_RESULTS 1
// Note: Max sum(+ve coefficients) = 1.125 * scale
static INLINE void get_cubic_kernel_dbl(double x, double *kernel) {
assert(0 <= x && x < 1);
double x2 = x * x;
double x3 = x2 * x;
kernel[0] = -0.5 * x + x2 - 0.5 * x3;
kernel[1] = 1.0 - 2.5 * x2 + 1.5 * x3;
kernel[2] = 0.5 * x + 2.0 * x2 - 1.5 * x3;
kernel[3] = -0.5 * x2 + 0.5 * x3;
}
static INLINE void get_cubic_kernel_int(double x, int16_t *kernel) {
double kernel_dbl[4];
get_cubic_kernel_dbl(x, kernel_dbl);
kernel[0] = (int16_t)rint(kernel_dbl[0] * (1 << DISFLOW_INTERP_BITS));
kernel[1] = (int16_t)rint(kernel_dbl[1] * (1 << DISFLOW_INTERP_BITS));
kernel[2] = (int16_t)rint(kernel_dbl[2] * (1 << DISFLOW_INTERP_BITS));
kernel[3] = (int16_t)rint(kernel_dbl[3] * (1 << DISFLOW_INTERP_BITS));
}
#if CHECK_RESULTS
static INLINE int get_cubic_value_int(const int *p, const int16_t *kernel) {
return kernel[0] * p[0] + kernel[1] * p[1] + kernel[2] * p[2] +
kernel[3] * p[3];
}
#endif // CHECK_RESULTS
// Compare two regions of width x height pixels, one rooted at position
// (x, y) in src and the other at (x + u, y + v) in ref.
// This function returns the sum of squared pixel differences between
// the two regions.
//
// TODO(rachelbarker): Test speed/quality impact of using bilinear interpolation
// instad of bicubic interpolation
static INLINE void compute_flow_error(const uint8_t *src, const uint8_t *ref,
int width, int height, int stride, int x,
int y, double u, double v, int16_t *dt) {
// This function is written to do 8x8 convolutions only
assert(DISFLOW_PATCH_SIZE == 8);
// Split offset into integer and fractional parts, and compute cubic
// interpolation kernels
const int u_int = (int)floor(u);
const int v_int = (int)floor(v);
const double u_frac = u - floor(u);
const double v_frac = v - floor(v);
int16_t h_kernel[4];
int16_t v_kernel[4];
get_cubic_kernel_int(u_frac, h_kernel);
get_cubic_kernel_int(v_frac, v_kernel);
// Storage for intermediate values between the two convolution directions
int16_t tmp_[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 3)];
int16_t *tmp = tmp_ + DISFLOW_PATCH_SIZE; // Offset by one row
// Clamp coordinates so that all pixels we fetch will remain within the
// allocated border region, but allow them to go far enough out that
// the border pixels' values do not change.
// Since we are calculating an 8x8 block, the bottom-right pixel
// in the block has coordinates (x0 + 7, y0 + 7). Then, the cubic
// interpolation has 4 taps, meaning that the output of pixel
// (x_w, y_w) depends on the pixels in the range
// ([x_w - 1, x_w + 2], [y_w - 1, y_w + 2]).
//
// Thus the most extreme coordinates which will be fetched are
// (x0 - 1, y0 - 1) and (x0 + 9, y0 + 9).
const int x0 = clamp(x + u_int, -9, width);
const int y0 = clamp(y + v_int, -9, height);
// Horizontal convolution
// Prepare the kernel vectors
// We split the kernel into two vectors with kernel indices:
// 0, 1, 0, 1, 0, 1, 0, 1, and
// 2, 3, 2, 3, 2, 3, 2, 3
__m128i h_kernel_01 = xx_set2_epi16(h_kernel[0], h_kernel[1]);
__m128i h_kernel_23 = xx_set2_epi16(h_kernel[2], h_kernel[3]);
__m128i round_const_h = _mm_set1_epi32(1 << (DISFLOW_INTERP_BITS - 6 - 1));
for (int i = -1; i < DISFLOW_PATCH_SIZE + 2; ++i) {
const int y_w = y0 + i;
const uint8_t *ref_row = &ref[y_w * stride + (x0 - 1)];
int16_t *tmp_row = &tmp[i * DISFLOW_PATCH_SIZE];
// Load this row of pixels.
// For an 8x8 patch, we need to load the 8 image pixels + 3 extras,
// for a total of 11 pixels. Here we load 16 pixels, but only use
// the first 11.
__m128i row = _mm_loadu_si128((__m128i *)ref_row);
// Expand pixels to int16s
__m128i px_0to7_i16 = _mm_cvtepu8_epi16(row);
__m128i px_4to10_i16 = _mm_cvtepu8_epi16(_mm_srli_si128(row, 4));
// Relevant multiply instruction
// This multiplies pointwise, then sums in pairs.
//_mm_madd_epi16();
// Compute first four outputs
// input pixels 0, 1, 1, 2, 2, 3, 3, 4
// * kernel 0, 1, 0, 1, 0, 1, 0, 1
__m128i px0 =
_mm_unpacklo_epi16(px_0to7_i16, _mm_srli_si128(px_0to7_i16, 2));
// input pixels 2, 3, 3, 4, 4, 5, 5, 6
// * kernel 2, 3, 2, 3, 2, 3, 2, 3
__m128i px1 = _mm_unpacklo_epi16(_mm_srli_si128(px_0to7_i16, 4),
_mm_srli_si128(px_0to7_i16, 6));
// Convolve with kernel and sum 2x2 boxes to form first 4 outputs
__m128i sum0 = _mm_add_epi32(_mm_madd_epi16(px0, h_kernel_01),
_mm_madd_epi16(px1, h_kernel_23));
__m128i out0 = _mm_srai_epi32(_mm_add_epi32(sum0, round_const_h),
DISFLOW_INTERP_BITS - 6);
// Compute second four outputs
__m128i px2 =
_mm_unpacklo_epi16(px_4to10_i16, _mm_srli_si128(px_4to10_i16, 2));
__m128i px3 = _mm_unpacklo_epi16(_mm_srli_si128(px_4to10_i16, 4),
_mm_srli_si128(px_4to10_i16, 6));
__m128i sum1 = _mm_add_epi32(_mm_madd_epi16(px2, h_kernel_01),
_mm_madd_epi16(px3, h_kernel_23));
// Round by just enough bits that the result is
// guaranteed to fit into an i16. Then the next stage can use 16 x 16 -> 32
// bit multiplies, which should be a fair bit faster than 32 x 32 -> 32
// as it does now
// This means shifting down so we have 6 extra bits, for a maximum value
// of +18360, which can occur if u_frac == 0.5 and the input pixels are
// {0, 255, 255, 0}.
__m128i out1 = _mm_srai_epi32(_mm_add_epi32(sum1, round_const_h),
DISFLOW_INTERP_BITS - 6);
_mm_storeu_si128((__m128i *)tmp_row, _mm_packs_epi32(out0, out1));
#if CHECK_RESULTS && !defined(NDEBUG)
// Cross-check
for (int j = 0; j < DISFLOW_PATCH_SIZE; ++j) {
const int x_w = x0 + j;
int arr[4];
arr[0] = (int)ref[y_w * stride + (x_w - 1)];
arr[1] = (int)ref[y_w * stride + (x_w + 0)];
arr[2] = (int)ref[y_w * stride + (x_w + 1)];
arr[3] = (int)ref[y_w * stride + (x_w + 2)];
// Apply kernel and round, keeping 6 extra bits of precision.
//
// 6 is the maximum allowable number of extra bits which will avoid
// the intermediate values overflowing an int16_t. The most extreme
// intermediate value occurs when:
// * The input pixels are [0, 255, 255, 0]
// * u_frac = 0.5
// In this case, the un-scaled output is 255 * 1.125 = 286.875.
// As an integer with 6 fractional bits, that is 18360, which fits
// in an int16_t. But with 7 fractional bits it would be 36720,
// which is too large.
const int c_value = ROUND_POWER_OF_TWO(get_cubic_value_int(arr, h_kernel),
DISFLOW_INTERP_BITS - 6);
(void)c_value; // Suppress warnings
assert(tmp_row[j] == c_value);
}
#endif // CHECK_RESULTS
}
// Vertical convolution
const int round_bits = DISFLOW_INTERP_BITS + 6 - DISFLOW_DERIV_SCALE_LOG2;
__m128i round_const_v = _mm_set1_epi32(1 << (round_bits - 1));
__m128i v_kernel_01 = xx_set2_epi16(v_kernel[0], v_kernel[1]);
__m128i v_kernel_23 = xx_set2_epi16(v_kernel[2], v_kernel[3]);
for (int i = 0; i < DISFLOW_PATCH_SIZE; ++i) {
int16_t *tmp_row = &tmp[i * DISFLOW_PATCH_SIZE];
// Load 4 rows of 8 x 16-bit values
__m128i px0 = _mm_loadu_si128((__m128i *)(tmp_row - DISFLOW_PATCH_SIZE));
__m128i px1 = _mm_loadu_si128((__m128i *)tmp_row);
__m128i px2 = _mm_loadu_si128((__m128i *)(tmp_row + DISFLOW_PATCH_SIZE));
__m128i px3 =
_mm_loadu_si128((__m128i *)(tmp_row + 2 * DISFLOW_PATCH_SIZE));
// We want to calculate px0 * v_kernel[0] + px1 * v_kernel[1] + ... ,
// but each multiply expands its output to 32 bits. So we need to be
// a little clever about how we do this
__m128i sum0 = _mm_add_epi32(
_mm_madd_epi16(_mm_unpacklo_epi16(px0, px1), v_kernel_01),
_mm_madd_epi16(_mm_unpacklo_epi16(px2, px3), v_kernel_23));
__m128i sum1 = _mm_add_epi32(
_mm_madd_epi16(_mm_unpackhi_epi16(px0, px1), v_kernel_01),
_mm_madd_epi16(_mm_unpackhi_epi16(px2, px3), v_kernel_23));
__m128i sum0_rounded =
_mm_srai_epi32(_mm_add_epi32(sum0, round_const_v), round_bits);
__m128i sum1_rounded =
_mm_srai_epi32(_mm_add_epi32(sum1, round_const_v), round_bits);
__m128i warped = _mm_packs_epi32(sum0_rounded, sum1_rounded);
__m128i src_pixels_u8 =
_mm_loadl_epi64((__m128i *)&src[(y + i) * stride + x]);
__m128i src_pixels = _mm_slli_epi16(_mm_cvtepu8_epi16(src_pixels_u8), 3);
// Calculate delta from the target patch
__m128i err = _mm_sub_epi16(warped, src_pixels);
_mm_storeu_si128((__m128i *)&dt[i * DISFLOW_PATCH_SIZE], err);
#if CHECK_RESULTS
for (int j = 0; j < DISFLOW_PATCH_SIZE; ++j) {
int16_t *p = &tmp[i * DISFLOW_PATCH_SIZE + j];
int arr[4] = { p[-DISFLOW_PATCH_SIZE], p[0], p[DISFLOW_PATCH_SIZE],
p[2 * DISFLOW_PATCH_SIZE] };
const int result = get_cubic_value_int(arr, v_kernel);
// Apply kernel and round.
// This time, we have to round off the 6 extra bits which were kept
// earlier, but we also want to keep DISFLOW_DERIV_SCALE_LOG2 extra bits
// of precision to match the scale of the dx and dy arrays.
const int c_warped = ROUND_POWER_OF_TWO(result, round_bits);
const int c_src_px = src[(x + j) + (y + i) * stride] << 3;
const int c_err = c_warped - c_src_px;
(void)c_err;
assert(dt[i * DISFLOW_PATCH_SIZE + j] == c_err);
}
#endif // CHECK_RESULTS
}
}
static INLINE void sobel_filter_x(const uint8_t *src, int src_stride,
int16_t *dst, int dst_stride) {
int16_t tmp_[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 2)];
int16_t *tmp = tmp_ + DISFLOW_PATCH_SIZE;
const int taps = 3;
// Horizontal filter
// As the kernel is simply {1, 0, -1}, we implement this as simply
// out[x] = image[x-1] - image[x+1]
// rather than doing a "proper" convolution operation
for (int y = -1; y < DISFLOW_PATCH_SIZE + 1; ++y) {
const uint8_t *src_row = src + y * src_stride;
int16_t *tmp_row = tmp + y * DISFLOW_PATCH_SIZE;
// Load pixels and expand to 16 bits
__m128i row = _mm_loadu_si128((__m128i *)(src_row - 1));
__m128i px0 = _mm_cvtepu8_epi16(row);
__m128i px2 = _mm_cvtepu8_epi16(_mm_srli_si128(row, 2));
__m128i out = _mm_sub_epi16(px0, px2);
// Store to intermediate array
_mm_storeu_si128((__m128i *)tmp_row, out);
#if CHECK_RESULTS
// Cross-check
static const int16_t h_kernel[3] = { 1, 0, -1 };
for (int x = 0; x < DISFLOW_PATCH_SIZE; ++x) {
int sum = 0;
for (int k = 0; k < taps; ++k) {
sum += h_kernel[k] * src_row[x + k - 1];
}
(void)sum;
assert(tmp_row[x] == sum);
}
#endif // CHECK_RESULTS
}
// Vertical filter
// Here the kernel is {1, 2, 1}, which can be implemented
// with simple sums rather than multiplies and adds.
// In order to minimize dependency chains, we evaluate in the order
// (image[y - 1] + image[y + 1]) + (image[y] << 1)
// This way, the first addition and the shift can happen in parallel
for (int y = 0; y < DISFLOW_PATCH_SIZE; ++y) {
const int16_t *tmp_row = tmp + y * DISFLOW_PATCH_SIZE;
int16_t *dst_row = dst + y * dst_stride;
__m128i px0 = _mm_loadu_si128((__m128i *)(tmp_row - DISFLOW_PATCH_SIZE));
__m128i px1 = _mm_loadu_si128((__m128i *)tmp_row);
__m128i px2 = _mm_loadu_si128((__m128i *)(tmp_row + DISFLOW_PATCH_SIZE));
__m128i out =
_mm_add_epi16(_mm_add_epi16(px0, px2), _mm_slli_epi16(px1, 1));
_mm_storeu_si128((__m128i *)dst_row, out);
#if CHECK_RESULTS
static const int16_t v_kernel[3] = { 1, 2, 1 };
for (int x = 0; x < DISFLOW_PATCH_SIZE; ++x) {
int sum = 0;
for (int k = 0; k < taps; ++k) {
sum += v_kernel[k] * tmp[(y + k - 1) * DISFLOW_PATCH_SIZE + x];
}
(void)sum;
assert(dst_row[x] == sum);
}
#endif // CHECK_RESULTS
}
}
static INLINE void sobel_filter_y(const uint8_t *src, int src_stride,
int16_t *dst, int dst_stride) {
int16_t tmp_[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 2)];
int16_t *tmp = tmp_ + DISFLOW_PATCH_SIZE;
const int taps = 3;
// Horizontal filter
// Here the kernel is {1, 2, 1}, which can be implemented
// with simple sums rather than multiplies and adds.
// In order to minimize dependency chains, we evaluate in the order
// (image[y - 1] + image[y + 1]) + (image[y] << 1)
// This way, the first addition and the shift can happen in parallel
for (int y = -1; y < DISFLOW_PATCH_SIZE + 1; ++y) {
const uint8_t *src_row = src + y * src_stride;
int16_t *tmp_row = tmp + y * DISFLOW_PATCH_SIZE;
// Load pixels and expand to 16 bits
__m128i row = _mm_loadu_si128((__m128i *)(src_row - 1));
__m128i px0 = _mm_cvtepu8_epi16(row);
__m128i px1 = _mm_cvtepu8_epi16(_mm_srli_si128(row, 1));
__m128i px2 = _mm_cvtepu8_epi16(_mm_srli_si128(row, 2));
__m128i out =
_mm_add_epi16(_mm_add_epi16(px0, px2), _mm_slli_epi16(px1, 1));
// Store to intermediate array
_mm_storeu_si128((__m128i *)tmp_row, out);
#if CHECK_RESULTS
// Cross-check
static const int16_t h_kernel[3] = { 1, 2, 1 };
for (int x = 0; x < DISFLOW_PATCH_SIZE; ++x) {
int sum = 0;
for (int k = 0; k < taps; ++k) {
sum += h_kernel[k] * src_row[x + k - 1];
}
(void)sum;
assert(tmp_row[x] == sum);
}
#endif // CHECK_RESULTS
}
// Vertical filter
// As the kernel is simply {1, 0, -1}, we implement this as simply
// out[x] = image[x-1] - image[x+1]
// rather than doing a "proper" convolution operation
for (int y = 0; y < DISFLOW_PATCH_SIZE; ++y) {
const int16_t *tmp_row = tmp + y * DISFLOW_PATCH_SIZE;
int16_t *dst_row = dst + y * dst_stride;
__m128i px0 = _mm_loadu_si128((__m128i *)(tmp_row - DISFLOW_PATCH_SIZE));
__m128i px2 = _mm_loadu_si128((__m128i *)(tmp_row + DISFLOW_PATCH_SIZE));
__m128i out = _mm_sub_epi16(px0, px2);
_mm_storeu_si128((__m128i *)dst_row, out);
#if CHECK_RESULTS
static const int16_t v_kernel[3] = { 1, 0, -1 };
for (int x = 0; x < DISFLOW_PATCH_SIZE; ++x) {
int sum = 0;
for (int k = 0; k < taps; ++k) {
sum += v_kernel[k] * tmp[(y + k - 1) * DISFLOW_PATCH_SIZE + x];
}
(void)sum;
assert(dst_row[x] == sum);
}
#endif // CHECK_RESULTS
}
}
static INLINE void compute_flow_vector(const int16_t *dx, int dx_stride,
const int16_t *dy, int dy_stride,
const int16_t *dt, int dt_stride,
int *b) {
__m128i b0_acc = _mm_setzero_si128();
__m128i b1_acc = _mm_setzero_si128();
for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
// Need to load 8 values of dx, 8 of dy, 8 of dt, which conveniently
// works out to one register each. Then just calculate dx * dt, dy * dt,
// and (implicitly) sum horizontally in pairs.
// This gives four 32-bit partial sums for each of b[0] and b[1],
// which can be accumulated and summed at the end.
__m128i dx_row = _mm_loadu_si128((__m128i *)&dx[i * dx_stride]);
__m128i dy_row = _mm_loadu_si128((__m128i *)&dy[i * dy_stride]);
__m128i dt_row = _mm_loadu_si128((__m128i *)&dt[i * dt_stride]);
b0_acc = _mm_add_epi32(b0_acc, _mm_madd_epi16(dx_row, dt_row));
b1_acc = _mm_add_epi32(b1_acc, _mm_madd_epi16(dy_row, dt_row));
}
// We need to set b[0] = sum(b0_acc), b[1] = sum(b1_acc).
// We might as well use a `hadd` instruction to do 4 of the additions
// needed here. Then that just leaves two more additions, which can be
// done in scalar code
__m128i partial_sum = _mm_hadd_epi32(b0_acc, b1_acc);
b[0] = _mm_extract_epi32(partial_sum, 0) + _mm_extract_epi32(partial_sum, 1);
b[1] = _mm_extract_epi32(partial_sum, 2) + _mm_extract_epi32(partial_sum, 3);
#if CHECK_RESULTS
int c_result[2] = { 0 };
for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
for (int j = 0; j < DISFLOW_PATCH_SIZE; j++) {
c_result[0] += dx[i * dx_stride + j] * dt[i * dt_stride + j];
c_result[1] += dy[i * dy_stride + j] * dt[i * dt_stride + j];
}
}
assert(b[0] == c_result[0]);
assert(b[1] == c_result[1]);
#endif // CHECK_RESULTS
}
static INLINE void compute_flow_matrix(const int16_t *dx, int dx_stride,
const int16_t *dy, int dy_stride,
double *M) {
__m128i acc[4] = { 0 };
for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
__m128i dx_row = _mm_loadu_si128((__m128i *)&dx[i * dx_stride]);
__m128i dy_row = _mm_loadu_si128((__m128i *)&dy[i * dy_stride]);
acc[0] = _mm_add_epi32(acc[0], _mm_madd_epi16(dx_row, dx_row));
acc[1] = _mm_add_epi32(acc[1], _mm_madd_epi16(dx_row, dy_row));
// Don't compute acc[2], as it should be equal to acc[1]
acc[3] = _mm_add_epi32(acc[3], _mm_madd_epi16(dy_row, dy_row));
}
// Condense sums
__m128i partial_sum_0 = _mm_hadd_epi32(acc[0], acc[1]);
__m128i partial_sum_1 = _mm_hadd_epi32(acc[1], acc[3]);
__m128i result = _mm_hadd_epi32(partial_sum_0, partial_sum_1);
// Apply regularization
// We follow the standard regularization method of adding `k * I` before
// inverting. This ensures that the matrix will be invertible.
//
// Setting the regularization strength k to 1 seems to work well here, as
// typical values coming from the other equations are very large (1e5 to
// 1e6, with an upper limit of around 6e7, at the time of writing).
// It also preserves the property that all matrix values are whole numbers,
// which is convenient for integerized SIMD implementation.
result = _mm_add_epi32(result, _mm_set_epi32(1, 0, 0, 1));
#if CHECK_RESULTS
int tmp[4] = { 0 };
for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {
for (int j = 0; j < DISFLOW_PATCH_SIZE; j++) {
tmp[0] += dx[i * dx_stride + j] * dx[i * dx_stride + j];
tmp[1] += dx[i * dx_stride + j] * dy[i * dy_stride + j];
// Don't compute tmp[2], as it should be equal to tmp[1]
tmp[3] += dy[i * dy_stride + j] * dy[i * dy_stride + j];
}
}
// Apply regularization
tmp[0] += 1;
tmp[3] += 1;
tmp[2] = tmp[1];
assert(tmp[0] == _mm_extract_epi32(result, 0));
assert(tmp[1] == _mm_extract_epi32(result, 1));
assert(tmp[2] == _mm_extract_epi32(result, 2));
assert(tmp[3] == _mm_extract_epi32(result, 3));
#endif // CHECK_RESULTS
// Convert results to doubles and store
_mm_storeu_pd(M, _mm_cvtepi32_pd(result));
_mm_storeu_pd(M + 2, _mm_cvtepi32_pd(_mm_srli_si128(result, 8)));
}
// Try to invert the matrix M
// Note: Due to the nature of how a least-squares matrix is constructed, all of
// the eigenvalues will be >= 0, and therefore det M >= 0 as well.
// The regularization term `+ k * I` further ensures that det M >= k^2.
// As mentioned in compute_flow_matrix(), here we use k = 1, so det M >= 1.
// So we don't have to worry about non-invertible matrices here.
static INLINE void invert_2x2(const double *M, double *M_inv) {
double det = (M[0] * M[3]) - (M[1] * M[2]);
assert(det >= 1);
const double det_inv = 1 / det;
M_inv[0] = M[3] * det_inv;
M_inv[1] = -M[1] * det_inv;
M_inv[2] = -M[2] * det_inv;
M_inv[3] = M[0] * det_inv;
}
void aom_compute_flow_at_point_sse4_1(const uint8_t *src, const uint8_t *ref,
int x, int y, int width, int height,
int stride, double *u, double *v) {
double M[4];
double M_inv[4];
int b[2];
int16_t dt[DISFLOW_PATCH_SIZE * DISFLOW_PATCH_SIZE];
int16_t dx[DISFLOW_PATCH_SIZE * DISFLOW_PATCH_SIZE];
int16_t dy[DISFLOW_PATCH_SIZE * DISFLOW_PATCH_SIZE];
// Compute gradients within this patch
const uint8_t *src_patch = &src[y * stride + x];
sobel_filter_x(src_patch, stride, dx, DISFLOW_PATCH_SIZE);
sobel_filter_y(src_patch, stride, dy, DISFLOW_PATCH_SIZE);
compute_flow_matrix(dx, DISFLOW_PATCH_SIZE, dy, DISFLOW_PATCH_SIZE, M);
invert_2x2(M, M_inv);
for (int itr = 0; itr < DISFLOW_MAX_ITR; itr++) {
compute_flow_error(src, ref, width, height, stride, x, y, *u, *v, dt);
compute_flow_vector(dx, DISFLOW_PATCH_SIZE, dy, DISFLOW_PATCH_SIZE, dt,
DISFLOW_PATCH_SIZE, b);
// Solve flow equations to find a better estimate for the flow vector
// at this point
const double step_u = M_inv[0] * b[0] + M_inv[1] * b[1];
const double step_v = M_inv[2] * b[0] + M_inv[3] * b[1];
*u += fclamp(step_u * DISFLOW_STEP_SIZE, -2, 2);
*v += fclamp(step_v * DISFLOW_STEP_SIZE, -2, 2);
if (fabs(step_u) + fabs(step_v) < DISFLOW_STEP_SIZE_THRESOLD) {
// Stop iteration when we're close to convergence
break;
}
}
}