disflow_sve.c - mozsearch

/*

 * Copyright (c) 2024, Alliance for Open Media. All rights reserved.

 * This source code is subject to the terms of the BSD 2 Clause License and

 * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License

 * was not distributed with this source code in the LICENSE file, you can

 * obtain it at www.aomedia.org/license/software. 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 www.aomedia.org/license/patent.

*/

#include "aom_dsp/flow_estimation/disflow.h"

#include <arm_neon.h>

#include <arm_sve.h>

#include <math.h>

#include "aom_dsp/arm/aom_neon_sve_bridge.h"

#include "aom_dsp/arm/mem_neon.h"

#include "aom_dsp/arm/sum_neon.h"

#include "aom_dsp/flow_estimation/arm/disflow_neon.h"

#include "config/aom_config.h"

#include "config/aom_dsp_rtcd.h"

DECLARE_ALIGNED(16, static const uint16_t, kDeinterleaveTbl[8]) = {

  0, 2, 4, 6, 1, 3, 5, 7,

};

// 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.

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) {

  // 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);

  int h_kernel[4];

  int v_kernel[4];

  get_cubic_kernel_int(u_frac, h_kernel);

  get_cubic_kernel_int(v_frac, v_kernel);

  int16_t tmp_[DISFLOW_PATCH_SIZE * (DISFLOW_PATCH_SIZE + 3)];

  // 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.

  const uint8_t *ref_start = ref + (y0 - 1) * stride + (x0 - 1);

  const int16x4_t h_kernel_s16 = vmovn_s32(vld1q_s32(h_kernel));

  const int16x8_t h_filter = vcombine_s16(h_kernel_s16, vdup_n_s16(0));

  const uint16x8_t idx = vld1q_u16(kDeinterleaveTbl);

  for (int i = 0; i < DISFLOW_PATCH_SIZE + 3; ++i) {

    svuint16_t r0 = svld1ub_u16(svptrue_b16(), ref_start + i * stride + 0);

    svuint16_t r1 = svld1ub_u16(svptrue_b16(), ref_start + i * stride + 1);

    svuint16_t r2 = svld1ub_u16(svptrue_b16(), ref_start + i * stride + 2);

    svuint16_t r3 = svld1ub_u16(svptrue_b16(), ref_start + i * stride + 3);

    int16x8_t s0 = vreinterpretq_s16_u16(svget_neonq_u16(r0));

    int16x8_t s1 = vreinterpretq_s16_u16(svget_neonq_u16(r1));

    int16x8_t s2 = vreinterpretq_s16_u16(svget_neonq_u16(r2));

    int16x8_t s3 = vreinterpretq_s16_u16(svget_neonq_u16(r3));

    int64x2_t sum04 = aom_svdot_lane_s16(vdupq_n_s64(0), s0, h_filter, 0);

    int64x2_t sum15 = aom_svdot_lane_s16(vdupq_n_s64(0), s1, h_filter, 0);

    int64x2_t sum26 = aom_svdot_lane_s16(vdupq_n_s64(0), s2, h_filter, 0);

    int64x2_t sum37 = aom_svdot_lane_s16(vdupq_n_s64(0), s3, h_filter, 0);

    int32x4_t res0 = vcombine_s32(vmovn_s64(sum04), vmovn_s64(sum15));

    int32x4_t res1 = vcombine_s32(vmovn_s64(sum26), vmovn_s64(sum37));

    // 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.

    int16x8_t res = vcombine_s16(vrshrn_n_s32(res0, DISFLOW_INTERP_BITS - 6),

                                 vrshrn_n_s32(res1, DISFLOW_INTERP_BITS - 6));

    res = aom_tbl_s16(res, idx);

    vst1q_s16(tmp_ + i * DISFLOW_PATCH_SIZE, res);

  // Vertical convolution.

  int16x4_t v_filter = vmovn_s32(vld1q_s32(v_kernel));

  int16_t *tmp_start = tmp_ + DISFLOW_PATCH_SIZE;

  for (int i = 0; i < DISFLOW_PATCH_SIZE; ++i) {

    int16x8_t t0 = vld1q_s16(tmp_start + (i - 1) * DISFLOW_PATCH_SIZE);

    int16x8_t t1 = vld1q_s16(tmp_start + i * DISFLOW_PATCH_SIZE);

    int16x8_t t2 = vld1q_s16(tmp_start + (i + 1) * DISFLOW_PATCH_SIZE);

    int16x8_t t3 = vld1q_s16(tmp_start + (i + 2) * DISFLOW_PATCH_SIZE);

    int32x4_t sum_lo = vmull_lane_s16(vget_low_s16(t0), v_filter, 0);

    sum_lo = vmlal_lane_s16(sum_lo, vget_low_s16(t1), v_filter, 1);

    sum_lo = vmlal_lane_s16(sum_lo, vget_low_s16(t2), v_filter, 2);

    sum_lo = vmlal_lane_s16(sum_lo, vget_low_s16(t3), v_filter, 3);

    int32x4_t sum_hi = vmull_lane_s16(vget_high_s16(t0), v_filter, 0);

    sum_hi = vmlal_lane_s16(sum_hi, vget_high_s16(t1), v_filter, 1);

    sum_hi = vmlal_lane_s16(sum_hi, vget_high_s16(t2), v_filter, 2);

    sum_hi = vmlal_lane_s16(sum_hi, vget_high_s16(t3), v_filter, 3);

    uint8x8_t s = vld1_u8(src + (i + y) * stride + x);

    int16x8_t s_s16 = vreinterpretq_s16_u16(vshll_n_u8(s, 3));

    // 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.

    sum_lo = vrshrq_n_s32(sum_lo,

                          DISFLOW_INTERP_BITS + 6 - DISFLOW_DERIV_SCALE_LOG2);

    sum_hi = vrshrq_n_s32(sum_hi,

                          DISFLOW_INTERP_BITS + 6 - DISFLOW_DERIV_SCALE_LOG2);

    int32x4_t err_lo = vsubw_s16(sum_lo, vget_low_s16(s_s16));

    int32x4_t err_hi = vsubw_s16(sum_hi, vget_high_s16(s_s16));

    vst1q_s16(dt + i * DISFLOW_PATCH_SIZE,

              vcombine_s16(vmovn_s32(err_lo), vmovn_s32(err_hi)));

// Computes the components of the system of equations used to solve for

// a flow vector.

//

// The flow equations are a least-squares system, derived as follows:

//

// For each pixel in the patch, we calculate the current error `dt`,

// and the x and y gradients `dx` and `dy` of the source patch.

// This means that, to first order, the squared error for this pixel is

//

//    (dt + u * dx + v * dy)^2

//

// where (u, v) are the incremental changes to the flow vector.

//

// We then want to find the values of u and v which minimize the sum

// of the squared error across all pixels. Conveniently, this fits exactly

// into the form of a least squares problem, with one equation

//

//   u * dx + v * dy = -dt

//

// for each pixel.

//

// Summing across all pixels in a square window of size DISFLOW_PATCH_SIZE,

// and absorbing the - sign elsewhere, this results in the least squares system

//

//   M = |sum(dx * dx)  sum(dx * dy)|

//       |sum(dx * dy)  sum(dy * dy)|

//

//   b = |sum(dx * dt)|

//       |sum(dy * dt)|

static inline void compute_flow_matrix(const int16_t *dx, int dx_stride,

                                       const int16_t *dy, int dy_stride,

                                       double *M_inv) {

  int64x2_t sum[3] = { vdupq_n_s64(0), vdupq_n_s64(0), vdupq_n_s64(0) };

  for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {

    int16x8_t x = vld1q_s16(dx + i * dx_stride);

    int16x8_t y = vld1q_s16(dy + i * dy_stride);

    sum[0] = aom_sdotq_s16(sum[0], x, x);

    sum[1] = aom_sdotq_s16(sum[1], x, y);

    sum[2] = aom_sdotq_s16(sum[2], y, y);

  sum[0] = vpaddq_s64(sum[0], sum[1]);

  sum[2] = vpaddq_s64(sum[1], sum[2]);

  int32x4_t res = vcombine_s32(vmovn_s64(sum[0]), vmovn_s64(sum[2]));

  // 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.

  double M0 = (double)vgetq_lane_s32(res, 0) + 1;

  double M1 = (double)vgetq_lane_s32(res, 1);

  double M2 = (double)vgetq_lane_s32(res, 2);

  double M3 = (double)vgetq_lane_s32(res, 3) + 1;

  // Invert matrix M.

  double det = (M0 * M3) - (M1 * M2);

  assert(det >= 1);

  const double det_inv = 1 / det;

  M_inv[0] = M3 * det_inv;

  M_inv[1] = -M1 * det_inv;

  M_inv[2] = -M2 * det_inv;

  M_inv[3] = M0 * det_inv;

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) {

  int64x2_t b_s64[2] = { vdupq_n_s64(0), vdupq_n_s64(0) };

  for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) {

    int16x8_t dx16 = vld1q_s16(dx + i * dx_stride);

    int16x8_t dy16 = vld1q_s16(dy + i * dy_stride);

    int16x8_t dt16 = vld1q_s16(dt + i * dt_stride);

    b_s64[0] = aom_sdotq_s16(b_s64[0], dx16, dt16);

    b_s64[1] = aom_sdotq_s16(b_s64[1], dy16, dt16);

  b_s64[0] = vpaddq_s64(b_s64[0], b_s64[1]);

  vst1_s32(b, vmovn_s64(b_s64[0]));

void aom_compute_flow_at_point_sve(const uint8_t *src, const uint8_t *ref,

                                   int x, int y, int width, int height,

                                   int stride, double *u, double *v) {

  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_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;

Source code

Revision control

Copy as Markdown

Other Tools