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disflow_neon.c (11367B)

---

/*
* Copyright (c) 2023, 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 <math.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"

// 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);
 int16x4_t h_filter = vmovn_s32(vld1q_s32(h_kernel));

 for (int i = 0; i < DISFLOW_PATCH_SIZE + 3; ++i) {
   uint8x16_t r = vld1q_u8(ref_start + i * stride);
   uint16x8_t r0 = vmovl_u8(vget_low_u8(r));
   uint16x8_t r1 = vmovl_u8(vget_high_u8(r));

   int16x8_t s0 = vreinterpretq_s16_u16(r0);
   int16x8_t s1 = vreinterpretq_s16_u16(vextq_u16(r0, r1, 1));
   int16x8_t s2 = vreinterpretq_s16_u16(vextq_u16(r0, r1, 2));
   int16x8_t s3 = vreinterpretq_s16_u16(vextq_u16(r0, r1, 3));

   int32x4_t sum_lo = vmull_lane_s16(vget_low_s16(s0), h_filter, 0);
   sum_lo = vmlal_lane_s16(sum_lo, vget_low_s16(s1), h_filter, 1);
   sum_lo = vmlal_lane_s16(sum_lo, vget_low_s16(s2), h_filter, 2);
   sum_lo = vmlal_lane_s16(sum_lo, vget_low_s16(s3), h_filter, 3);

   int32x4_t sum_hi = vmull_lane_s16(vget_high_s16(s0), h_filter, 0);
   sum_hi = vmlal_lane_s16(sum_hi, vget_high_s16(s1), h_filter, 1);
   sum_hi = vmlal_lane_s16(sum_hi, vget_high_s16(s2), h_filter, 2);
   sum_hi = vmlal_lane_s16(sum_hi, vget_high_s16(s3), h_filter, 3);

   // 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 sum = vcombine_s16(vrshrn_n_s32(sum_lo, DISFLOW_INTERP_BITS - 6),
                                vrshrn_n_s32(sum_hi, DISFLOW_INTERP_BITS - 6));
   vst1q_s16(tmp_ + i * DISFLOW_PATCH_SIZE, sum);
 }

 // 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) {
 int32x4_t sum[4] = { vdupq_n_s32(0), vdupq_n_s32(0), vdupq_n_s32(0),
                      vdupq_n_s32(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] = vmlal_s16(sum[0], vget_low_s16(x), vget_low_s16(x));
   sum[0] = vmlal_s16(sum[0], vget_high_s16(x), vget_high_s16(x));

   sum[1] = vmlal_s16(sum[1], vget_low_s16(x), vget_low_s16(y));
   sum[1] = vmlal_s16(sum[1], vget_high_s16(x), vget_high_s16(y));

   sum[3] = vmlal_s16(sum[3], vget_low_s16(y), vget_low_s16(y));
   sum[3] = vmlal_s16(sum[3], vget_high_s16(y), vget_high_s16(y));
 }
 sum[2] = sum[1];

 int32x4_t res = horizontal_add_4d_s32x4(sum);

 // 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) {
 int32x4_t b_s32[2] = { vdupq_n_s32(0), vdupq_n_s32(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_s32[0] = vmlal_s16(b_s32[0], vget_low_s16(dx16), vget_low_s16(dt16));
   b_s32[0] = vmlal_s16(b_s32[0], vget_high_s16(dx16), vget_high_s16(dt16));

   b_s32[1] = vmlal_s16(b_s32[1], vget_low_s16(dy16), vget_low_s16(dt16));
   b_s32[1] = vmlal_s16(b_s32[1], vget_high_s16(dy16), vget_high_s16(dt16));
 }

 int32x4_t b_red = horizontal_add_2d_s32(b_s32[0], b_s32[1]);
 vst1_s32(b, add_pairwise_s32x4(b_red));
}

void aom_compute_flow_at_point_neon(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;
   }
 }
}