diff options
Diffstat (limited to 'third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.c')
| -rw-r--r-- | third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.c | 368 |
1 files changed, 368 insertions, 0 deletions
diff --git a/third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.c b/third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.c new file mode 100644 index 0000000000..ee42be7393 --- /dev/null +++ b/third_party/aom/aom_dsp/flow_estimation/arm/disflow_neon.c @@ -0,0 +1,368 @@ +/* + * 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 "config/aom_config.h" +#include "config/aom_dsp_rtcd.h" + +static INLINE void get_cubic_kernel_dbl(double x, double kernel[4]) { + // Check that the fractional position is in range. + // + // Note: x is calculated from (eg.) `u_frac = u - floor(u)`. + // Mathematically, this implies that 0 <= x < 1. However, in practice it is + // possible to have x == 1 due to floating point rounding. This is fine, + // and we still interpolate correctly if we allow x = 1. + 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, int kernel[4]) { + double kernel_dbl[4]; + get_cubic_kernel_dbl(x, kernel_dbl); + + kernel[0] = (int)rint(kernel_dbl[0] * (1 << DISFLOW_INTERP_BITS)); + kernel[1] = (int)rint(kernel_dbl[1] * (1 << DISFLOW_INTERP_BITS)); + kernel[2] = (int)rint(kernel_dbl[2] * (1 << DISFLOW_INTERP_BITS)); + kernel[3] = (int)rint(kernel_dbl[3] * (1 << DISFLOW_INTERP_BITS)); +} + +// 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))); + } +} + +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)]; + + // Horizontal filter, using kernel {1, 0, -1}. + const uint8_t *src_start = src - 1 * src_stride - 1; + + for (int i = 0; i < DISFLOW_PATCH_SIZE + 2; i++) { + uint8x16_t s = vld1q_u8(src_start + i * src_stride); + uint8x8_t s0 = vget_low_u8(s); + uint8x8_t s2 = vget_low_u8(vextq_u8(s, s, 2)); + + // Given that the kernel is {1, 0, -1} the convolution is a simple + // subtraction. + int16x8_t diff = vreinterpretq_s16_u16(vsubl_u8(s0, s2)); + + vst1q_s16(tmp + i * DISFLOW_PATCH_SIZE, diff); + } + + // Vertical filter, using kernel {1, 2, 1}. + // This kernel can be split into two 2-taps kernels of value {1, 1}. + // That way we need only 3 add operations to perform the convolution, one of + // which can be reused for the next line. + int16x8_t s0 = vld1q_s16(tmp); + int16x8_t s1 = vld1q_s16(tmp + DISFLOW_PATCH_SIZE); + int16x8_t sum01 = vaddq_s16(s0, s1); + for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) { + int16x8_t s2 = vld1q_s16(tmp + (i + 2) * DISFLOW_PATCH_SIZE); + + int16x8_t sum12 = vaddq_s16(s1, s2); + int16x8_t sum = vaddq_s16(sum01, sum12); + + vst1q_s16(dst + i * dst_stride, sum); + + sum01 = sum12; + s1 = s2; + } +} + +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)]; + + // Horizontal filter, using kernel {1, 2, 1}. + // This kernel can be split into two 2-taps kernels of value {1, 1}. + // That way we need only 3 add operations to perform the convolution. + const uint8_t *src_start = src - 1 * src_stride - 1; + + for (int i = 0; i < DISFLOW_PATCH_SIZE + 2; i++) { + uint8x16_t s = vld1q_u8(src_start + i * src_stride); + uint8x8_t s0 = vget_low_u8(s); + uint8x8_t s1 = vget_low_u8(vextq_u8(s, s, 1)); + uint8x8_t s2 = vget_low_u8(vextq_u8(s, s, 2)); + + uint16x8_t sum01 = vaddl_u8(s0, s1); + uint16x8_t sum12 = vaddl_u8(s1, s2); + uint16x8_t sum = vaddq_u16(sum01, sum12); + + vst1q_s16(tmp + i * DISFLOW_PATCH_SIZE, vreinterpretq_s16_u16(sum)); + } + + // Vertical filter, using kernel {1, 0, -1}. + // Load the whole block at once to avoid redundant loads during convolution. + int16x8_t t[10]; + load_s16_8x10(tmp, DISFLOW_PATCH_SIZE, &t[0], &t[1], &t[2], &t[3], &t[4], + &t[5], &t[6], &t[7], &t[8], &t[9]); + + for (int i = 0; i < DISFLOW_PATCH_SIZE; i++) { + // Given that the kernel is {1, 0, -1} the convolution is a simple + // subtraction. + int16x8_t diff = vsubq_s16(t[i], t[i + 2]); + + vst1q_s16(dst + i * dst_stride, diff); + } +} + +// 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; + } + } +} |