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/*
* Copyright (c) 2016, 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 <math.h>
#include <limits.h>
#include "config/aom_config.h"
#include "av1/common/av1_common_int.h"
#include "av1/encoder/encoder.h"
#include "av1/encoder/mathutils.h"
#include "av1/encoder/optical_flow.h"
#include "av1/encoder/sparse_linear_solver.h"
#include "av1/encoder/reconinter_enc.h"
#include "aom_mem/aom_mem.h"
#if CONFIG_OPTICAL_FLOW_API
void av1_init_opfl_params(OPFL_PARAMS *opfl_params) {
opfl_params->pyramid_levels = OPFL_PYRAMID_LEVELS;
opfl_params->warping_steps = OPFL_WARPING_STEPS;
opfl_params->lk_params = NULL;
}
void av1_init_lk_params(LK_PARAMS *lk_params) {
lk_params->window_size = OPFL_WINDOW_SIZE;
}
// Helper function to determine whether a frame is encoded with high bit-depth.
static INLINE int is_frame_high_bitdepth(const YV12_BUFFER_CONFIG *frame) {
return (frame->flags & YV12_FLAG_HIGHBITDEPTH) ? 1 : 0;
}
// Helper function to determine whether optical flow method is sparse.
static INLINE int is_sparse(const OPFL_PARAMS *opfl_params) {
return (opfl_params->flags & OPFL_FLAG_SPARSE) ? 1 : 0;
}
static void gradients_over_window(const YV12_BUFFER_CONFIG *frame,
const YV12_BUFFER_CONFIG *ref_frame,
const double x_coord, const double y_coord,
const int window_size, const int bit_depth,
double *ix, double *iy, double *it,
LOCALMV *mv);
// coefficients for bilinear interpolation on unit square
static int pixel_interp(const double x, const double y, const double b00,
const double b01, const double b10, const double b11) {
const int xint = (int)x;
const int yint = (int)y;
const double xdec = x - xint;
const double ydec = y - yint;
const double a = (1 - xdec) * (1 - ydec);
const double b = xdec * (1 - ydec);
const double c = (1 - xdec) * ydec;
const double d = xdec * ydec;
// if x, y are already integers, this results to b00
int interp = (int)round(a * b00 + b * b01 + c * b10 + d * b11);
return interp;
}
// bilinear interpolation to find subpixel values
static AOM_INLINE int get_subpixels(const YV12_BUFFER_CONFIG *frame, int *pred,
const int w, const int h, LOCALMV mv,
const double x_coord,
const double y_coord) {
double left = x_coord + mv.row;
double top = y_coord + mv.col;
const int fromedge = 2;
const int height = frame->y_crop_height;
const int width = frame->y_crop_width;
if (left < 1) left = 1;
if (top < 1) top = 1;
// could use elements past boundary where stride > width
if (top > height - fromedge) top = height - fromedge;
if (left > width - fromedge) left = width - fromedge;
const uint8_t *buf = frame->y_buffer;
const int s = frame->y_stride;
int prev = -1;
int xint;
int yint;
int idx = 0;
for (int y = prev; y < prev + h; y++) {
for (int x = prev; x < prev + w; x++) {
double xx = left + x;
double yy = top + y;
xint = (int)xx;
yint = (int)yy;
int interp = pixel_interp(
xx, yy, buf[yint * s + xint], buf[yint * s + (xint + 1)],
buf[(yint + 1) * s + xint], buf[(yint + 1) * s + (xint + 1)]);
pred[idx++] = interp;
}
}
return 0;
}
// Scharr filter to compute spatial gradient
static void spatial_gradient(const YV12_BUFFER_CONFIG *frame, const int x_coord,
const int y_coord, const int direction,
double *derivative) {
double *filter;
// Scharr filters
double gx[9] = { -3, 0, 3, -10, 0, 10, -3, 0, 3 };
double gy[9] = { -3, -10, -3, 0, 0, 0, 3, 10, 3 };
if (direction == 0) { // x direction
filter = gx;
} else { // y direction
filter = gy;
}
int idx = 0;
double d = 0;
for (int yy = -1; yy <= 1; yy++) {
for (int xx = -1; xx <= 1; xx++) {
d += filter[idx] *
frame->y_buffer[(y_coord + yy) * frame->y_stride + (x_coord + xx)];
idx++;
}
}
// normalization scaling factor for scharr
*derivative = d / 32.0;
}
// Determine the spatial gradient at subpixel locations
// For example, when reducing images for pyramidal LK,
// corners found in original image may be at subpixel locations.
static void gradient_interp(double *fullpel_deriv, const double x_coord,
const double y_coord, const int w, const int h,
double *derivative) {
const int xint = (int)x_coord;
const int yint = (int)y_coord;
double interp;
if (xint + 1 > w - 1 || yint + 1 > h - 1) {
interp = fullpel_deriv[yint * w + xint];
} else {
interp = pixel_interp(x_coord, y_coord, fullpel_deriv[yint * w + xint],
fullpel_deriv[yint * w + (xint + 1)],
fullpel_deriv[(yint + 1) * w + xint],
fullpel_deriv[(yint + 1) * w + (xint + 1)]);
}
*derivative = interp;
}
static void temporal_gradient(const YV12_BUFFER_CONFIG *frame,
const YV12_BUFFER_CONFIG *frame2,
const double x_coord, const double y_coord,
const int bit_depth, double *derivative,
LOCALMV *mv) {
const int w = 2;
const int h = 2;
uint8_t pred1[4];
uint8_t pred2[4];
const int y = (int)y_coord;
const int x = (int)x_coord;
const double ydec = y_coord - y;
const double xdec = x_coord - x;
const int is_intrabc = 0; // Is intra-copied?
const int is_high_bitdepth = is_frame_high_bitdepth(frame2);
const int subsampling_x = 0, subsampling_y = 0; // for y-buffer
const int_interpfilters interp_filters =
av1_broadcast_interp_filter(MULTITAP_SHARP);
const int plane = 0; // y-plane
const struct buf_2d ref_buf2 = { NULL, frame2->y_buffer, frame2->y_crop_width,
frame2->y_crop_height, frame2->y_stride };
struct scale_factors scale;
av1_setup_scale_factors_for_frame(&scale, frame->y_crop_width,
frame->y_crop_height, frame->y_crop_width,
frame->y_crop_height);
InterPredParams inter_pred_params;
av1_init_inter_params(&inter_pred_params, w, h, y, x, subsampling_x,
subsampling_y, bit_depth, is_high_bitdepth, is_intrabc,
&scale, &ref_buf2, interp_filters);
inter_pred_params.interp_filter_params[0] =
&av1_interp_filter_params_list[interp_filters.as_filters.x_filter];
inter_pred_params.interp_filter_params[1] =
&av1_interp_filter_params_list[interp_filters.as_filters.y_filter];
inter_pred_params.conv_params = get_conv_params(0, plane, bit_depth);
MV newmv = { .row = (int16_t)round((mv->row + xdec) * 8),
.col = (int16_t)round((mv->col + ydec) * 8) };
av1_enc_build_one_inter_predictor(pred2, w, &newmv, &inter_pred_params);
const struct buf_2d ref_buf1 = { NULL, frame->y_buffer, frame->y_crop_width,
frame->y_crop_height, frame->y_stride };
av1_init_inter_params(&inter_pred_params, w, h, y, x, subsampling_x,
subsampling_y, bit_depth, is_high_bitdepth, is_intrabc,
&scale, &ref_buf1, interp_filters);
inter_pred_params.interp_filter_params[0] =
&av1_interp_filter_params_list[interp_filters.as_filters.x_filter];
inter_pred_params.interp_filter_params[1] =
&av1_interp_filter_params_list[interp_filters.as_filters.y_filter];
inter_pred_params.conv_params = get_conv_params(0, plane, bit_depth);
MV zeroMV = { .row = (int16_t)round(xdec * 8),
.col = (int16_t)round(ydec * 8) };
av1_enc_build_one_inter_predictor(pred1, w, &zeroMV, &inter_pred_params);
*derivative = pred2[0] - pred1[0];
}
// Numerical differentiate over window_size x window_size surrounding (x,y)
// location. Alters ix, iy, it to contain numerical partial derivatives
static void gradients_over_window(const YV12_BUFFER_CONFIG *frame,
const YV12_BUFFER_CONFIG *ref_frame,
const double x_coord, const double y_coord,
const int window_size, const int bit_depth,
double *ix, double *iy, double *it,
LOCALMV *mv) {
const double left = x_coord - window_size / 2.0;
const double top = y_coord - window_size / 2.0;
// gradient operators need pixel before and after (start at 1)
const double x_start = AOMMAX(1, left);
const double y_start = AOMMAX(1, top);
const int frame_height = frame->y_crop_height;
const int frame_width = frame->y_crop_width;
double deriv_x;
double deriv_y;
double deriv_t;
const double x_end = AOMMIN(x_coord + window_size / 2.0, frame_width - 2);
const double y_end = AOMMIN(y_coord + window_size / 2.0, frame_height - 2);
const int xs = (int)AOMMAX(1, x_start - 1);
const int ys = (int)AOMMAX(1, y_start - 1);
const int xe = (int)AOMMIN(x_end + 2, frame_width - 2);
const int ye = (int)AOMMIN(y_end + 2, frame_height - 2);
// with normalization, gradients may be double values
double *fullpel_dx = aom_malloc((ye - ys) * (xe - xs) * sizeof(deriv_x));
double *fullpel_dy = aom_malloc((ye - ys) * (xe - xs) * sizeof(deriv_y));
// TODO(any): This could be more efficient in the case that x_coord
// and y_coord are integers.. but it may look more messy.
// calculate spatial gradients at full pixel locations
for (int j = ys; j < ye; j++) {
for (int i = xs; i < xe; i++) {
spatial_gradient(frame, i, j, 0, &deriv_x);
spatial_gradient(frame, i, j, 1, &deriv_y);
int idx = (j - ys) * (xe - xs) + (i - xs);
fullpel_dx[idx] = deriv_x;
fullpel_dy[idx] = deriv_y;
}
}
// compute numerical differentiation for every pixel in window
// (this potentially includes subpixels)
for (double j = y_start; j < y_end; j++) {
for (double i = x_start; i < x_end; i++) {
temporal_gradient(frame, ref_frame, i, j, bit_depth, &deriv_t, mv);
gradient_interp(fullpel_dx, i - xs, j - ys, xe - xs, ye - ys, &deriv_x);
gradient_interp(fullpel_dy, i - xs, j - ys, xe - xs, ye - ys, &deriv_y);
int idx = (int)(j - top) * window_size + (int)(i - left);
ix[idx] = deriv_x;
iy[idx] = deriv_y;
it[idx] = deriv_t;
}
}
// TODO(any): to avoid setting deriv arrays to zero for every iteration,
// could instead pass these two values back through function call
// int first_idx = (int)(y_start - top) * window_size + (int)(x_start - left);
// int width = window_size - ((int)(x_start - left) + (int)(left + window_size
// - x_end));
aom_free(fullpel_dx);
aom_free(fullpel_dy);
}
// To compute eigenvalues of 2x2 matrix: Solve for lambda where
// Determinant(matrix - lambda*identity) == 0
static void eigenvalues_2x2(const double *matrix, double *eig) {
const double a = 1;
const double b = -1 * matrix[0] - matrix[3];
const double c = -1 * matrix[1] * matrix[2] + matrix[0] * matrix[3];
// quadratic formula
const double discriminant = b * b - 4 * a * c;
eig[0] = (-b - sqrt(discriminant)) / (2.0 * a);
eig[1] = (-b + sqrt(discriminant)) / (2.0 * a);
// double check that eigenvalues are ordered by magnitude
if (fabs(eig[0]) > fabs(eig[1])) {
double tmp = eig[0];
eig[0] = eig[1];
eig[1] = tmp;
}
}
// Shi-Tomasi corner detection criteria
static double corner_score(const YV12_BUFFER_CONFIG *frame_to_filter,
const YV12_BUFFER_CONFIG *ref_frame, const int x,
const int y, double *i_x, double *i_y, double *i_t,
const int n, const int bit_depth) {
double eig[2];
LOCALMV mv = { .row = 0, .col = 0 };
// TODO(any): technically, ref_frame and i_t are not used by corner score
// so these could be replaced by dummy variables,
// or change this to spatial gradient function over window only
gradients_over_window(frame_to_filter, ref_frame, x, y, n, bit_depth, i_x,
i_y, i_t, &mv);
double Mres1[1] = { 0 }, Mres2[1] = { 0 }, Mres3[1] = { 0 };
multiply_mat(i_x, i_x, Mres1, 1, n * n, 1);
multiply_mat(i_x, i_y, Mres2, 1, n * n, 1);
multiply_mat(i_y, i_y, Mres3, 1, n * n, 1);
double M[4] = { Mres1[0], Mres2[0], Mres2[0], Mres3[0] };
eigenvalues_2x2(M, eig);
return fabs(eig[0]);
}
// Finds corners in frame_to_filter
// For less strict requirements (i.e. more corners), decrease threshold
static int detect_corners(const YV12_BUFFER_CONFIG *frame_to_filter,
const YV12_BUFFER_CONFIG *ref_frame,
const int maxcorners, int *ref_corners,
const int bit_depth) {
const int frame_height = frame_to_filter->y_crop_height;
const int frame_width = frame_to_filter->y_crop_width;
// TODO(any): currently if maxcorners is decreased, then it only means
// corners will be omited from bottom-right of image. if maxcorners
// is actually used, then this algorithm would need to re-iterate
// and choose threshold based on that
assert(maxcorners == frame_height * frame_width);
int countcorners = 0;
const double threshold = 0.1;
double score;
const int n = 3;
double i_x[9] = { 0, 0, 0, 0, 0, 0, 0, 0, 0 };
double i_y[9] = { 0, 0, 0, 0, 0, 0, 0, 0, 0 };
double i_t[9] = { 0, 0, 0, 0, 0, 0, 0, 0, 0 };
const int fromedge = n;
double max_score = corner_score(frame_to_filter, ref_frame, fromedge,
fromedge, i_x, i_y, i_t, n, bit_depth);
// rough estimate of max corner score in image
for (int x = fromedge; x < frame_width - fromedge; x += 1) {
for (int y = fromedge; y < frame_height - fromedge; y += frame_height / 5) {
for (int i = 0; i < n * n; i++) {
i_x[i] = 0;
i_y[i] = 0;
i_t[i] = 0;
}
score = corner_score(frame_to_filter, ref_frame, x, y, i_x, i_y, i_t, n,
bit_depth);
if (score > max_score) {
max_score = score;
}
}
}
// score all the points and choose corners over threshold
for (int x = fromedge; x < frame_width - fromedge; x += 1) {
for (int y = fromedge;
(y < frame_height - fromedge) && countcorners < maxcorners; y += 1) {
for (int i = 0; i < n * n; i++) {
i_x[i] = 0;
i_y[i] = 0;
i_t[i] = 0;
}
score = corner_score(frame_to_filter, ref_frame, x, y, i_x, i_y, i_t, n,
bit_depth);
if (score > threshold * max_score) {
ref_corners[countcorners * 2] = x;
ref_corners[countcorners * 2 + 1] = y;
countcorners++;
}
}
}
return countcorners;
}
// weights is an nxn matrix. weights is filled with a gaussian function,
// with independent variable: distance from the center point.
static void gaussian(const double sigma, const int n, const int normalize,
double *weights) {
double total_weight = 0;
for (int j = 0; j < n; j++) {
for (int i = 0; i < n; i++) {
double distance = sqrt(pow(n / 2 - i, 2) + pow(n / 2 - j, 2));
double weight = exp(-0.5 * pow(distance / sigma, 2));
weights[j * n + i] = weight;
total_weight += weight;
}
}
if (normalize == 1) {
for (int j = 0; j < n; j++) {
weights[j] = weights[j] / total_weight;
}
}
}
static double convolve(const double *filter, const int *img, const int size) {
double result = 0;
for (int i = 0; i < size; i++) {
result += filter[i] * img[i];
}
return result;
}
// Applies a Gaussian low-pass smoothing filter to produce
// a corresponding lower resolution image with halved dimensions
static void reduce(uint8_t *img, int height, int width, int stride,
uint8_t *reduced_img) {
const int new_width = width / 2;
const int window_size = 5;
const double gaussian_filter[25] = {
1. / 256, 1.0 / 64, 3. / 128, 1. / 64, 1. / 256, 1. / 64, 1. / 16,
3. / 32, 1. / 16, 1. / 64, 3. / 128, 3. / 32, 9. / 64, 3. / 32,
3. / 128, 1. / 64, 1. / 16, 3. / 32, 1. / 16, 1. / 64, 1. / 256,
1. / 64, 3. / 128, 1. / 64, 1. / 256
};
// filter is 5x5 so need prev and forward 2 pixels
int img_section[25];
for (int y = 0; y < height - 1; y += 2) {
for (int x = 0; x < width - 1; x += 2) {
int i = 0;
for (int yy = y - window_size / 2; yy <= y + window_size / 2; yy++) {
for (int xx = x - window_size / 2; xx <= x + window_size / 2; xx++) {
int yvalue = yy;
int xvalue = xx;
// copied pixels outside the boundary
if (yvalue < 0) yvalue = 0;
if (xvalue < 0) xvalue = 0;
if (yvalue >= height) yvalue = height - 1;
if (xvalue >= width) xvalue = width - 1;
img_section[i++] = img[yvalue * stride + xvalue];
}
}
reduced_img[(y / 2) * new_width + (x / 2)] = (uint8_t)convolve(
gaussian_filter, img_section, window_size * window_size);
}
}
}
static int cmpfunc(const void *a, const void *b) {
return (*(int *)a - *(int *)b);
}
static void filter_mvs(const MV_FILTER_TYPE mv_filter, const int frame_height,
const int frame_width, LOCALMV *localmvs, MV *mvs) {
const int n = 5; // window size
// for smoothing filter
const double gaussian_filter[25] = {
1. / 256, 1. / 64, 3. / 128, 1. / 64, 1. / 256, 1. / 64, 1. / 16,
3. / 32, 1. / 16, 1. / 64, 3. / 128, 3. / 32, 9. / 64, 3. / 32,
3. / 128, 1. / 64, 1. / 16, 3. / 32, 1. / 16, 1. / 64, 1. / 256,
1. / 64, 3. / 128, 1. / 64, 1. / 256
};
// for median filter
int mvrows[25];
int mvcols[25];
if (mv_filter != MV_FILTER_NONE) {
for (int y = 0; y < frame_height; y++) {
for (int x = 0; x < frame_width; x++) {
int center_idx = y * frame_width + x;
int i = 0;
double filtered_row = 0;
double filtered_col = 0;
for (int yy = y - n / 2; yy <= y + n / 2; yy++) {
for (int xx = x - n / 2; xx <= x + n / 2; xx++) {
int yvalue = yy;
int xvalue = xx;
// copied pixels outside the boundary
if (yvalue < 0) yvalue = 0;
if (xvalue < 0) xvalue = 0;
if (yvalue >= frame_height) yvalue = frame_height - 1;
if (xvalue >= frame_width) xvalue = frame_width - 1;
int index = yvalue * frame_width + xvalue;
if (mv_filter == MV_FILTER_SMOOTH) {
filtered_row += mvs[index].row * gaussian_filter[i];
filtered_col += mvs[index].col * gaussian_filter[i];
} else if (mv_filter == MV_FILTER_MEDIAN) {
mvrows[i] = mvs[index].row;
mvcols[i] = mvs[index].col;
}
i++;
}
}
MV mv = mvs[center_idx];
if (mv_filter == MV_FILTER_SMOOTH) {
mv.row = (int16_t)filtered_row;
mv.col = (int16_t)filtered_col;
} else if (mv_filter == MV_FILTER_MEDIAN) {
qsort(mvrows, 25, sizeof(mv.row), cmpfunc);
qsort(mvcols, 25, sizeof(mv.col), cmpfunc);
mv.row = mvrows[25 / 2];
mv.col = mvcols[25 / 2];
}
LOCALMV localmv = { .row = ((double)mv.row) / 8,
.col = ((double)mv.row) / 8 };
localmvs[y * frame_width + x] = localmv;
// if mvs array is immediately updated here, then the result may
// propagate to other pixels.
}
}
for (int i = 0; i < frame_height * frame_width; i++) {
MV mv = { .row = (int16_t)round(8 * localmvs[i].row),
.col = (int16_t)round(8 * localmvs[i].col) };
mvs[i] = mv;
}
}
}
// Computes optical flow at a single pyramid level,
// using Lucas-Kanade algorithm.
// Modifies mvs array.
static void lucas_kanade(const YV12_BUFFER_CONFIG *from_frame,
const YV12_BUFFER_CONFIG *to_frame, const int level,
const LK_PARAMS *lk_params, const int num_ref_corners,
int *ref_corners, const int mv_stride,
const int bit_depth, LOCALMV *mvs) {
assert(lk_params->window_size > 0 && lk_params->window_size % 2 == 0);
const int n = lk_params->window_size;
// algorithm is sensitive to window size
double *i_x = (double *)aom_malloc(n * n * sizeof(*i_x));
double *i_y = (double *)aom_malloc(n * n * sizeof(*i_y));
double *i_t = (double *)aom_malloc(n * n * sizeof(*i_t));
const int expand_multiplier = (int)pow(2, level);
double sigma = 0.2 * n;
double *weights = (double *)aom_malloc(n * n * sizeof(*weights));
// normalizing doesn't really affect anything since it's applied
// to every component of M and b
gaussian(sigma, n, 0, weights);
for (int i = 0; i < num_ref_corners; i++) {
const double x_coord = 1.0 * ref_corners[i * 2] / expand_multiplier;
const double y_coord = 1.0 * ref_corners[i * 2 + 1] / expand_multiplier;
int highres_x = ref_corners[i * 2];
int highres_y = ref_corners[i * 2 + 1];
int mv_idx = highres_y * (mv_stride) + highres_x;
LOCALMV mv_old = mvs[mv_idx];
mv_old.row = mv_old.row / expand_multiplier;
mv_old.col = mv_old.col / expand_multiplier;
// using this instead of memset, since it's not completely
// clear if zero memset works on double arrays
for (int j = 0; j < n * n; j++) {
i_x[j] = 0;
i_y[j] = 0;
i_t[j] = 0;
}
gradients_over_window(from_frame, to_frame, x_coord, y_coord, n, bit_depth,
i_x, i_y, i_t, &mv_old);
double Mres1[1] = { 0 }, Mres2[1] = { 0 }, Mres3[1] = { 0 };
double bres1[1] = { 0 }, bres2[1] = { 0 };
for (int j = 0; j < n * n; j++) {
Mres1[0] += weights[j] * i_x[j] * i_x[j];
Mres2[0] += weights[j] * i_x[j] * i_y[j];
Mres3[0] += weights[j] * i_y[j] * i_y[j];
bres1[0] += weights[j] * i_x[j] * i_t[j];
bres2[0] += weights[j] * i_y[j] * i_t[j];
}
double M[4] = { Mres1[0], Mres2[0], Mres2[0], Mres3[0] };
double b[2] = { -1 * bres1[0], -1 * bres2[0] };
double eig[2] = { 1, 1 };
eigenvalues_2x2(M, eig);
double threshold = 0.1;
if (fabs(eig[0]) > threshold) {
// if M is not invertible, then displacement
// will default to zeros
double u[2] = { 0, 0 };
linsolve(2, M, 2, b, u);
int mult = 1;
if (level != 0)
mult = expand_multiplier; // mv doubles when resolution doubles
LOCALMV mv = { .row = (mult * (u[0] + mv_old.row)),
.col = (mult * (u[1] + mv_old.col)) };
mvs[mv_idx] = mv;
mvs[mv_idx] = mv;
}
}
aom_free(weights);
aom_free(i_t);
aom_free(i_x);
aom_free(i_y);
}
// Warp the src_frame to warper_frame according to mvs.
// mvs point to src_frame
static void warp_back_frame(YV12_BUFFER_CONFIG *warped_frame,
const YV12_BUFFER_CONFIG *src_frame,
const LOCALMV *mvs, int mv_stride) {
int w, h;
const int fw = src_frame->y_crop_width;
const int fh = src_frame->y_crop_height;
const int src_fs = src_frame->y_stride, warped_fs = warped_frame->y_stride;
const uint8_t *src_buf = src_frame->y_buffer;
uint8_t *warped_buf = warped_frame->y_buffer;
double temp;
for (h = 0; h < fh; h++) {
for (w = 0; w < fw; w++) {
double cord_x = (double)w + mvs[h * mv_stride + w].col;
double cord_y = (double)h + mvs[h * mv_stride + w].row;
cord_x = fclamp(cord_x, 0, (double)(fw - 1));
cord_y = fclamp(cord_y, 0, (double)(fh - 1));
const int floorx = (int)floor(cord_x);
const int floory = (int)floor(cord_y);
const double fracx = cord_x - (double)floorx;
const double fracy = cord_y - (double)floory;
temp = 0;
for (int hh = 0; hh < 2; hh++) {
const double weighth = hh ? (fracy) : (1 - fracy);
for (int ww = 0; ww < 2; ww++) {
const double weightw = ww ? (fracx) : (1 - fracx);
int y = floory + hh;
int x = floorx + ww;
y = clamp(y, 0, fh - 1);
x = clamp(x, 0, fw - 1);
temp += (double)src_buf[y * src_fs + x] * weightw * weighth;
}
}
warped_buf[h * warped_fs + w] = (uint8_t)round(temp);
}
}
}
// Same as warp_back_frame, but using a better interpolation filter.
static void warp_back_frame_intp(YV12_BUFFER_CONFIG *warped_frame,
const YV12_BUFFER_CONFIG *src_frame,
const LOCALMV *mvs, int mv_stride) {
int w, h;
const int fw = src_frame->y_crop_width;
const int fh = src_frame->y_crop_height;
const int warped_fs = warped_frame->y_stride;
uint8_t *warped_buf = warped_frame->y_buffer;
const int blk = 2;
uint8_t temp_blk[4];
const int is_intrabc = 0; // Is intra-copied?
const int is_high_bitdepth = is_frame_high_bitdepth(src_frame);
const int subsampling_x = 0, subsampling_y = 0; // for y-buffer
const int_interpfilters interp_filters =
av1_broadcast_interp_filter(MULTITAP_SHARP2);
const int plane = 0; // y-plane
const struct buf_2d ref_buf2 = { NULL, src_frame->y_buffer,
src_frame->y_crop_width,
src_frame->y_crop_height,
src_frame->y_stride };
const int bit_depth = src_frame->bit_depth;
struct scale_factors scale;
av1_setup_scale_factors_for_frame(
&scale, src_frame->y_crop_width, src_frame->y_crop_height,
src_frame->y_crop_width, src_frame->y_crop_height);
for (h = 0; h < fh; h++) {
for (w = 0; w < fw; w++) {
InterPredParams inter_pred_params;
av1_init_inter_params(&inter_pred_params, blk, blk, h, w, subsampling_x,
subsampling_y, bit_depth, is_high_bitdepth,
is_intrabc, &scale, &ref_buf2, interp_filters);
inter_pred_params.interp_filter_params[0] =
&av1_interp_filter_params_list[interp_filters.as_filters.x_filter];
inter_pred_params.interp_filter_params[1] =
&av1_interp_filter_params_list[interp_filters.as_filters.y_filter];
inter_pred_params.conv_params = get_conv_params(0, plane, bit_depth);
MV newmv = { .row = (int16_t)round((mvs[h * mv_stride + w].row) * 8),
.col = (int16_t)round((mvs[h * mv_stride + w].col) * 8) };
av1_enc_build_one_inter_predictor(temp_blk, blk, &newmv,
&inter_pred_params);
warped_buf[h * warped_fs + w] = temp_blk[0];
}
}
}
#define DERIVATIVE_FILTER_LENGTH 7
double filter[DERIVATIVE_FILTER_LENGTH] = { -1.0 / 60, 9.0 / 60, -45.0 / 60, 0,
45.0 / 60, -9.0 / 60, 1.0 / 60 };
// Get gradient of the whole frame
static void get_frame_gradients(const YV12_BUFFER_CONFIG *from_frame,
const YV12_BUFFER_CONFIG *to_frame, double *ix,
double *iy, double *it, int grad_stride) {
int w, h, k, idx;
const int fw = from_frame->y_crop_width;
const int fh = from_frame->y_crop_height;
const int from_fs = from_frame->y_stride, to_fs = to_frame->y_stride;
const uint8_t *from_buf = from_frame->y_buffer;
const uint8_t *to_buf = to_frame->y_buffer;
const int lh = DERIVATIVE_FILTER_LENGTH;
const int hleft = (lh - 1) / 2;
for (h = 0; h < fh; h++) {
for (w = 0; w < fw; w++) {
// x
ix[h * grad_stride + w] = 0;
for (k = 0; k < lh; k++) {
// if we want to make this block dependent, need to extend the
// boundaries using other initializations.
idx = w + k - hleft;
idx = clamp(idx, 0, fw - 1);
ix[h * grad_stride + w] += filter[k] * 0.5 *
((double)from_buf[h * from_fs + idx] +
(double)to_buf[h * to_fs + idx]);
}
// y
iy[h * grad_stride + w] = 0;
for (k = 0; k < lh; k++) {
// if we want to make this block dependent, need to extend the
// boundaries using other initializations.
idx = h + k - hleft;
idx = clamp(idx, 0, fh - 1);
iy[h * grad_stride + w] += filter[k] * 0.5 *
((double)from_buf[idx * from_fs + w] +
(double)to_buf[idx * to_fs + w]);
}
// t
it[h * grad_stride + w] =
(double)to_buf[h * to_fs + w] - (double)from_buf[h * from_fs + w];
}
}
}
// Solve for linear equations given by the H-S method
static void solve_horn_schunck(const double *ix, const double *iy,
const double *it, int grad_stride, int width,
int height, const LOCALMV *init_mvs,
int init_mv_stride, LOCALMV *mvs,
int mv_stride) {
// TODO(bohanli): May just need to allocate the buffers once per optical flow
// calculation
int *row_pos = aom_calloc(width * height * 28, sizeof(*row_pos));
int *col_pos = aom_calloc(width * height * 28, sizeof(*col_pos));
double *values = aom_calloc(width * height * 28, sizeof(*values));
double *mv_vec = aom_calloc(width * height * 2, sizeof(*mv_vec));
double *mv_init_vec = aom_calloc(width * height * 2, sizeof(*mv_init_vec));
double *temp_b = aom_calloc(width * height * 2, sizeof(*temp_b));
double *b = aom_calloc(width * height * 2, sizeof(*b));
// the location idx for neighboring pixels, k < 4 are the 4 direct neighbors
const int check_locs_y[12] = { 0, 0, -1, 1, -1, -1, 1, 1, 0, 0, -2, 2 };
const int check_locs_x[12] = { -1, 1, 0, 0, -1, 1, -1, 1, -2, 2, 0, 0 };
int h, w, checkh, checkw, k;
const int offset = height * width;
SPARSE_MTX A;
int c = 0;
const double lambda = 100;
for (w = 0; w < width; w++) {
for (h = 0; h < height; h++) {
mv_init_vec[w * height + h] = init_mvs[h * init_mv_stride + w].col;
mv_init_vec[w * height + h + offset] =
init_mvs[h * init_mv_stride + w].row;
}
}
// get matrix A
for (w = 0; w < width; w++) {
for (h = 0; h < height; h++) {
int center_num_direct = 4;
const int center_idx = w * height + h;
if (w == 0 || w == width - 1) center_num_direct--;
if (h == 0 || h == height - 1) center_num_direct--;
// diagonal entry for this row from the center pixel
double cor_w = center_num_direct * center_num_direct + center_num_direct;
row_pos[c] = center_idx;
col_pos[c] = center_idx;
values[c] = lambda * cor_w;
c++;
row_pos[c] = center_idx + offset;
col_pos[c] = center_idx + offset;
values[c] = lambda * cor_w;
c++;
// other entries from direct neighbors
for (k = 0; k < 4; k++) {
checkh = h + check_locs_y[k];
checkw = w + check_locs_x[k];
if (checkh < 0 || checkh >= height || checkw < 0 || checkw >= width) {
continue;
}
int this_idx = checkw * height + checkh;
int this_num_direct = 4;
if (checkw == 0 || checkw == width - 1) this_num_direct--;
if (checkh == 0 || checkh == height - 1) this_num_direct--;
cor_w = -center_num_direct - this_num_direct;
row_pos[c] = center_idx;
col_pos[c] = this_idx;
values[c] = lambda * cor_w;
c++;
row_pos[c] = center_idx + offset;
col_pos[c] = this_idx + offset;
values[c] = lambda * cor_w;
c++;
}
// entries from neighbors on the diagonal corners
for (k = 4; k < 8; k++) {
checkh = h + check_locs_y[k];
checkw = w + check_locs_x[k];
if (checkh < 0 || checkh >= height || checkw < 0 || checkw >= width) {
continue;
}
int this_idx = checkw * height + checkh;
cor_w = 2;
row_pos[c] = center_idx;
col_pos[c] = this_idx;
values[c] = lambda * cor_w;
c++;
row_pos[c] = center_idx + offset;
col_pos[c] = this_idx + offset;
values[c] = lambda * cor_w;
c++;
}
// entries from neighbors with dist of 2
for (k = 8; k < 12; k++) {
checkh = h + check_locs_y[k];
checkw = w + check_locs_x[k];
if (checkh < 0 || checkh >= height || checkw < 0 || checkw >= width) {
continue;
}
int this_idx = checkw * height + checkh;
cor_w = 1;
row_pos[c] = center_idx;
col_pos[c] = this_idx;
values[c] = lambda * cor_w;
c++;
row_pos[c] = center_idx + offset;
col_pos[c] = this_idx + offset;
values[c] = lambda * cor_w;
c++;
}
}
}
av1_init_sparse_mtx(row_pos, col_pos, values, c, 2 * width * height,
2 * width * height, &A);
// subtract init mv part from b
av1_mtx_vect_multi_left(&A, mv_init_vec, temp_b, 2 * width * height);
for (int i = 0; i < 2 * width * height; i++) {
b[i] = -temp_b[i];
}
av1_free_sparse_mtx_elems(&A);
// add cross terms to A and modify b with ExEt / EyEt
for (w = 0; w < width; w++) {
for (h = 0; h < height; h++) {
int curidx = w * height + h;
// modify b
b[curidx] += -ix[h * grad_stride + w] * it[h * grad_stride + w];
b[curidx + offset] += -iy[h * grad_stride + w] * it[h * grad_stride + w];
// add cross terms to A
row_pos[c] = curidx;
col_pos[c] = curidx + offset;
values[c] = ix[h * grad_stride + w] * iy[h * grad_stride + w];
c++;
row_pos[c] = curidx + offset;
col_pos[c] = curidx;
values[c] = ix[h * grad_stride + w] * iy[h * grad_stride + w];
c++;
}
}
// Add diagonal terms to A
for (int i = 0; i < c; i++) {
if (row_pos[i] == col_pos[i]) {
if (row_pos[i] < offset) {
w = row_pos[i] / height;
h = row_pos[i] % height;
values[i] += pow(ix[h * grad_stride + w], 2);
} else {
w = (row_pos[i] - offset) / height;
h = (row_pos[i] - offset) % height;
values[i] += pow(iy[h * grad_stride + w], 2);
}
}
}
av1_init_sparse_mtx(row_pos, col_pos, values, c, 2 * width * height,
2 * width * height, &A);
// solve for the mvs
av1_conjugate_gradient_sparse(&A, b, 2 * width * height, mv_vec);
// copy mvs
for (w = 0; w < width; w++) {
for (h = 0; h < height; h++) {
mvs[h * mv_stride + w].col = mv_vec[w * height + h];
mvs[h * mv_stride + w].row = mv_vec[w * height + h + offset];
}
}
aom_free(row_pos);
aom_free(col_pos);
aom_free(values);
aom_free(mv_vec);
aom_free(mv_init_vec);
aom_free(b);
aom_free(temp_b);
av1_free_sparse_mtx_elems(&A);
}
// Calculate optical flow from from_frame to to_frame using the H-S method.
static void horn_schunck(const YV12_BUFFER_CONFIG *from_frame,
const YV12_BUFFER_CONFIG *to_frame, const int level,
const int mv_stride, const int mv_height,
const int mv_width, const OPFL_PARAMS *opfl_params,
LOCALMV *mvs) {
// mvs are always on level 0, here we define two new mv arrays that is of size
// of this level.
const int fw = from_frame->y_crop_width;
const int fh = from_frame->y_crop_height;
const int factor = (int)pow(2, level);
int w, h, k, init_mv_stride;
LOCALMV *init_mvs;
if (level == 0) {
init_mvs = mvs;
init_mv_stride = mv_stride;
} else {
init_mvs = aom_calloc(fw * fh, sizeof(*mvs));
init_mv_stride = fw;
for (h = 0; h < fh; h++) {
for (w = 0; w < fw; w++) {
init_mvs[h * init_mv_stride + w].row =
mvs[h * factor * mv_stride + w * factor].row / (double)factor;
init_mvs[h * init_mv_stride + w].col =
mvs[h * factor * mv_stride + w * factor].col / (double)factor;
}
}
}
LOCALMV *refine_mvs = aom_calloc(fw * fh, sizeof(*mvs));
// temp frame for warping
YV12_BUFFER_CONFIG temp_frame;
temp_frame.y_buffer =
(uint8_t *)aom_calloc(fh * fw, sizeof(*temp_frame.y_buffer));
temp_frame.y_crop_height = fh;
temp_frame.y_crop_width = fw;
temp_frame.y_stride = fw;
// gradient buffers
double *ix = aom_calloc(fw * fh, sizeof(*ix));
double *iy = aom_calloc(fw * fh, sizeof(*iy));
double *it = aom_calloc(fw * fh, sizeof(*it));
// For each warping step
for (k = 0; k < opfl_params->warping_steps; k++) {
// warp from_frame with init_mv
if (level == 0) {
warp_back_frame_intp(&temp_frame, to_frame, init_mvs, init_mv_stride);
} else {
warp_back_frame(&temp_frame, to_frame, init_mvs, init_mv_stride);
}
// calculate frame gradients
get_frame_gradients(from_frame, &temp_frame, ix, iy, it, fw);
// form linear equations and solve mvs
solve_horn_schunck(ix, iy, it, fw, fw, fh, init_mvs, init_mv_stride,
refine_mvs, fw);
// update init_mvs
for (h = 0; h < fh; h++) {
for (w = 0; w < fw; w++) {
init_mvs[h * init_mv_stride + w].col += refine_mvs[h * fw + w].col;
init_mvs[h * init_mv_stride + w].row += refine_mvs[h * fw + w].row;
}
}
}
// copy back the mvs if needed
if (level != 0) {
for (h = 0; h < mv_height; h++) {
for (w = 0; w < mv_width; w++) {
mvs[h * mv_stride + w].row =
init_mvs[h / factor * init_mv_stride + w / factor].row *
(double)factor;
mvs[h * mv_stride + w].col =
init_mvs[h / factor * init_mv_stride + w / factor].col *
(double)factor;
}
}
}
if (level != 0) aom_free(init_mvs);
aom_free(refine_mvs);
aom_free(temp_frame.y_buffer);
aom_free(ix);
aom_free(iy);
aom_free(it);
}
// Apply optical flow iteratively at each pyramid level
static void pyramid_optical_flow(const YV12_BUFFER_CONFIG *from_frame,
const YV12_BUFFER_CONFIG *to_frame,
const int bit_depth,
const OPFL_PARAMS *opfl_params,
const OPTFLOW_METHOD method, LOCALMV *mvs) {
assert(opfl_params->pyramid_levels > 0 &&
opfl_params->pyramid_levels <= MAX_PYRAMID_LEVELS);
int levels = opfl_params->pyramid_levels;
const int frame_height = from_frame->y_crop_height;
const int frame_width = from_frame->y_crop_width;
if ((frame_height / pow(2.0, levels - 1) < 50 ||
frame_height / pow(2.0, levels - 1) < 50) &&
levels > 1)
levels = levels - 1;
uint8_t *images1[MAX_PYRAMID_LEVELS];
uint8_t *images2[MAX_PYRAMID_LEVELS];
images1[0] = from_frame->y_buffer;
images2[0] = to_frame->y_buffer;
YV12_BUFFER_CONFIG *buffers1 = aom_malloc(levels * sizeof(*buffers1));
YV12_BUFFER_CONFIG *buffers2 = aom_malloc(levels * sizeof(*buffers2));
buffers1[0] = *from_frame;
buffers2[0] = *to_frame;
int fw = frame_width;
int fh = frame_height;
for (int i = 1; i < levels; i++) {
// TODO(bohanli): may need to extend buffers for better interpolation SIMD
images1[i] = (uint8_t *)aom_calloc(fh / 2 * fw / 2, sizeof(*images1[i]));
images2[i] = (uint8_t *)aom_calloc(fh / 2 * fw / 2, sizeof(*images2[i]));
int stride;
if (i == 1)
stride = from_frame->y_stride;
else
stride = fw;
reduce(images1[i - 1], fh, fw, stride, images1[i]);
reduce(images2[i - 1], fh, fw, stride, images2[i]);
fh /= 2;
fw /= 2;
YV12_BUFFER_CONFIG a = { .y_buffer = images1[i],
.y_crop_width = fw,
.y_crop_height = fh,
.y_stride = fw };
YV12_BUFFER_CONFIG b = { .y_buffer = images2[i],
.y_crop_width = fw,
.y_crop_height = fh,
.y_stride = fw };
buffers1[i] = a;
buffers2[i] = b;
}
// Compute corners for specific frame
int *ref_corners = NULL;
int num_ref_corners = 0;
if (is_sparse(opfl_params)) {
int maxcorners = from_frame->y_crop_width * from_frame->y_crop_height;
ref_corners = aom_malloc(maxcorners * 2 * sizeof(*ref_corners));
num_ref_corners = detect_corners(from_frame, to_frame, maxcorners,
ref_corners, bit_depth);
}
const int stop_level = 0;
for (int i = levels - 1; i >= stop_level; i--) {
if (method == LUCAS_KANADE) {
assert(is_sparse(opfl_params));
lucas_kanade(&buffers1[i], &buffers2[i], i, opfl_params->lk_params,
num_ref_corners, ref_corners, buffers1[0].y_crop_width,
bit_depth, mvs);
} else if (method == HORN_SCHUNCK) {
assert(!is_sparse(opfl_params));
horn_schunck(&buffers1[i], &buffers2[i], i, buffers1[0].y_crop_width,
buffers1[0].y_crop_height, buffers1[0].y_crop_width,
opfl_params, mvs);
}
}
for (int i = 1; i < levels; i++) {
aom_free(images1[i]);
aom_free(images2[i]);
}
aom_free(ref_corners);
aom_free(buffers1);
aom_free(buffers2);
}
// Computes optical flow by applying algorithm at
// multiple pyramid levels of images (lower-resolution, smoothed images)
// This accounts for larger motions.
// Inputs:
// from_frame Frame buffer.
// to_frame: Frame buffer. MVs point from_frame -> to_frame.
// from_frame_idx: Index of from_frame.
// to_frame_idx: Index of to_frame. Return all zero MVs when idx are equal.
// bit_depth:
// opfl_params: contains algorithm-specific parameters.
// mv_filter: MV_FILTER_NONE, MV_FILTER_SMOOTH, or MV_FILTER_MEDIAN.
// method: LUCAS_KANADE, HORN_SCHUNCK
// mvs: pointer to MVs. Contains initialization, and modified
// based on optical flow. Must have
// dimensions = from_frame->y_crop_width * from_frame->y_crop_height
void av1_optical_flow(const YV12_BUFFER_CONFIG *from_frame,
const YV12_BUFFER_CONFIG *to_frame,
const int from_frame_idx, const int to_frame_idx,
const int bit_depth, const OPFL_PARAMS *opfl_params,
const MV_FILTER_TYPE mv_filter,
const OPTFLOW_METHOD method, MV *mvs) {
const int frame_height = from_frame->y_crop_height;
const int frame_width = from_frame->y_crop_width;
// TODO(any): deal with the case where frames are not of the same dimensions
assert(frame_height == to_frame->y_crop_height &&
frame_width == to_frame->y_crop_width);
if (from_frame_idx == to_frame_idx) {
// immediately return all zero mvs when frame indices are equal
for (int yy = 0; yy < frame_height; yy++) {
for (int xx = 0; xx < frame_width; xx++) {
MV mv = { .row = 0, .col = 0 };
mvs[yy * frame_width + xx] = mv;
}
}
return;
}
// Initialize double mvs based on input parameter mvs array
LOCALMV *localmvs =
aom_malloc(frame_height * frame_width * sizeof(*localmvs));
filter_mvs(MV_FILTER_SMOOTH, frame_height, frame_width, localmvs, mvs);
for (int i = 0; i < frame_width * frame_height; i++) {
MV mv = mvs[i];
LOCALMV localmv = { .row = ((double)mv.row) / 8,
.col = ((double)mv.col) / 8 };
localmvs[i] = localmv;
}
// Apply optical flow algorithm
pyramid_optical_flow(from_frame, to_frame, bit_depth, opfl_params, method,
localmvs);
// Update original mvs array
for (int j = 0; j < frame_height; j++) {
for (int i = 0; i < frame_width; i++) {
int idx = j * frame_width + i;
if (j + localmvs[idx].row < 0 || j + localmvs[idx].row >= frame_height ||
i + localmvs[idx].col < 0 || i + localmvs[idx].col >= frame_width) {
continue;
}
MV mv = { .row = (int16_t)round(8 * localmvs[idx].row),
.col = (int16_t)round(8 * localmvs[idx].col) };
mvs[idx] = mv;
}
}
filter_mvs(mv_filter, frame_height, frame_width, localmvs, mvs);
aom_free(localmvs);
}
#endif