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#include "precomp.hpp"
//
// 2D dense optical flow algorithm from the following paper:
// Michael Tao, Jiamin Bai, Pushmeet Kohli, and Sylvain Paris.
// "SimpleFlow: A Non-iterative, Sublinear Optical Flow Algorithm"
// Computer Graphics Forum (Eurographics 2012)
// http://graphics.berkeley.edu/papers/Tao-SAN-2012-05/
//
namespace cv
{
namespace optflow
{
static const uchar MASK_TRUE_VALUE = (uchar)255;
inline static float dist(const Vec3b& p1, const Vec3b& p2) {
return (float)((p1[0] - p2[0]) * (p1[0] - p2[0]) +
(p1[1] - p2[1]) * (p1[1] - p2[1]) +
(p1[2] - p2[2]) * (p1[2] - p2[2]));
}
inline static float dist(const Vec2f& p1, const Vec2f& p2) {
return (p1[0] - p2[0]) * (p1[0] - p2[0]) +
(p1[1] - p2[1]) * (p1[1] - p2[1]);
}
template<class T>
inline static T min(T t1, T t2, T t3) {
return (t1 <= t2 && t1 <= t3) ? t1 : min(t2, t3);
}
static void removeOcclusions(const Mat& flow,
const Mat& flow_inv,
float occ_thr,
Mat& confidence) {
const int rows = flow.rows;
const int cols = flow.cols;
if (!confidence.data) {
confidence = Mat::zeros(rows, cols, CV_32F);
}
for (int r = 0; r < rows; ++r) {
for (int c = 0; c < cols; ++c) {
if (dist(flow.at<Vec2f>(r, c), -flow_inv.at<Vec2f>(r, c)) > occ_thr) {
confidence.at<float>(r, c) = 0;
} else {
confidence.at<float>(r, c) = 1;
}
}
}
}
static void wd(Mat& d, int top_shift, int bottom_shift, int left_shift, int right_shift, float sigma) {
for (int dr = -top_shift, r = 0; dr <= bottom_shift; ++dr, ++r) {
for (int dc = -left_shift, c = 0; dc <= right_shift; ++dc, ++c) {
d.at<float>(r, c) = (float)-(dr*dr + dc*dc);
}
}
d *= 1.0 / (2.0 * sigma * sigma);
exp(d, d);
}
static void wc(const Mat& image, Mat& d, int r0, int c0,
int top_shift, int bottom_shift, int left_shift, int right_shift, float sigma) {
const Vec3b centeral_point = image.at<Vec3b>(r0, c0);
int left_border = c0-left_shift, right_border = c0+right_shift;
for (int dr = r0-top_shift, r = 0; dr <= r0+bottom_shift; ++dr, ++r) {
const Vec3b *row = image.ptr<Vec3b>(dr);
float *d_row = d.ptr<float>(r);
for (int dc = left_border, c = 0; dc <= right_border; ++dc, ++c) {
d_row[c] = -dist(centeral_point, row[dc]);
}
}
d *= 1.0 / (2.0 * sigma * sigma);
exp(d, d);
}
static void crossBilateralFilter(const Mat& image,
const Mat& edge_image,
const Mat confidence,
Mat& dst, int d,
float sigma_color, float sigma_space,
bool flag=false) {
const int rows = image.rows;
const int cols = image.cols;
Mat image_extended, edge_image_extended, confidence_extended;
copyMakeBorder(image, image_extended, d, d, d, d, BORDER_DEFAULT);
copyMakeBorder(edge_image, edge_image_extended, d, d, d, d, BORDER_DEFAULT);
copyMakeBorder(confidence, confidence_extended, d, d, d, d, BORDER_CONSTANT, Scalar(0));
Mat weights_space(2*d+1, 2*d+1, CV_32F);
wd(weights_space, d, d, d, d, sigma_space);
Mat weights(2*d+1, 2*d+1, CV_32F);
Mat weighted_sum(2*d+1, 2*d+1, CV_32F);
std::vector<Mat> image_extended_channels;
split(image_extended, image_extended_channels);
for (int row = 0; row < rows; ++row) {
for (int col = 0; col < cols; ++col) {
wc(edge_image_extended, weights, row+d, col+d, d, d, d, d, sigma_color);
Range window_rows(row,row+2*d+1);
Range window_cols(col,col+2*d+1);
multiply(weights, confidence_extended(window_rows, window_cols), weights);
multiply(weights, weights_space, weights);
float weights_sum = (float)sum(weights)[0];
for (int ch = 0; ch < 2; ++ch) {
multiply(weights, image_extended_channels[ch](window_rows, window_cols), weighted_sum);
float total_sum = (float)sum(weighted_sum)[0];
dst.at<Vec2f>(row, col)[ch] = (flag && fabs(weights_sum) < 1e-9)
? image.at<float>(row, col)
: total_sum / weights_sum;
}
}
}
}
static void calcConfidence(const Mat& prev,
const Mat& next,
const Mat& flow,
Mat& confidence,
int max_flow) {
const int rows = prev.rows;
const int cols = prev.cols;
confidence = Mat::zeros(rows, cols, CV_32F);
for (int r0 = 0; r0 < rows; ++r0) {
for (int c0 = 0; c0 < cols; ++c0) {
Vec2f flow_at_point = flow.at<Vec2f>(r0, c0);
int u0 = cvRound(flow_at_point[0]);
if (r0 + u0 < 0) { u0 = -r0; }
if (r0 + u0 >= rows) { u0 = rows - 1 - r0; }
int v0 = cvRound(flow_at_point[1]);
if (c0 + v0 < 0) { v0 = -c0; }
if (c0 + v0 >= cols) { v0 = cols - 1 - c0; }
const int top_row_shift = -std::min(r0 + u0, max_flow);
const int bottom_row_shift = std::min(rows - 1 - (r0 + u0), max_flow);
const int left_col_shift = -std::min(c0 + v0, max_flow);
const int right_col_shift = std::min(cols - 1 - (c0 + v0), max_flow);
bool first_flow_iteration = true;
float sum_e = 0, min_e = 0;
for (int u = top_row_shift; u <= bottom_row_shift; ++u) {
for (int v = left_col_shift; v <= right_col_shift; ++v) {
float e = dist(prev.at<Vec3b>(r0, c0), next.at<Vec3b>(r0 + u0 + u, c0 + v0 + v));
if (first_flow_iteration) {
sum_e = e;
min_e = e;
first_flow_iteration = false;
} else {
sum_e += e;
min_e = std::min(min_e, e);
}
}
}
int windows_square = (bottom_row_shift - top_row_shift + 1) *
(right_col_shift - left_col_shift + 1);
confidence.at<float>(r0, c0) = (windows_square == 0) ? 0
: sum_e / windows_square - min_e;
CV_Assert(confidence.at<float>(r0, c0) >= 0);
}
}
}
static void calcOpticalFlowSingleScaleSF(const Mat& prev_extended,
const Mat& next_extended,
const Mat& mask,
Mat& flow,
int averaging_radius,
int max_flow,
float sigma_dist,
float sigma_color) {
const int averaging_radius_2 = averaging_radius << 1;
const int rows = prev_extended.rows - averaging_radius_2;
const int cols = prev_extended.cols - averaging_radius_2;
Mat weight_window(averaging_radius_2 + 1, averaging_radius_2 + 1, CV_32F);
Mat space_weight_window(averaging_radius_2 + 1, averaging_radius_2 + 1, CV_32F);
wd(space_weight_window, averaging_radius, averaging_radius, averaging_radius, averaging_radius, sigma_dist);
for (int r0 = 0; r0 < rows; ++r0) {
for (int c0 = 0; c0 < cols; ++c0) {
if (!mask.at<uchar>(r0, c0)) {
continue;
}
// TODO: do smth with this creepy staff
Vec2f flow_at_point = flow.at<Vec2f>(r0, c0);
int u0 = cvRound(flow_at_point[0]);
if (r0 + u0 < 0) { u0 = -r0; }
if (r0 + u0 >= rows) { u0 = rows - 1 - r0; }
int v0 = cvRound(flow_at_point[1]);
if (c0 + v0 < 0) { v0 = -c0; }
if (c0 + v0 >= cols) { v0 = cols - 1 - c0; }
const int top_row_shift = -std::min(r0 + u0, max_flow);
const int bottom_row_shift = std::min(rows - 1 - (r0 + u0), max_flow);
const int left_col_shift = -std::min(c0 + v0, max_flow);
const int right_col_shift = std::min(cols - 1 - (c0 + v0), max_flow);
float min_cost = FLT_MAX, best_u = (float)u0, best_v = (float)v0;
wc(prev_extended, weight_window, r0 + averaging_radius, c0 + averaging_radius,
averaging_radius, averaging_radius, averaging_radius, averaging_radius, sigma_color);
multiply(weight_window, space_weight_window, weight_window);
const int prev_extended_top_window_row = r0;
const int prev_extended_left_window_col = c0;
for (int u = top_row_shift; u <= bottom_row_shift; ++u) {
const int next_extended_top_window_row = r0 + u0 + u;
for (int v = left_col_shift; v <= right_col_shift; ++v) {
const int next_extended_left_window_col = c0 + v0 + v;
float cost = 0;
for (int r = 0; r <= averaging_radius_2; ++r) {
const Vec3b *prev_extended_window_row = prev_extended.ptr<Vec3b>(prev_extended_top_window_row + r);
const Vec3b *next_extended_window_row = next_extended.ptr<Vec3b>(next_extended_top_window_row + r);
const float* weight_window_row = weight_window.ptr<float>(r);
for (int c = 0; c <= averaging_radius_2; ++c) {
cost += weight_window_row[c] *
dist(prev_extended_window_row[prev_extended_left_window_col + c],
next_extended_window_row[next_extended_left_window_col + c]);
}
}
// cost should be divided by sum(weight_window), but because
// we interested only in min(cost) and sum(weight_window) is constant
// for every point - we remove it
if (cost < min_cost) {
min_cost = cost;
best_u = (float)(u + u0);
best_v = (float)(v + v0);
}
}
}
flow.at<Vec2f>(r0, c0) = Vec2f(best_u, best_v);
}
}
}
static Mat upscaleOpticalFlow(int new_rows,
int new_cols,
const Mat& image,
const Mat& confidence,
Mat& flow,
int averaging_radius,
float sigma_dist,
float sigma_color) {
crossBilateralFilter(flow, image, confidence, flow, averaging_radius, sigma_color, sigma_dist, true);
Mat new_flow;
resize(flow, new_flow, Size(new_cols, new_rows), 0, 0, INTER_NEAREST);
new_flow *= 2;
return new_flow;
}
static Mat calcIrregularityMat(const Mat& flow, int radius) {
const int rows = flow.rows;
const int cols = flow.cols;
Mat irregularity = Mat::zeros(rows, cols, CV_32F);
for (int r = 0; r < rows; ++r) {
const int start_row = std::max(0, r - radius);
const int end_row = std::min(rows - 1, r + radius);
for (int c = 0; c < cols; ++c) {
const int start_col = std::max(0, c - radius);
const int end_col = std::min(cols - 1, c + radius);
for (int dr = start_row; dr <= end_row; ++dr) {
for (int dc = start_col; dc <= end_col; ++dc) {
const float diff = dist(flow.at<Vec2f>(r, c), flow.at<Vec2f>(dr, dc));
if (diff > irregularity.at<float>(r, c)) {
irregularity.at<float>(r, c) = diff;
}
}
}
}
}
return irregularity;
}
static void selectPointsToRecalcFlow(const Mat& flow,
int irregularity_metric_radius,
float speed_up_thr,
int curr_rows,
int curr_cols,
const Mat& prev_speed_up,
Mat& speed_up,
Mat& mask) {
const int prev_rows = flow.rows;
const int prev_cols = flow.cols;
Mat is_flow_regular = calcIrregularityMat(flow, irregularity_metric_radius)
< speed_up_thr;
Mat done = Mat::zeros(prev_rows, prev_cols, CV_8U);
speed_up = Mat::zeros(curr_rows, curr_cols, CV_8U);
mask = Mat::zeros(curr_rows, curr_cols, CV_8U);
for (int r = 0; r < is_flow_regular.rows; ++r) {
for (int c = 0; c < is_flow_regular.cols; ++c) {
if (!done.at<uchar>(r, c)) {
if (is_flow_regular.at<uchar>(r, c) &&
2*r + 1 < curr_rows && 2*c + 1< curr_cols) {
bool all_flow_in_region_regular = true;
int speed_up_at_this_point = prev_speed_up.at<uchar>(r, c);
int step = (1 << speed_up_at_this_point) - 1;
int prev_top = r;
int prev_bottom = std::min(r + step, prev_rows - 1);
int prev_left = c;
int prev_right = std::min(c + step, prev_cols - 1);
for (int rr = prev_top; rr <= prev_bottom; ++rr) {
for (int cc = prev_left; cc <= prev_right; ++cc) {
done.at<uchar>(rr, cc) = 1;
if (!is_flow_regular.at<uchar>(rr, cc)) {
all_flow_in_region_regular = false;
}
}
}
int curr_top = std::min(2 * r, curr_rows - 1);
int curr_bottom = std::min(2*(r + step) + 1, curr_rows - 1);
int curr_left = std::min(2 * c, curr_cols - 1);
int curr_right = std::min(2*(c + step) + 1, curr_cols - 1);
if (all_flow_in_region_regular &&
curr_top != curr_bottom &&
curr_left != curr_right) {
mask.at<uchar>(curr_top, curr_left) = MASK_TRUE_VALUE;
mask.at<uchar>(curr_bottom, curr_left) = MASK_TRUE_VALUE;
mask.at<uchar>(curr_top, curr_right) = MASK_TRUE_VALUE;
mask.at<uchar>(curr_bottom, curr_right) = MASK_TRUE_VALUE;
for (int rr = curr_top; rr <= curr_bottom; ++rr) {
for (int cc = curr_left; cc <= curr_right; ++cc) {
speed_up.at<uchar>(rr, cc) = (uchar)(speed_up_at_this_point + 1);
}
}
} else {
for (int rr = curr_top; rr <= curr_bottom; ++rr) {
for (int cc = curr_left; cc <= curr_right; ++cc) {
mask.at<uchar>(rr, cc) = MASK_TRUE_VALUE;
}
}
}
} else {
done.at<uchar>(r, c) = 1;
for (int dr = 0; dr <= 1; ++dr) {
int nr = 2*r + dr;
for (int dc = 0; dc <= 1; ++dc) {
int nc = 2*c + dc;
if (nr < curr_rows && nc < curr_cols) {
mask.at<uchar>(nr, nc) = MASK_TRUE_VALUE;
}
}
}
}
}
}
}
}
static inline float extrapolateValueInRect(int height, int width,
float v11, float v12,
float v21, float v22,
int r, int c) {
if (r == 0 && c == 0) { return v11;}
if (r == 0 && c == width) { return v12;}
if (r == height && c == 0) { return v21;}
if (r == height && c == width) { return v22;}
CV_Assert(height > 0 && width > 0);
float qr = float(r) / height;
float pr = 1.0f - qr;
float qc = float(c) / width;
float pc = 1.0f - qc;
return v11*pr*pc + v12*pr*qc + v21*qr*pc + v22*qc*qr;
}
static void extrapolateFlow(Mat& flow,
const Mat& speed_up) {
const int rows = flow.rows;
const int cols = flow.cols;
Mat done = Mat::zeros(rows, cols, CV_8U);
for (int r = 0; r < rows; ++r) {
for (int c = 0; c < cols; ++c) {
if (!done.at<uchar>(r, c) && speed_up.at<uchar>(r, c) > 1) {
int step = (1 << speed_up.at<uchar>(r, c)) - 1;
int top = r;
int bottom = std::min(r + step, rows - 1);
int left = c;
int right = std::min(c + step, cols - 1);
int height = bottom - top;
int width = right - left;
for (int rr = top; rr <= bottom; ++rr) {
for (int cc = left; cc <= right; ++cc) {
done.at<uchar>(rr, cc) = 1;
Vec2f flow_at_point;
Vec2f top_left = flow.at<Vec2f>(top, left);
Vec2f top_right = flow.at<Vec2f>(top, right);
Vec2f bottom_left = flow.at<Vec2f>(bottom, left);
Vec2f bottom_right = flow.at<Vec2f>(bottom, right);
flow_at_point[0] = extrapolateValueInRect(height, width,
top_left[0], top_right[0],
bottom_left[0], bottom_right[0],
rr-top, cc-left);
flow_at_point[1] = extrapolateValueInRect(height, width,
top_left[1], top_right[1],
bottom_left[1], bottom_right[1],
rr-top, cc-left);
flow.at<Vec2f>(rr, cc) = flow_at_point;
}
}
}
}
}
}
static void buildPyramidWithResizeMethod(const Mat& src,
std::vector<Mat>& pyramid,
int layers,
int interpolation_type) {
pyramid.push_back(src);
for (int i = 1; i <= layers; ++i) {
Mat prev = pyramid[i - 1];
if (prev.rows <= 1 || prev.cols <= 1) {
break;
}
Mat next;
resize(prev, next, Size((prev.cols + 1) / 2, (prev.rows + 1) / 2), 0, 0, interpolation_type);
pyramid.push_back(next);
}
}
CV_EXPORTS_W void calcOpticalFlowSF(InputArray _from,
InputArray _to,
OutputArray _resulted_flow,
int layers,
int averaging_radius,
int max_flow,
double sigma_dist,
double sigma_color,
int postprocess_window,
double sigma_dist_fix,
double sigma_color_fix,
double occ_thr,
int upscale_averaging_radius,
double upscale_sigma_dist,
double upscale_sigma_color,
double speed_up_thr)
{
Mat from = _from.getMat();
Mat to = _to.getMat();
std::vector<Mat> pyr_from_images;
std::vector<Mat> pyr_to_images;
buildPyramidWithResizeMethod(from, pyr_from_images, layers - 1, INTER_CUBIC);
buildPyramidWithResizeMethod(to, pyr_to_images, layers - 1, INTER_CUBIC);
CV_Assert((int)pyr_from_images.size() == layers && (int)pyr_to_images.size() == layers);
Mat curr_from, curr_to, prev_from, prev_to;
Mat curr_from_extended, curr_to_extended;
curr_from = pyr_from_images[layers - 1];
curr_to = pyr_to_images[layers - 1];
copyMakeBorder(curr_from, curr_from_extended,
averaging_radius, averaging_radius, averaging_radius, averaging_radius,
BORDER_DEFAULT);
copyMakeBorder(curr_to, curr_to_extended,
averaging_radius, averaging_radius, averaging_radius, averaging_radius,
BORDER_DEFAULT);
Mat mask = Mat::ones(curr_from.size(), CV_8U);
Mat mask_inv = Mat::ones(curr_from.size(), CV_8U);
Mat flow = Mat::zeros(curr_from.size(), CV_32FC2);
Mat flow_inv = Mat::zeros(curr_to.size(), CV_32FC2);
Mat confidence;
Mat confidence_inv;
calcOpticalFlowSingleScaleSF(curr_from_extended,
curr_to_extended,
mask,
flow,
averaging_radius,
max_flow,
(float)sigma_dist,
(float)sigma_color);
calcOpticalFlowSingleScaleSF(curr_to_extended,
curr_from_extended,
mask_inv,
flow_inv,
averaging_radius,
max_flow,
(float)sigma_dist,
(float)sigma_color);
removeOcclusions(flow,
flow_inv,
(float)occ_thr,
confidence);
removeOcclusions(flow_inv,
flow,
(float)occ_thr,
confidence_inv);
Mat speed_up = Mat::zeros(curr_from.size(), CV_8U);
Mat speed_up_inv = Mat::zeros(curr_from.size(), CV_8U);
for (int curr_layer = layers - 2; curr_layer >= 0; --curr_layer) {
curr_from = pyr_from_images[curr_layer];
curr_to = pyr_to_images[curr_layer];
prev_from = pyr_from_images[curr_layer + 1];
prev_to = pyr_to_images[curr_layer + 1];
copyMakeBorder(curr_from, curr_from_extended,
averaging_radius, averaging_radius, averaging_radius, averaging_radius,
BORDER_DEFAULT);
copyMakeBorder(curr_to, curr_to_extended,
averaging_radius, averaging_radius, averaging_radius, averaging_radius,
BORDER_DEFAULT);
const int curr_rows = curr_from.rows;
const int curr_cols = curr_from.cols;
Mat new_speed_up, new_speed_up_inv;
selectPointsToRecalcFlow(flow,
averaging_radius,
(float)speed_up_thr,
curr_rows,
curr_cols,
speed_up,
new_speed_up,
mask);
selectPointsToRecalcFlow(flow_inv,
averaging_radius,
(float)speed_up_thr,
curr_rows,
curr_cols,
speed_up_inv,
new_speed_up_inv,
mask_inv);
speed_up = new_speed_up;
speed_up_inv = new_speed_up_inv;
flow = upscaleOpticalFlow(curr_rows,
curr_cols,
prev_from,
confidence,
flow,
upscale_averaging_radius,
(float)upscale_sigma_dist,
(float)upscale_sigma_color);
flow_inv = upscaleOpticalFlow(curr_rows,
curr_cols,
prev_to,
confidence_inv,
flow_inv,
upscale_averaging_radius,
(float)upscale_sigma_dist,
(float)upscale_sigma_color);
calcConfidence(curr_from, curr_to, flow, confidence, max_flow);
calcOpticalFlowSingleScaleSF(curr_from_extended,
curr_to_extended,
mask,
flow,
averaging_radius,
max_flow,
(float)sigma_dist,
(float)sigma_color);
calcConfidence(curr_to, curr_from, flow_inv, confidence_inv, max_flow);
calcOpticalFlowSingleScaleSF(curr_to_extended,
curr_from_extended,
mask_inv,
flow_inv,
averaging_radius,
max_flow,
(float)sigma_dist,
(float)sigma_color);
extrapolateFlow(flow, speed_up);
extrapolateFlow(flow_inv, speed_up_inv);
//TODO: should we remove occlusions for the last stage?
removeOcclusions(flow, flow_inv, (float)occ_thr, confidence);
removeOcclusions(flow_inv, flow, (float)occ_thr, confidence_inv);
}
crossBilateralFilter(flow, curr_from, confidence, flow,
postprocess_window, (float)sigma_color_fix, (float)sigma_dist_fix);
GaussianBlur(flow, flow, Size(3, 3), 5);
_resulted_flow.create(flow.size(), CV_32FC2);
Mat resulted_flow = _resulted_flow.getMat();
int from_to[] = {0,1 , 1,0};
mixChannels(&flow, 1, &resulted_flow, 1, from_to, 2);
}
CV_EXPORTS_W void calcOpticalFlowSF(InputArray from,
InputArray to,
OutputArray flow,
int layers,
int averaging_block_size,
int max_flow) {
calcOpticalFlowSF(from, to, flow, layers, averaging_block_size, max_flow,
4.1, 25.5, 18, 55.0, 25.5, 0.35, 18, 55.0, 25.5, 10);
}
}
}
