| /* |
| * Copyright (c) 2018 ARM Limited. |
| * |
| * SPDX-License-Identifier: MIT |
| * |
| * Permission is hereby granted, free of charge, to any person obtaining a copy |
| * of this software and associated documentation files (the "Software"), to |
| * deal in the Software without restriction, including without limitation the |
| * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or |
| * sell copies of the Software, and to permit persons to whom the Software is |
| * furnished to do so, subject to the following conditions: |
| * |
| * The above copyright notice and this permission notice shall be included in all |
| * copies or substantial portions of the Software. |
| * |
| * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
| * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
| * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
| * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE |
| * SOFTWARE. |
| */ |
| #include "OpticalFlow.h" |
| |
| #include "GaussianPyramidHalf.h" |
| #include "Scharr.h" |
| #include "Utils.h" |
| |
| namespace arm_compute |
| { |
| namespace test |
| { |
| namespace validation |
| { |
| namespace reference |
| { |
| namespace |
| { |
| using KeyPointArray = std::vector<KeyPoint>; |
| using InternalKeyPointArray = std::vector<InternalKeyPoint>; |
| |
| // Constants used for Lucas-Kanade Algorithm |
| constexpr int W_BITS = 14; |
| constexpr float D0 = 1 << W_BITS; |
| constexpr float DETERMINANT_THRESHOLD = 1.0e-07f; |
| constexpr float EIGENVALUE_THRESHOLD = 1.0e-04f; |
| constexpr float FLT_SCALE = 1.0f / (1 << 20); |
| |
| // Creates an InternalKeyPointArray for tracking non-integral pixel coordinates |
| InternalKeyPointArray create_internal_keypoints(const KeyPointArray &keypoints) |
| { |
| InternalKeyPointArray internal_keypoints; |
| |
| for(auto keypoint : keypoints) |
| { |
| InternalKeyPoint internal_keypoint; |
| |
| internal_keypoint.x = static_cast<float>(keypoint.x); |
| internal_keypoint.y = static_cast<float>(keypoint.y); |
| internal_keypoint.tracking_status = static_cast<bool>(keypoint.tracking_status); |
| |
| internal_keypoints.push_back(internal_keypoint); |
| } |
| |
| return internal_keypoints; |
| } |
| |
| // Scale tracked points based on Pyramid level |
| void scale_tracked_points(size_t level, size_t num_levels, bool use_initial_estimate, |
| InternalKeyPointArray &old_points_internal, InternalKeyPointArray &new_points_internal, |
| const KeyPointArray &old_points, const KeyPointArray &new_points_estimates) |
| { |
| if(level == num_levels - 1) // lowest resolution |
| { |
| const float scale = std::pow(SCALE_PYRAMID_HALF, level); |
| |
| for(size_t i = 0; i < old_points.size(); ++i) |
| { |
| old_points_internal.at(i).x = old_points.at(i).x * scale; |
| old_points_internal.at(i).y = old_points.at(i).y * scale; |
| old_points_internal.at(i).tracking_status = true; |
| |
| InternalKeyPoint keypoint_to_track; |
| |
| if(use_initial_estimate) |
| { |
| keypoint_to_track.x = new_points_estimates.at(i).x * scale; |
| keypoint_to_track.y = new_points_estimates.at(i).y * scale; |
| keypoint_to_track.tracking_status = (new_points_estimates.at(i).tracking_status == 1); |
| } |
| else |
| { |
| keypoint_to_track.x = old_points_internal.at(i).x; |
| keypoint_to_track.y = old_points_internal.at(i).y; |
| keypoint_to_track.tracking_status = true; |
| } |
| |
| new_points_internal.at(i) = keypoint_to_track; |
| } |
| } |
| else |
| { |
| for(size_t i = 0; i < old_points.size(); ++i) |
| { |
| old_points_internal.at(i).x /= SCALE_PYRAMID_HALF; |
| old_points_internal.at(i).y /= SCALE_PYRAMID_HALF; |
| new_points_internal.at(i).x /= SCALE_PYRAMID_HALF; |
| new_points_internal.at(i).y /= SCALE_PYRAMID_HALF; |
| } |
| } |
| } |
| |
| bool is_invalid_keypoint(const InternalKeyPoint &keypoint, const ValidRegion &valid_region, size_t window_dimension) |
| { |
| const int half_window = window_dimension / 2; |
| const int x = std::floor(keypoint.x); |
| const int y = std::floor(keypoint.y); |
| |
| return (x - half_window < valid_region.start(0)) || (x + half_window >= valid_region.end(0) - 1) || (y - half_window < valid_region.start(1)) || (y + half_window >= valid_region.end(1) - 1); |
| } |
| |
| template <typename T> |
| constexpr int INT_ROUND(T x, int n) |
| { |
| return (x + (1 << (n - 1))) >> n; |
| } |
| |
| // Return the bilinear value at a specified coordinate with different border modes |
| template <typename T> |
| int bilinear_interpolate(const SimpleTensor<T> &in, Coordinates id, float wx, float wy, BorderMode border_mode, T constant_border_value, int scale) |
| { |
| const int level = id.x(); |
| const int idy = id.y(); |
| |
| const float dx = wx; |
| const float dy = wy; |
| const float dx_1 = 1.0f - dx; |
| const float dy_1 = 1.0f - dy; |
| |
| const T border_value = constant_border_value; |
| |
| id.set(0, level); |
| id.set(1, idy); |
| const T tl = tensor_elem_at(in, id, border_mode, border_value); |
| id.set(0, level + 1); |
| id.set(1, idy); |
| const T tr = tensor_elem_at(in, id, border_mode, border_value); |
| id.set(0, level); |
| id.set(1, idy + 1); |
| const T bl = tensor_elem_at(in, id, border_mode, border_value); |
| id.set(0, level + 1); |
| id.set(1, idy + 1); |
| const T br = tensor_elem_at(in, id, border_mode, border_value); |
| |
| // weights |
| const int w00 = roundf(dx_1 * dy_1 * D0); |
| const int w01 = roundf(dx * dy_1 * D0); |
| const int w10 = roundf(dx_1 * dy * D0); |
| const int w11 = D0 - w00 - w01 - w10; |
| |
| return static_cast<int>(INT_ROUND(tl * w00 + tr * w01 + bl * w10 + br * w11, scale)); |
| } |
| |
| template <typename T> |
| std::vector<int> compute_derivative(const SimpleTensor<T> &input, const InternalKeyPoint &keypoint, |
| BorderMode border_mode, uint8_t constant_border_value, size_t window_dimension, int scale) |
| { |
| std::vector<int> bilinear_values; |
| |
| const int half_window = window_dimension / 2; |
| |
| float keypoint_int_x = 0; |
| float keypoint_int_y = 0; |
| |
| const float wx = std::modf(keypoint.x, &keypoint_int_x); |
| const float wy = std::modf(keypoint.y, &keypoint_int_y); |
| |
| Coordinates tl_window(static_cast<int>(keypoint_int_x) - half_window, static_cast<int>(keypoint_int_y) - half_window); |
| Coordinates br_window(static_cast<int>(keypoint_int_x) + half_window, static_cast<int>(keypoint_int_y) + half_window); |
| |
| for(int y = tl_window.y(); y <= br_window.y(); ++y) |
| { |
| for(int x = tl_window.x(); x <= br_window.x(); ++x) |
| { |
| bilinear_values.push_back(bilinear_interpolate(input, Coordinates(x, y), wx, wy, border_mode, static_cast<T>(constant_border_value), scale)); |
| } |
| } |
| |
| return bilinear_values; |
| } |
| |
| std::tuple<float, float, float> compute_spatial_gradient_matrix(const std::vector<int> &bilinear_ix, const std::vector<int> &bilinear_iy) |
| { |
| ARM_COMPUTE_ERROR_ON(bilinear_ix.size() != bilinear_iy.size()); |
| |
| int iA11 = 0; |
| int iA12 = 0; |
| int iA22 = 0; |
| |
| for(size_t i = 0; i < bilinear_ix.size(); ++i) |
| { |
| int ixval = bilinear_ix[i]; |
| int iyval = bilinear_iy[i]; |
| |
| iA11 += ixval * ixval; |
| iA12 += ixval * iyval; |
| iA22 += iyval * iyval; |
| } |
| |
| return std::make_tuple(iA11 * FLT_SCALE, iA12 * FLT_SCALE, iA22 * FLT_SCALE); |
| } |
| |
| std::tuple<double, double> compute_temporal_gradient_vector(const std::vector<int> &bilinear_it_old, |
| const std::vector<int> &bilinear_it_new, |
| const std::vector<int> &bilinear_ix, |
| const std::vector<int> &bilinear_iy) |
| { |
| ARM_COMPUTE_ERROR_ON(bilinear_ix.size() != bilinear_iy.size()); |
| ARM_COMPUTE_ERROR_ON(bilinear_it_old.size() != bilinear_it_new.size()); |
| |
| int ib1 = 0; |
| int ib2 = 0; |
| |
| for(size_t i = 0; i < bilinear_ix.size(); ++i) |
| { |
| int ixval = bilinear_ix[i]; |
| int iyval = bilinear_iy[i]; |
| int ival = bilinear_it_old[i]; |
| int jval = bilinear_it_new[i]; |
| |
| const int diff = jval - ival; |
| |
| ib1 += diff * ixval; |
| ib2 += diff * iyval; |
| } |
| |
| const double b1 = ib1 * FLT_SCALE; |
| const double b2 = ib2 * FLT_SCALE; |
| |
| return std::make_tuple(b1, b2); |
| } |
| } // namespace |
| |
| template <typename T> |
| std::vector<KeyPoint> optical_flow(const SimpleTensor<T> &old_input, const SimpleTensor<T> &new_input, |
| const OpticalFlowParameters ¶ms, size_t num_levels, |
| const std::vector<KeyPoint> &old_points, const std::vector<KeyPoint> &new_points_estimates, |
| BorderMode border_mode, uint8_t constant_border_value) |
| { |
| const int filter_size = 3; // scharr filter size |
| const size_t max_iterations = 1000; // fixed by kernel |
| const size_t window_dimension = params.window_dimension; |
| const size_t num_iterations = (params.termination == Termination::TERM_CRITERIA_EPSILON) ? max_iterations : params.num_iterations; |
| |
| KeyPointArray new_points(old_points.size()); |
| |
| InternalKeyPointArray old_points_internal = create_internal_keypoints(old_points); |
| InternalKeyPointArray new_points_internal = create_internal_keypoints(new_points_estimates); |
| |
| SimpleTensor<int16_t> scharr_gx; |
| SimpleTensor<int16_t> scharr_gy; |
| |
| // Create pyramids |
| std::vector<SimpleTensor<T>> old_pyramid = gaussian_pyramid_half(old_input, border_mode, constant_border_value, num_levels); |
| std::vector<SimpleTensor<T>> new_pyramid = gaussian_pyramid_half(new_input, border_mode, constant_border_value, num_levels); |
| |
| // Iterate over each level of the pyramid |
| for(size_t idx = num_levels; idx > 0; --idx) |
| { |
| const size_t level = idx - 1; |
| |
| // Calculate scharr gradients |
| std::tie(scharr_gx, scharr_gy) = scharr<int16_t, T>(old_pyramid[level], filter_size, border_mode, constant_border_value, GradientDimension::GRAD_XY); |
| |
| scale_tracked_points(level, num_levels, params.use_initial_estimate, old_points_internal, new_points_internal, old_points, new_points_estimates); |
| |
| // Calculate valid region based on image dimensions of current pyramid level |
| const ValidRegion valid_region = shape_to_valid_region(old_pyramid[level].shape(), (border_mode == BorderMode::UNDEFINED), BorderSize(filter_size / 2)); |
| |
| for(size_t i = 0; i < old_points.size(); ++i) |
| { |
| InternalKeyPoint &old_keypoint = old_points_internal.at(i); |
| InternalKeyPoint &new_keypoint = new_points_internal.at(i); |
| |
| // Helper function for untracking keypoints when on the lowest pyramid level (high resolution) |
| const auto untrack_keypoint = [&](bool predicate) |
| { |
| if(predicate && (level == 0)) |
| { |
| new_keypoint.tracking_status = false; |
| return true; |
| } |
| return predicate; |
| }; |
| |
| if(!old_keypoint.tracking_status) |
| { |
| continue; |
| } |
| |
| // Check if tracked coordinate is outside image coordinate |
| if(untrack_keypoint(is_invalid_keypoint(old_keypoint, valid_region, window_dimension))) |
| { |
| continue; |
| } |
| |
| // Compute spatial derivative |
| std::vector<int> bilinear_ix = compute_derivative(scharr_gx, old_keypoint, border_mode, constant_border_value, window_dimension, W_BITS); |
| std::vector<int> bilinear_iy = compute_derivative(scharr_gy, old_keypoint, border_mode, constant_border_value, window_dimension, W_BITS); |
| |
| float A11 = 0.f; |
| float A12 = 0.f; |
| float A22 = 0.f; |
| std::tie(A11, A12, A22) = compute_spatial_gradient_matrix(bilinear_ix, bilinear_iy); |
| |
| // Calculate criteria for lost tracking : Matrix A is invertible |
| // 1. The determinant of the matrix is less than DETERMINANT_THRESHOLD |
| // 2. The minimum eigenvalue of the matrix is less than EIGENVALUE_THRESHOLD |
| const float trace_A = A11 + A22; |
| const float determinant = A11 * A22 - A12 * A12; |
| const float discriminant = (trace_A * trace_A) - 4.0f * (determinant); |
| const float eigenvalue_A = (trace_A - std::sqrt(discriminant)) / 2.0f; |
| |
| // Divide by window_dimension squared to reduce the floating point accummulation error |
| const float eigenvalue = eigenvalue_A / (window_dimension * window_dimension); |
| |
| // Check if it is a good point to track |
| if(untrack_keypoint(eigenvalue < EIGENVALUE_THRESHOLD || determinant < DETERMINANT_THRESHOLD)) |
| { |
| continue; |
| } |
| |
| float prev_delta_x = 0.f; |
| float prev_delta_y = 0.f; |
| |
| for(size_t j = 0; j < num_iterations; ++j) |
| { |
| // Check if tracked coordinate is outside image coordinate |
| if(untrack_keypoint(is_invalid_keypoint(new_keypoint, valid_region, window_dimension))) |
| { |
| break; |
| } |
| |
| // Compute temporal derivative |
| std::vector<int> bilinear_it_old = compute_derivative(old_pyramid[level], old_keypoint, border_mode, constant_border_value, window_dimension, W_BITS - 5); |
| std::vector<int> bilinear_it_new = compute_derivative(new_pyramid[level], new_keypoint, border_mode, constant_border_value, window_dimension, W_BITS - 5); |
| |
| double b1 = 0.f; |
| double b2 = 0.f; |
| std::tie(b1, b2) = compute_temporal_gradient_vector(bilinear_it_old, bilinear_it_new, bilinear_ix, bilinear_iy); |
| |
| // Compute motion vector -> A^-1 * -b |
| const float delta_x = (A12 * b2 - A22 * b1) / determinant; |
| const float delta_y = (A12 * b1 - A11 * b2) / determinant; |
| |
| // Update the new position |
| new_keypoint.x += delta_x; |
| new_keypoint.y += delta_y; |
| |
| const float magnitude_squared = delta_x * delta_x + delta_y * delta_y; |
| |
| // Check if termination criteria is EPSILON and if it is satisfied |
| if(magnitude_squared <= params.epsilon && (params.termination == Termination::TERM_CRITERIA_EPSILON || params.termination == Termination::TERM_CRITERIA_BOTH)) |
| { |
| break; |
| } |
| |
| // Check convergence analyzing the previous delta |
| if(j > 0 && (std::fabs(delta_x + prev_delta_x) < 0.01f && std::fabs(delta_y + prev_delta_y) < 0.01f)) |
| { |
| new_keypoint.x -= delta_x * SCALE_PYRAMID_HALF; |
| new_keypoint.y -= delta_y * SCALE_PYRAMID_HALF; |
| |
| break; |
| } |
| |
| prev_delta_x = delta_x; |
| prev_delta_y = delta_y; |
| } |
| } |
| } |
| |
| // Copy optical flow coordinates to output vector |
| for(size_t i = 0; i < old_points.size(); ++i) |
| { |
| const InternalKeyPoint &new_keypoint = new_points_internal.at(i); |
| |
| new_points.at(i).x = roundf(new_keypoint.x); |
| new_points.at(i).y = roundf(new_keypoint.y); |
| new_points.at(i).tracking_status = new_keypoint.tracking_status ? 1 : 0; |
| } |
| |
| return new_points; |
| } |
| |
| template std::vector<KeyPoint> optical_flow(const SimpleTensor<uint8_t> &old_input, const SimpleTensor<uint8_t> &new_input, |
| const OpticalFlowParameters ¶ms, size_t num_levels, |
| const std::vector<KeyPoint> &old_points, const std::vector<KeyPoint> &new_points_estimates, |
| BorderMode border_mode, uint8_t constant_border_value); |
| } // namespace reference |
| } // namespace validation |
| } // namespace test |
| } // namespace arm_compute |