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-/*
- * 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 &params, 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 &params, 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