// This file is part of OpenCV project. // It is subject to the license terms in the LICENSE file found in the top-level directory // of this distribution and at http://opencv.org/license.html. #include "../precomp.hpp" #include "../usac.hpp" namespace cv { namespace usac { int Quality::getInliers(const Ptr &error, const Mat &model, std::vector &inliers, double threshold) { const auto &errors = error->getErrors(model); int num_inliers = 0; for (int point = 0; point < (int)inliers.size(); point++) if (errors[point] < threshold) inliers[num_inliers++] = point; return num_inliers; } int Quality::getInliers(const Ptr &error, const Mat &model, std::vector &inliers_mask, double threshold) { std::fill(inliers_mask.begin(), inliers_mask.end(), false); const auto &errors = error->getErrors(model); int num_inliers = 0; for (int point = 0; point < (int)inliers_mask.size(); point++) if (errors[point] < threshold) { inliers_mask[point] = true; num_inliers++; } return num_inliers; } int Quality::getInliers (const std::vector &errors, std::vector &inliers, double threshold) { std::fill(inliers.begin(), inliers.end(), false); int cnt = 0, inls = 0; for (const auto e : errors) { if (e < threshold) { inliers[cnt] = true; inls++; } cnt++; } return inls; } int Quality::getInliers (const std::vector &errors, std::vector &inliers, double threshold) { int cnt = 0, inls = 0; for (const auto e : errors) { if (e < threshold) inliers[inls++] = cnt; cnt++; } return inls; } class RansacQualityImpl : public RansacQuality { private: const Ptr error; const int points_size; const double threshold; double best_score; public: RansacQualityImpl (int points_size_, double threshold_, const Ptr &error_) : error (error_), points_size(points_size_), threshold(threshold_) { best_score = std::numeric_limits::max(); } Score getScore (const Mat &model) const override { error->setModelParameters(model); int inlier_number = 0; const auto preemptive_thr = -points_size - best_score; for (int point = 0; point < points_size; point++) if (error->getError(point) < threshold) inlier_number++; else if (inlier_number - point < preemptive_thr) break; // score is negative inlier number! If less then better return {inlier_number, -static_cast(inlier_number)}; } Score getScore (const std::vector &errors) const override { int inlier_number = 0; for (int point = 0; point < points_size; point++) if (errors[point] < threshold) inlier_number++; // score is negative inlier number! If less then better return {inlier_number, -static_cast(inlier_number)}; } void setBestScore(float best_score_) override { if (best_score > best_score_) best_score = best_score_; } int getInliers (const Mat &model, std::vector &inliers) const override { return Quality::getInliers(error, model, inliers, threshold); } int getInliers (const Mat &model, std::vector &inliers, double thr) const override { return Quality::getInliers(error, model, inliers, thr); } int getInliers (const Mat &model, std::vector &inliers_mask) const override { return Quality::getInliers(error, model, inliers_mask, threshold); } double getThreshold () const override { return threshold; } int getPointsSize () const override { return points_size; } Ptr getErrorFnc () const override { return error; } }; Ptr RansacQuality::create(int points_size_, double threshold_, const Ptr &error_) { return makePtr(points_size_, threshold_, error_); } class MsacQualityImpl : public MsacQuality { protected: const Ptr error; const int points_size; const double threshold, k_msac; const float norm_thr, one_over_thr; float best_score; public: MsacQualityImpl (int points_size_, double threshold_, const Ptr &error_, double k_msac_) : error (error_), points_size (points_size_), threshold (threshold_), k_msac(k_msac_), norm_thr(static_cast(threshold*k_msac)), one_over_thr(1.f/norm_thr), best_score(std::numeric_limits::max()) {} inline Score getScore (const Mat &model) const override { error->setModelParameters(model); float err, sum_errors = 0; int inlier_number = 0; const auto preemptive_thr = points_size + best_score; for (int point = 0; point < points_size; point++) { err = error->getError(point); if (err < norm_thr) { sum_errors -= (1 - err * one_over_thr); if (err < threshold) inlier_number++; } else if (sum_errors + point > preemptive_thr) break; } return {inlier_number, sum_errors}; } Score getScore (const std::vector &errors) const override { float sum_errors = 0; int inlier_number = 0; for (int point = 0; point < points_size; point++) { const auto err = errors[point]; if (err < norm_thr) { sum_errors -= (1 - err * one_over_thr); if (err < threshold) inlier_number++; } } return {inlier_number, sum_errors}; } void setBestScore(float best_score_) override { if (best_score > best_score_) best_score = best_score_; } int getInliers (const Mat &model, std::vector &inliers) const override { return Quality::getInliers(error, model, inliers, threshold); } int getInliers (const Mat &model, std::vector &inliers, double thr) const override { return Quality::getInliers(error, model, inliers, thr); } int getInliers (const Mat &model, std::vector &inliers_mask) const override { return Quality::getInliers(error, model, inliers_mask, threshold); } double getThreshold () const override { return threshold; } int getPointsSize () const override { return points_size; } Ptr getErrorFnc () const override { return error; } }; Ptr MsacQuality::create(int points_size_, double threshold_, const Ptr &error_, double k_msac) { return makePtr(points_size_, threshold_, error_, k_msac); } class MagsacQualityImpl : public MagsacQuality { private: const Ptr error; const Ptr gamma_generator; const int points_size; // for example, maximum standard deviation of noise. const double maximum_threshold_sqr, tentative_inlier_threshold; // Calculate the gamma value of k const double gamma_value_of_k; double previous_best_loss; float maximum_sigma_2_per_2; // Calculating 2^(DoF + 1) / \sigma_{max} which will be used for the estimation and, // due to being constant, it is better to calculate it a priori. double two_ad_dof_plus_one_per_maximum_sigma, rescale_err, norm_loss; const std::vector &stored_complete_gamma_values, &stored_lower_incomplete_gamma_values; unsigned int stored_incomplete_gamma_number_min1; public: MagsacQualityImpl (double maximum_thr, int points_size_, const Ptr &error_, const Ptr &gamma_generator_, double tentative_inlier_threshold_, int DoF, double sigma_quantile, double upper_incomplete_of_sigma_quantile) : error (error_), gamma_generator(gamma_generator_), points_size(points_size_), maximum_threshold_sqr(maximum_thr*maximum_thr), tentative_inlier_threshold(tentative_inlier_threshold_), gamma_value_of_k (upper_incomplete_of_sigma_quantile), stored_complete_gamma_values (gamma_generator->getCompleteGammaValues()), stored_lower_incomplete_gamma_values (gamma_generator->getIncompleteGammaValues()) { previous_best_loss = std::numeric_limits::max(); const auto maximum_sigma = (float)sqrt(maximum_threshold_sqr) / sigma_quantile; const auto maximum_sigma_2 = (float) (maximum_sigma * maximum_sigma); maximum_sigma_2_per_2 = maximum_sigma_2 / 2.f; const auto maximum_sigma_2_times_2 = maximum_sigma_2 * 2.f; two_ad_dof_plus_one_per_maximum_sigma = pow(2.0, (DoF + 1.0)*.5)/maximum_sigma; rescale_err = gamma_generator->getScaleOfGammaCompleteValues() / maximum_sigma_2_times_2; stored_incomplete_gamma_number_min1 = static_cast(gamma_generator->getTableSize()-1); double max_loss = 1e-10; // MAGSAC maximum / minimum loss does not have to be in extremum residuals // make 30 iterations to find maximum loss const double step = maximum_threshold_sqr / 30; double sqr_res = 0; while (sqr_res < maximum_threshold_sqr) { auto x= static_cast(rescale_err * sqr_res); if (x > stored_incomplete_gamma_number_min1) x = stored_incomplete_gamma_number_min1; const double loss = two_ad_dof_plus_one_per_maximum_sigma * (maximum_sigma_2_per_2 * stored_lower_incomplete_gamma_values[x] + sqr_res * 0.25 * (stored_complete_gamma_values[x] - gamma_value_of_k)); if (max_loss < loss) max_loss = loss; sqr_res += step; } norm_loss = two_ad_dof_plus_one_per_maximum_sigma / max_loss; } // https://github.com/danini/magsac Score getScore (const Mat &model) const override { error->setModelParameters(model); double total_loss = 0.0; int num_tentative_inliers = 0; const auto preemptive_thr = points_size + previous_best_loss; for (int point_idx = 0; point_idx < points_size; point_idx++) { const float squared_residual = error->getError(point_idx); if (squared_residual < tentative_inlier_threshold) num_tentative_inliers++; if (squared_residual < maximum_threshold_sqr) { // consider point as inlier // Get the position of the gamma value in the lookup table auto x = static_cast(rescale_err * squared_residual); // If the sought gamma value is not stored in the lookup, return the closest element if (x > stored_incomplete_gamma_number_min1) x = stored_incomplete_gamma_number_min1; // Calculate the loss implied by the current point total_loss -= (1 - (maximum_sigma_2_per_2 * stored_lower_incomplete_gamma_values[x] + squared_residual * 0.25 * (stored_complete_gamma_values[x] - gamma_value_of_k)) * norm_loss); } else if (total_loss + point_idx > preemptive_thr) break; } return {num_tentative_inliers, (float)total_loss}; } Score getScore (const std::vector &errors) const override { double total_loss = 0.0; int num_tentative_inliers = 0; for (int point_idx = 0; point_idx < points_size; point_idx++) { const float squared_residual = errors[point_idx]; if (squared_residual < tentative_inlier_threshold) num_tentative_inliers++; if (squared_residual < maximum_threshold_sqr) { auto x = static_cast(rescale_err * squared_residual); if (x > stored_incomplete_gamma_number_min1) x = stored_incomplete_gamma_number_min1; total_loss -= (1 - (maximum_sigma_2_per_2 * stored_lower_incomplete_gamma_values[x] + squared_residual * 0.25 * (stored_complete_gamma_values[x] - gamma_value_of_k)) * norm_loss); } } return {num_tentative_inliers, (float)total_loss}; } void setBestScore (float best_loss) override { if (previous_best_loss > best_loss) previous_best_loss = best_loss; } int getInliers (const Mat &model, std::vector &inliers) const override { return Quality::getInliers(error, model, inliers, tentative_inlier_threshold); } int getInliers (const Mat &model, std::vector &inliers, double thr) const override { return Quality::getInliers(error, model, inliers, thr); } int getInliers (const Mat &model, std::vector &inliers_mask) const override { return Quality::getInliers(error, model, inliers_mask, tentative_inlier_threshold); } double getThreshold () const override { return tentative_inlier_threshold; } int getPointsSize () const override { return points_size; } Ptr getErrorFnc () const override { return error; } }; Ptr MagsacQuality::create(double maximum_thr, int points_size_, const Ptr &error_, const Ptr &gamma_generator, double tentative_inlier_threshold_, int DoF, double sigma_quantile, double upper_incomplete_of_sigma_quantile) { return makePtr(maximum_thr, points_size_, error_, gamma_generator, tentative_inlier_threshold_, DoF, sigma_quantile, upper_incomplete_of_sigma_quantile); } class LMedsQualityImpl : public LMedsQuality { private: const Ptr error; const int points_size; const double threshold; public: LMedsQualityImpl (int points_size_, double threshold_, const Ptr &error_) : error (error_), points_size (points_size_), threshold (threshold_) {} // Finds median of errors. Score getScore (const Mat &model) const override { std::vector errors = error->getErrors(model); int inlier_number = 0; for (int point = 0; point < points_size; point++) if (errors[point] < threshold) inlier_number++; // score is median of errors return {inlier_number, Utils::findMedian (errors)}; } Score getScore (const std::vector &errors_) const override { std::vector errors = errors_; int inlier_number = 0; for (int point = 0; point < points_size; point++) if (errors[point] < threshold) inlier_number++; // score is median of errors return {inlier_number, Utils::findMedian (errors)}; } void setBestScore (float /*best_score*/) override {} int getPointsSize () const override { return points_size; } int getInliers (const Mat &model, std::vector &inliers) const override { return Quality::getInliers(error, model, inliers, threshold); } int getInliers (const Mat &model, std::vector &inliers, double thr) const override { return Quality::getInliers(error, model, inliers, thr); } int getInliers (const Mat &model, std::vector &inliers_mask) const override { return Quality::getInliers(error, model, inliers_mask, threshold); } double getThreshold () const override { return threshold; } Ptr getErrorFnc () const override { return error; } }; Ptr LMedsQuality::create(int points_size_, double threshold_, const Ptr &error_) { return makePtr(points_size_, threshold_, error_); } class ModelVerifierImpl : public ModelVerifier { private: Ptr quality; public: ModelVerifierImpl (const Ptr &q) : quality(q) {} inline bool isModelGood(const Mat &model, Score &score) override { score = quality->getScore(model); return true; } void update (const Score &/*score*/, int /*iteration*/) override {} void reset() override {} void updateSPRT (double , double , double , double , double , const Score &) override {} }; Ptr ModelVerifier::create(const Ptr &quality) { return makePtr(quality); } class AdaptiveSPRTImpl : public AdaptiveSPRT { private: RNG rng; const Ptr err; const Ptr quality; const int points_size; int highest_inlier_number, last_iteration; // time t_M needed to instantiate a model hypothesis given a sample // Let m_S be the number of models that are verified per sample const double inlier_threshold, norm_thr, one_over_thr; // alpha is false negative rate, alpha = 1 / A double t_M, lowest_sum_errors, current_epsilon, current_delta, current_A, delta_to_epsilon, complement_delta_to_complement_epsilon, time_ver_corr_sprt = 0, time_ver_corr = 0, one_over_complement_alpha, avg_num_checked_pts; std::vector sprt_histories, empty; std::vector points_random_pool; std::vector errors; bool do_sprt, adapt, IS_ADAPTIVE; const ScoreMethod score_type; double m_S; public: AdaptiveSPRTImpl (int state, const Ptr &quality_, int points_size_, double inlier_threshold_, double prob_pt_of_good_model, double prob_pt_of_bad_model, double time_sample, double avg_num_models, ScoreMethod score_type_, double k_mlesac_, bool is_adaptive) : rng(state), err(quality_->getErrorFnc()), quality(quality_), points_size(points_size_), inlier_threshold (quality->getThreshold()), norm_thr(inlier_threshold_*k_mlesac_), one_over_thr (1/norm_thr), t_M (time_sample), score_type (score_type_), m_S (avg_num_models) { // Generate array of random points for randomized evaluation points_random_pool = std::vector (points_size_); // fill values from 0 to points_size-1 for (int i = 0; i < points_size; i++) points_random_pool[i] = i; randShuffle(points_random_pool, 1, &rng); // reserve (approximately) some space for sprt vector. sprt_histories.reserve(20); highest_inlier_number = last_iteration = 0; lowest_sum_errors = std::numeric_limits::max(); if (score_type_ != ScoreMethod::SCORE_METHOD_MSAC) errors = std::vector(points_size_); IS_ADAPTIVE = is_adaptive; delta_to_epsilon = one_over_complement_alpha = complement_delta_to_complement_epsilon = current_A = -1; avg_num_checked_pts = points_size_; adapt = IS_ADAPTIVE; do_sprt = !IS_ADAPTIVE; if (IS_ADAPTIVE) { // all these variables will be initialized later current_epsilon = prob_pt_of_good_model; current_delta = prob_pt_of_bad_model; } else { current_epsilon = current_delta = 1e-5; createTest(prob_pt_of_good_model, prob_pt_of_bad_model); } } /* * p(x(r)|Hb) p(x(j)|Hb) * lambda(j) = Product (----------) = lambda(j-1) * ---------- * p(x(r)|Hg) p(x(j)|Hg) * Set j = 1 * 1. Check whether j-th data point is consistent with the * model * 2. Compute the likelihood ratio λj eq. (1) * 3. If λj > A, decide the model is ’bad’ (model "re-jected"), * else increment j or continue testing * 4. If j = N the number of correspondences decide model "accepted" * * Verifies model and returns model score. * Returns true if model is good, false - otherwise. * @model: model to verify * @current_hypothesis: current RANSAC iteration * Return: true if model is good, false - otherwise. */ inline bool isModelGood (const Mat &model, Score &out_score) override { // update error object with current model bool last_model_is_good = true; double sum_errors = 0; int tested_inliers = 0; if (! do_sprt || adapt) { // if adapt or not sprt then compute model score directly out_score = quality->getScore(model); tested_inliers = out_score.inlier_number; sum_errors = out_score.score; } else { // do sprt and not adapt err->setModelParameters(model); double lambda = 1; int random_pool_idx = rng.uniform(0, points_size), tested_point; if (score_type == ScoreMethod::SCORE_METHOD_MSAC) { const auto preemptive_thr = points_size + lowest_sum_errors; for (tested_point = 0; tested_point < points_size; tested_point++) { if (random_pool_idx == points_size) random_pool_idx = 0; const float error = err->getError (points_random_pool[random_pool_idx++]); if (error < inlier_threshold) { tested_inliers++; lambda *= delta_to_epsilon; } else { lambda *= complement_delta_to_complement_epsilon; // since delta is always higher than epsilon, then lambda can increase only // when point is not consistent with model if (lambda > current_A) break; } if (error < norm_thr) sum_errors -= (1 - error * one_over_thr); else if (sum_errors + tested_point > preemptive_thr) break; } } else { // save errors into array here for (tested_point = 0; tested_point < points_size; tested_point++) { if (random_pool_idx == points_size) random_pool_idx = 0; const int pt = points_random_pool[random_pool_idx++]; const float error = err->getError (pt); if (error < inlier_threshold) { tested_inliers++; lambda *= delta_to_epsilon; } else { lambda *= complement_delta_to_complement_epsilon; if (lambda > current_A) break; } errors[pt] = error; } } last_model_is_good = tested_point == points_size; } if (last_model_is_good && do_sprt) { out_score.inlier_number = tested_inliers; if (score_type == ScoreMethod::SCORE_METHOD_MSAC) out_score.score = static_cast(sum_errors); else if (score_type == ScoreMethod::SCORE_METHOD_RANSAC) out_score.score = -static_cast(tested_inliers); else out_score = quality->getScore(errors); } return last_model_is_good; } // update SPRT parameters = called only once inside usac void updateSPRT (double time_model_est, double time_corr_ver, double new_avg_models, double new_delta, double new_epsilon, const Score &best_score) override { if (adapt) { adapt = false; m_S = new_avg_models; t_M = time_model_est / time_corr_ver; time_ver_corr = time_corr_ver; time_ver_corr_sprt = time_corr_ver * 1.05; createTest(new_epsilon, new_delta); highest_inlier_number = best_score.inlier_number; lowest_sum_errors = best_score.score; } } const std::vector &getSPRTvector () const override { return adapt ? empty : sprt_histories; } void update (const Score &score, int iteration) override { if (adapt || highest_inlier_number > score.inlier_number) return; if (sprt_histories.size() == 1 && sprt_histories.back().tested_samples == 0) sprt_histories.back().tested_samples = iteration; else if (! sprt_histories.empty()) sprt_histories.back().tested_samples += iteration - last_iteration; SPRT_history new_sprt_history; new_sprt_history.epsilon = (double)score.inlier_number / points_size; highest_inlier_number = score.inlier_number; lowest_sum_errors = score.score; createTest(static_cast(highest_inlier_number) / points_size, current_delta); new_sprt_history.delta = current_delta; new_sprt_history.A = current_A; sprt_histories.emplace_back(new_sprt_history); last_iteration = iteration; } int avgNumCheckedPts () const override { return do_sprt ? (int)avg_num_checked_pts + 1 : points_size; } void reset() override { adapt = true; do_sprt = false; highest_inlier_number = last_iteration = 0; lowest_sum_errors = DBL_MAX; sprt_histories.clear(); } private: // Update current epsilon, delta and threshold (A). bool createTest (double epsilon, double delta) { if (fabs(current_epsilon - epsilon) < FLT_EPSILON && fabs(current_delta - delta) < FLT_EPSILON) return false; // if epsilon is closed to 1 then set them to 0.99 to avoid numerical problems if (epsilon > 0.999999) epsilon = 0.999; // delta can't be higher than epsilon, because ratio delta / epsilon will be greater than 1 if (epsilon < delta) delta = epsilon-0.001; // avoid delta going too high as it is very unlikely // e.g., 30% of points are consistent with bad model is not very real if (delta > 0.3) delta = 0.3; const auto AC = estimateThresholdA (epsilon, delta); current_A = AC.first; const auto C = AC.second; current_delta = delta; current_epsilon = epsilon; one_over_complement_alpha = 1 / (1 - 1 / current_A); delta_to_epsilon = delta / epsilon; complement_delta_to_complement_epsilon = (1 - delta) / (1 - epsilon); if (IS_ADAPTIVE) { avg_num_checked_pts = std::min((log(current_A) / C) * one_over_complement_alpha, (double)points_size); do_sprt = time_ver_corr_sprt * avg_num_checked_pts < time_ver_corr * points_size; } return true; } std::pair estimateThresholdA (double epsilon, double delta) { const double C = (1 - delta) * log ((1 - delta) / (1 - epsilon)) + delta * log (delta / epsilon); // K = K1/K2 + 1 = (t_M / P_g) / (m_S / (C * P_g)) + 1 = (t_M * C)/m_S + 1 const double K = t_M * C / m_S + 1; double An, An_1 = K; // compute A using a recursive relation // A* = lim(n->inf)(An), the series typically converges within 4 iterations for (int i = 0; i < 10; i++) { An = K + log(An_1); if (fabs(An - An_1) < FLT_EPSILON) break; An_1 = An; } return std::make_pair(An, C); } }; Ptr AdaptiveSPRT::create (int state, const Ptr &quality, int points_size_, double inlier_threshold_, double prob_pt_of_good_model, double prob_pt_of_bad_model, double time_sample, double avg_num_models, ScoreMethod score_type_, double k_mlesac, bool is_adaptive) { return makePtr(state, quality, points_size_, inlier_threshold_, prob_pt_of_good_model, prob_pt_of_bad_model, time_sample, avg_num_models, score_type_, k_mlesac, is_adaptive); } }}