| // Ceres Solver - A fast non-linear least squares minimizer |
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| // Author: sameeragarwal@google.com (Sameer Agarwal) |
| // |
| // Preconditioners for linear systems that arise in Structure from |
| // Motion problems. VisibilityBasedPreconditioner implements: |
| // |
| // CLUSTER_JACOBI |
| // CLUSTER_TRIDIAGONAL |
| // |
| // Detailed descriptions of these preconditions beyond what is |
| // documented here can be found in |
| // |
| // Visibility Based Preconditioning for Bundle Adjustment |
| // A. Kushal & S. Agarwal, CVPR 2012. |
| // |
| // http://www.cs.washington.edu/homes/sagarwal/vbp.pdf |
| // |
| // The two preconditioners share enough code that its most efficient |
| // to implement them as part of the same code base. |
| |
| #ifndef CERES_INTERNAL_VISIBILITY_BASED_PRECONDITIONER_H_ |
| #define CERES_INTERNAL_VISIBILITY_BASED_PRECONDITIONER_H_ |
| |
| #include <memory> |
| #include <set> |
| #include <unordered_map> |
| #include <unordered_set> |
| #include <utility> |
| #include <vector> |
| |
| #include "ceres/block_structure.h" |
| #include "ceres/graph.h" |
| #include "ceres/linear_solver.h" |
| #include "ceres/pair_hash.h" |
| #include "ceres/preconditioner.h" |
| #include "ceres/sparse_cholesky.h" |
| |
| namespace ceres::internal { |
| |
| class BlockRandomAccessSparseMatrix; |
| class BlockSparseMatrix; |
| struct CompressedRowBlockStructure; |
| class SchurEliminatorBase; |
| |
| // This class implements visibility based preconditioners for |
| // Structure from Motion/Bundle Adjustment problems. The name |
| // VisibilityBasedPreconditioner comes from the fact that the sparsity |
| // structure of the preconditioner matrix is determined by analyzing |
| // the visibility structure of the scene, i.e. which cameras see which |
| // points. |
| // |
| // The key idea of visibility based preconditioning is to identify |
| // cameras that we expect have strong interactions, and then using the |
| // entries in the Schur complement matrix corresponding to these |
| // camera pairs as an approximation to the full Schur complement. |
| // |
| // CLUSTER_JACOBI identifies these camera pairs by clustering cameras, |
| // and considering all non-zero camera pairs within each cluster. The |
| // clustering in the current implementation is done using the |
| // Canonical Views algorithm of Simon et al. (see |
| // canonical_views_clustering.h). For the purposes of clustering, the |
| // similarity or the degree of interaction between a pair of cameras |
| // is measured by counting the number of points visible in both the |
| // cameras. Thus the name VisibilityBasedPreconditioner. Further, if we |
| // were to permute the parameter blocks such that all the cameras in |
| // the same cluster occur contiguously, the preconditioner matrix will |
| // be a block diagonal matrix with blocks corresponding to the |
| // clusters. Thus in analogy with the Jacobi preconditioner we refer |
| // to this as the CLUSTER_JACOBI preconditioner. |
| // |
| // CLUSTER_TRIDIAGONAL adds more mass to the CLUSTER_JACOBI |
| // preconditioner by considering the interaction between clusters and |
| // identifying strong interactions between cluster pairs. This is done |
| // by constructing a weighted graph on the clusters, with the weight |
| // on the edges connecting two clusters proportional to the number of |
| // 3D points visible to cameras in both the clusters. A degree-2 |
| // maximum spanning forest is identified in this graph and the camera |
| // pairs contained in the edges of this forest are added to the |
| // preconditioner. The detailed reasoning for this construction is |
| // explained in the paper mentioned above. |
| // |
| // Degree-2 spanning trees and forests have the property that they |
| // correspond to tri-diagonal matrices. Thus there exist a permutation |
| // of the camera blocks under which the CLUSTER_TRIDIAGONAL |
| // preconditioner matrix is a block tridiagonal matrix, and thus the |
| // name for the preconditioner. |
| // |
| // Thread Safety: This class is NOT thread safe. |
| // |
| // Example usage: |
| // |
| // LinearSolver::Options options; |
| // options.preconditioner_type = CLUSTER_JACOBI; |
| // options.elimination_groups.push_back(num_points); |
| // options.elimination_groups.push_back(num_cameras); |
| // VisibilityBasedPreconditioner preconditioner( |
| // *A.block_structure(), options); |
| // preconditioner.Update(A, nullptr); |
| // preconditioner.RightMultiplyAndAccumulate(x, y); |
| class CERES_NO_EXPORT VisibilityBasedPreconditioner |
| : public BlockSparseMatrixPreconditioner { |
| public: |
| // Initialize the symbolic structure of the preconditioner. bs is |
| // the block structure of the linear system to be solved. It is used |
| // to determine the sparsity structure of the preconditioner matrix. |
| // |
| // It has the same structural requirement as other Schur complement |
| // based solvers. Please see schur_eliminator.h for more details. |
| VisibilityBasedPreconditioner(const CompressedRowBlockStructure& bs, |
| Preconditioner::Options options); |
| VisibilityBasedPreconditioner(const VisibilityBasedPreconditioner&) = delete; |
| void operator=(const VisibilityBasedPreconditioner&) = delete; |
| |
| ~VisibilityBasedPreconditioner() override; |
| |
| // Preconditioner interface |
| void RightMultiplyAndAccumulate(const double* x, double* y) const final; |
| int num_rows() const final; |
| |
| friend class VisibilityBasedPreconditionerTest; |
| |
| private: |
| bool UpdateImpl(const BlockSparseMatrix& A, const double* D) final; |
| void ComputeClusterJacobiSparsity(const CompressedRowBlockStructure& bs); |
| void ComputeClusterTridiagonalSparsity(const CompressedRowBlockStructure& bs); |
| void InitStorage(const CompressedRowBlockStructure& bs); |
| void InitEliminator(const CompressedRowBlockStructure& bs); |
| LinearSolverTerminationType Factorize(); |
| void ScaleOffDiagonalCells(); |
| |
| void ClusterCameras(const std::vector<std::set<int>>& visibility); |
| void FlattenMembershipMap(const std::unordered_map<int, int>& membership_map, |
| std::vector<int>* membership_vector) const; |
| void ComputeClusterVisibility( |
| const std::vector<std::set<int>>& visibility, |
| std::vector<std::set<int>>* cluster_visibility) const; |
| std::unique_ptr<WeightedGraph<int>> CreateClusterGraph( |
| const std::vector<std::set<int>>& visibility) const; |
| void ForestToClusterPairs( |
| const WeightedGraph<int>& forest, |
| std::unordered_set<std::pair<int, int>, pair_hash>* cluster_pairs) const; |
| void ComputeBlockPairsInPreconditioner(const CompressedRowBlockStructure& bs); |
| bool IsBlockPairInPreconditioner(int block1, int block2) const; |
| bool IsBlockPairOffDiagonal(int block1, int block2) const; |
| |
| Preconditioner::Options options_; |
| |
| // Number of parameter blocks in the schur complement. |
| int num_blocks_; |
| int num_clusters_; |
| |
| // Sizes of the blocks in the schur complement. |
| std::vector<Block> blocks_; |
| |
| // Mapping from cameras to clusters. |
| std::vector<int> cluster_membership_; |
| |
| // Non-zero camera pairs from the schur complement matrix that are |
| // present in the preconditioner, sorted by row (first element of |
| // each pair), then column (second). |
| std::set<std::pair<int, int>> block_pairs_; |
| |
| // Set of cluster pairs (including self pairs (i,i)) in the |
| // preconditioner. |
| std::unordered_set<std::pair<int, int>, pair_hash> cluster_pairs_; |
| std::unique_ptr<SchurEliminatorBase> eliminator_; |
| |
| // Preconditioner matrix. |
| std::unique_ptr<BlockRandomAccessSparseMatrix> m_; |
| std::unique_ptr<SparseCholesky> sparse_cholesky_; |
| }; |
| |
| } // namespace ceres::internal |
| |
| #endif // CERES_INTERNAL_VISIBILITY_BASED_PRECONDITIONER_H_ |