internal/ceres/visibility_based_preconditioner.h

// 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/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<int> block_size_;

  // 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_