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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 <set>

#include <utility>

#include <vector>

#include "ceres/collections_port.h"

#include "ceres/graph.h"

#include "ceres/internal/macros.h"

#include "ceres/internal/scoped_ptr.h"

#include "ceres/linear_solver.h"

#include "ceres/preconditioner.h"

#include "ceres/sparse_cholesky.h"

namespace ceres {

namespace 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, NULL);

//   preconditioner.RightMultiply(x, y);

class 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,

                                const Preconditioner::Options& options);

  virtual ~VisibilityBasedPreconditioner();

  // Preconditioner interface

  virtual void RightMultiply(const double* x, double* y) const;

  virtual int num_rows() const;

  friend class VisibilityBasedPreconditionerTest;

 private:

  virtual bool UpdateImpl(const BlockSparseMatrix& A, const double* D);

  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 HashMap<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;

  WeightedGraph<int>* CreateClusterGraph(

      const std::vector<std::set<int> >& visibility) const;

  void ForestToClusterPairs(const WeightedGraph<int>& forest,

                            HashSet<std::pair<int, int> >* 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.

  HashSet<std::pair<int, int> > cluster_pairs_;

  scoped_ptr<SchurEliminatorBase> eliminator_;

  // Preconditioner matrix.

  scoped_ptr<BlockRandomAccessSparseMatrix> m_;

  scoped_ptr<SparseCholesky> sparse_cholesky_;

  CERES_DISALLOW_COPY_AND_ASSIGN(VisibilityBasedPreconditioner);

};

}  // namespace internal

}  // namespace ceres

#endif  // CERES_INTERNAL_VISIBILITY_BASED_PRECONDITIONER_H_