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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
// * Neither the name of Google Inc. nor the names of its contributors may be
// used to endorse or promote products derived from this software without
// specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.
//
// 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 <vector>
#include <utility>
#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/suitesparse.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);
//
#ifndef CERES_NO_SUITESPARSE
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 vector< set<int> >& visibility);
void FlattenMembershipMap(const HashMap<int, int>& membership_map,
vector<int>* membership_vector) const;
void ComputeClusterVisibility(const vector<set<int> >& visibility,
vector<set<int> >* cluster_visibility) const;
Graph<int>* CreateClusterGraph(const vector<set<int> >& visibility) const;
void ForestToClusterPairs(const Graph<int>& forest,
HashSet<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.
vector<int> block_size_;
// Mapping from cameras to clusters.
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).
set<pair<int, int> > block_pairs_;
// Set of cluster pairs (including self pairs (i,i)) in the
// preconditioner.
HashSet<pair<int, int> > cluster_pairs_;
scoped_ptr<SchurEliminatorBase> eliminator_;
// Preconditioner matrix.
scoped_ptr<BlockRandomAccessSparseMatrix> m_;
// RightMultiply is a const method for LinearOperators. It is
// implemented using CHOLMOD's sparse triangular matrix solve
// function. This however requires non-const access to the
// SuiteSparse context object, even though it does not result in any
// of the state of the preconditioner being modified.
SuiteSparse ss_;
// Symbolic and numeric factorization of the preconditioner.
cholmod_factor* factor_;
// Temporary vector used by RightMultiply.
cholmod_dense* tmp_rhs_;
CERES_DISALLOW_COPY_AND_ASSIGN(VisibilityBasedPreconditioner);
};
#else // SuiteSparse
// If SuiteSparse is not compiled in, the preconditioner is not
// available.
class VisibilityBasedPreconditioner : public BlockSparseMatrixPreconditioner {
public:
VisibilityBasedPreconditioner(const CompressedRowBlockStructure& bs,
const Preconditioner::Options& options) {
LOG(FATAL) << "Visibility based preconditioning is not available. Please "
"build Ceres with SuiteSparse.";
}
virtual ~VisibilityBasedPreconditioner() {}
virtual void RightMultiply(const double* x, double* y) const {}
virtual void LeftMultiply(const double* x, double* y) const {}
virtual int num_rows() const { return -1; }
virtual int num_cols() const { return -1; }
private:
bool UpdateImpl(const BlockSparseMatrix& A, const double* D) {
return false;
}
};
#endif // CERES_NO_SUITESPARSE
} // namespace internal
} // namespace ceres
#endif // CERES_INTERNAL_VISIBILITY_BASED_PRECONDITIONER_H_
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