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// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2017 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// 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 <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 {
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, nullptr);
// preconditioner.RightMultiply(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 RightMultiply(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 internal
} // namespace ceres
#endif // CERES_INTERNAL_VISIBILITY_BASED_PRECONDITIONER_H_
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