// 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) // // An implementation of the Canonical Views clustering algorithm from // "Scene Summarization for Online Image Collections", Ian Simon, Noah // Snavely, Steven M. Seitz, ICCV 2007. // // More details can be found at // http://grail.cs.washington.edu/projects/canonview/ // // Ceres uses this algorithm to perform view clustering for // constructing visibility based preconditioners. #ifndef CERES_INTERNAL_CANONICAL_VIEWS_CLUSTERING_H_ #define CERES_INTERNAL_CANONICAL_VIEWS_CLUSTERING_H_ // This include must come before any #ifndef check on Ceres compile options. #include "ceres/internal/port.h" #ifndef CERES_NO_SUITESPARSE #include <vector> #include "ceres/collections_port.h" #include "ceres/graph.h" namespace ceres { namespace internal { struct CanonicalViewsClusteringOptions; // Compute a partitioning of the vertices of the graph using the // canonical views clustering algorithm. // // In the following we will use the terms vertices and views // interchangably. Given a weighted Graph G(V,E), the canonical views // of G are the the set of vertices that best "summarize" the content // of the graph. If w_ij i s the weight connecting the vertex i to // vertex j, and C is the set of canonical views. Then the objective // of the canonical views algorithm is // // E[C] = sum_[i in V] max_[j in C] w_ij // - size_penalty_weight * |C| // - similarity_penalty_weight * sum_[i in C, j in C, j > i] w_ij // // alpha is the size penalty that penalizes large number of canonical // views. // // beta is the similarity penalty that penalizes canonical views that // are too similar to other canonical views. // // Thus the canonical views algorithm tries to find a canonical view // for each vertex in the graph which best explains it, while trying // to minimize the number of canonical views and the overlap between // them. // // We further augment the above objective function by allowing for per // vertex weights, higher weights indicating a higher preference for // being chosen as a canonical view. Thus if w_i is the vertex weight // for vertex i, the objective function is then // // E[C] = sum_[i in V] max_[j in C] w_ij // - size_penalty_weight * |C| // - similarity_penalty_weight * sum_[i in C, j in C, j > i] w_ij // + view_score_weight * sum_[i in C] w_i // // centers will contain the vertices that are the identified // as the canonical views/cluster centers, and membership is a map // from vertices to cluster_ids. The i^th cluster center corresponds // to the i^th cluster. // // It is possible depending on the configuration of the clustering // algorithm that some of the vertices may not be assigned to any // cluster. In this case they are assigned to a cluster with id = -1; void ComputeCanonicalViewsClustering( const CanonicalViewsClusteringOptions& options, const Graph<int>& graph, vector<int>* centers, HashMap<int, int>* membership); struct CanonicalViewsClusteringOptions { CanonicalViewsClusteringOptions() : min_views(3), size_penalty_weight(5.75), similarity_penalty_weight(100.0), view_score_weight(0.0) { } // The minimum number of canonical views to compute. int min_views; // Penalty weight for the number of canonical views. A higher // number will result in fewer canonical views. double size_penalty_weight; // Penalty weight for the diversity (orthogonality) of the // canonical views. A higher number will encourage less similar // canonical views. double similarity_penalty_weight; // Weight for per-view scores. Lower weight places less // confidence in the view scores. double view_score_weight; }; } // namespace internal } // namespace ceres #endif // CERES_NO_SUITESPARSE #endif // CERES_INTERNAL_CANONICAL_VIEWS_CLUSTERING_H_