| // Ceres Solver - A fast non-linear least squares minimizer |
| // Copyright 2015 Google Inc. All rights reserved. |
| // http://ceres-solver.org/ |
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| // 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_ |
| |
| #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 WeightedGraph<int>& graph, |
| std::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_INTERNAL_CANONICAL_VIEWS_CLUSTERING_H_ |