ceres-solver / ceres-solver / a3dde68770de810e0962e30575e6a810dff22650 / . / internal / ceres / canonical_views_clustering.h

// Ceres Solver - A fast non-linear least squares minimizer | |

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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 <unordered_map> | |

#include <vector> | |

#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 | |

// interchangeably. Given a weighted Graph G(V,E), the canonical views | |

// of G are 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, | |

std::unordered_map<int, int>* membership); | |

struct CanonicalViewsClusteringOptions { | |

// The minimum number of canonical views to compute. | |

int min_views = 3; | |

// Penalty weight for the number of canonical views. A higher | |

// number will result in fewer canonical views. | |

double size_penalty_weight = 5.75; | |

// Penalty weight for the diversity (orthogonality) of the | |

// canonical views. A higher number will encourage less similar | |

// canonical views. | |

double similarity_penalty_weight = 100; | |

// Weight for per-view scores. Lower weight places less | |

// confidence in the view scores. | |

double view_score_weight = 0.0; | |

}; | |

} // namespace internal | |

} // namespace ceres | |

#endif // CERES_INTERNAL_CANONICAL_VIEWS_CLUSTERING_H_ |