// 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 <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_