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-// 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 WeightedGraph<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_