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// Ceres Solver - A fast non-linear least squares minimizer
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// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
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// http://code.google.com/p/ceres-solver/
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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// * Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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// POSSIBILITY OF SUCH DAMAGE.
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// Author: sameeragarwal@google.com (Sameer Agarwal)
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// An implementation of the Canonical Views clustering algorithm from
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// "Scene Summarization for Online Image Collections", Ian Simon, Noah
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// Snavely, Steven M. Seitz, ICCV 2007.
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// More details can be found at
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// http://grail.cs.washington.edu/projects/canonview/
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// Ceres uses this algorithm to perform view clustering for
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// constructing visibility based preconditioners.
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#ifndef CERES_INTERNAL_CANONICAL_VIEWS_CLUSTERING_H_
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#define CERES_INTERNAL_CANONICAL_VIEWS_CLUSTERING_H_
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#include <glog/logging.h>
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#include "ceres/collections_port.h"
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#include "ceres/graph.h"
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#include "ceres/map_util.h"
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#include "ceres/internal/macros.h"
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class CanonicalViewsClusteringOptions;
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// Compute a partitioning of the vertices of the graph using the
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// canonical views clustering algorithm.
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// In the following we will use the terms vertices and views
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// interchangably. Given a weighted Graph G(V,E), the canonical views
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// of G are the the set of vertices that best "summarize" the content
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// of the graph. If w_ij i s the weight connecting the vertex i to
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// vertex j, and C is the set of canonical views. Then the objective
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// of the canonical views algorithm is
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// E[C] = sum_[i in V] max_[j in C] w_ij
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// - size_penalty_weight * |C|
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// - similarity_penalty_weight * sum_[i in C, j in C, j > i] w_ij
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// alpha is the size penalty that penalizes large number of canonical
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// beta is the similarity penalty that penalizes canonical views that
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// are too similar to other canonical views.
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// Thus the canonical views algorithm tries to find a canonical view
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// for each vertex in the graph which best explains it, while trying
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// to minimize the number of canonical views and the overlap between
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// We further augment the above objective function by allowing for per
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// vertex weights, higher weights indicating a higher preference for
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// being chosen as a canonical view. Thus if w_i is the vertex weight
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// for vertex i, the objective function is then
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// E[C] = sum_[i in V] max_[j in C] w_ij
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// - size_penalty_weight * |C|
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// - similarity_penalty_weight * sum_[i in C, j in C, j > i] w_ij
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// + view_score_weight * sum_[i in C] w_i
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// centers will contain the vertices that are the identified
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// as the canonical views/cluster centers, and membership is a map
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// from vertices to cluster_ids. The i^th cluster center corresponds
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// to the i^th cluster.
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// It is possible depending on the configuration of the clustering
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// algorithm that some of the vertices may not be assigned to any
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// cluster. In this case they are assigned to a cluster with id = -1;
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void ComputeCanonicalViewsClustering(
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const Graph<int>& graph,
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const CanonicalViewsClusteringOptions& options,
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vector<int>* centers,
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HashMap<int, int>* membership);
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struct CanonicalViewsClusteringOptions {
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CanonicalViewsClusteringOptions()
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size_penalty_weight(5.75),
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similarity_penalty_weight(100.0),
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view_score_weight(0.0) {
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// The minimum number of canonical views to compute.
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// Penalty weight for the number of canonical views. A higher
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// number will result in fewer canonical views.
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double size_penalty_weight;
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// Penalty weight for the diversity (orthogonality) of the
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// canonical views. A higher number will encourage less similar
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double similarity_penalty_weight;
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// Weight for per-view scores. Lower weight places less
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// confidence in the view scores.
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double view_score_weight;
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} // namespace internal
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#endif // CERES_INTERNAL_CANONICAL_VIEWS_CLUSTERING_H_
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internal/ceres/canonical_views_clustering.h
