Add support for multiple visibility clustering algorithms.
The original visibility based preconditioning paper and
implementation only used the canonical views algorithm.
This algorithm for large dense graphs can be particularly
expensive. As its worst case complexity is cubic in size
of the graph.
Further, for many uses the SCHUR_JACOBI preconditioner
was both effective enough while being cheap. It however
suffers from a fatal flaw. If the camera parameter blocks
are split between two or more parameter blocks, e.g,
extrinsics and intrinsics. The preconditioner because
it is block diagonal will not capture the interactions
between them.
Using CLUSTER_JACOBI or CLUSTER_TRIDIAGONAL will fix
this problem but as mentioned above this can be quite
expensive depending on the problem.
This change extends the visibility based preconditioner
to allow for multiple clustering algorithms. And adds
a simple thresholded single linkage clustering algorithm
which allows you to construct versions of CLUSTER_JACOBI
and CLUSTER_TRIDIAGONAL preconditioners that are cheap
to construct and are more effective than SCHUR_JACOBI.
Currently the constants controlling the threshold above
which edges are considered in the single linkage algorithm
are not exposed. This would be done in a future change.
Change-Id: I7ddc36790943f24b19c7f08b10694ae9a822f5c9
diff --git a/internal/ceres/single_linkage_clustering.cc b/internal/ceres/single_linkage_clustering.cc
new file mode 100644
index 0000000..54b4379
--- /dev/null
+++ b/internal/ceres/single_linkage_clustering.cc
@@ -0,0 +1,107 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2013 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)
+
+#ifndef CERES_NO_SUITESPARSE
+
+#include "ceres/single_linkage_clustering.h"
+
+#include "ceres/graph.h"
+#include "ceres/collections_port.h"
+#include "ceres/graph_algorithms.h"
+
+namespace ceres {
+namespace internal {
+
+int ComputeSingleLinkageClustering(
+ const SingleLinkageClusteringOptions& options,
+ const Graph<int>& graph,
+ HashMap<int, int>* membership) {
+ CHECK_NOTNULL(membership)->clear();
+
+ // Initially each vertex is in its own cluster.
+ const HashSet<int>& vertices = graph.vertices();
+ for (HashSet<int>::const_iterator it = vertices.begin();
+ it != vertices.end();
+ ++it) {
+ (*membership)[*it] = *it;
+ }
+
+ for (HashSet<int>::const_iterator it1 = vertices.begin();
+ it1 != vertices.end();
+ ++it1) {
+ const int vertex1 = *it1;
+ const HashSet<int>& neighbors = graph.Neighbors(vertex1);
+ for (HashSet<int>::const_iterator it2 = neighbors.begin();
+ it2 != neighbors.end();
+ ++it2) {
+ const int vertex2 = *it2;
+
+ // Since the graph is undirected, only pay attention to one side
+ // of the edge and ignore weak edges.
+ if ((vertex1 > vertex2) ||
+ (graph.EdgeWeight(vertex1, vertex2) < options.min_similarity)) {
+ continue;
+ }
+
+ // Use a union-find algorithm to keep track of the clusters.
+ const int c1 = FindConnectedComponent(vertex1, membership);
+ const int c2 = FindConnectedComponent(vertex2, membership);
+
+ if (c1 == c2) {
+ continue;
+ }
+
+ if (c1 < c2) {
+ (*membership)[c2] = c1;
+ } else {
+ (*membership)[c1] = c2;
+ }
+ }
+ }
+
+ // Make sure that every vertex is connected directly to the vertex
+ // identifying the cluster.
+ int num_clusters = 0;
+ for (HashMap<int, int>::iterator it = membership->begin();
+ it != membership->end();
+ ++it) {
+ it->second = FindConnectedComponent(it->first, membership);
+ if (it->first == it->second) {
+ ++num_clusters;
+ }
+ }
+
+ return num_clusters;
+}
+
+} // namespace internal
+} // namespace ceres
+
+#endif // CERES_NO_SUITESPARSE
