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+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2015 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// 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: kushalav@google.com (Avanish Kushal)
+// sameeragarwal@google.com (Sameer Agarwal)
+//
+// Functions to manipulate visibility information from the block
+// structure of sparse matrices.
+
+#ifndef CERES_INTERNAL_VISIBILITY_H_
+#define CERES_INTERNAL_VISIBILITY_H_
+
+#include <set>
+#include <vector>
+#include "ceres/graph.h"
+
+namespace ceres {
+namespace internal {
+
+struct CompressedRowBlockStructure;
+
+// Given a compressed row block structure, computes the set of
+// e_blocks "visible" to each f_block. If an e_block co-occurs with an
+// f_block in a residual block, it is visible to the f_block. The
+// first num_eliminate_blocks columns blocks are e_blocks and the rest
+// f_blocks.
+//
+// In a structure from motion problem, e_blocks correspond to 3D
+// points and f_blocks correspond to cameras.
+void ComputeVisibility(const CompressedRowBlockStructure& block_structure,
+ int num_eliminate_blocks,
+ std::vector<std::set<int>>* visibility);
+
+// Given f_block visibility as computed by the ComputeVisibility
+// function above, construct and return a graph whose vertices are
+// f_blocks and an edge connects two vertices if they have at least one
+// e_block in common. The weight of this edge is normalized dot
+// product between the visibility vectors of the two
+// vertices/f_blocks.
+//
+// This graph reflects the sparsity structure of reduced camera
+// matrix/Schur complement matrix obtained by eliminating the e_blocks
+// from the normal equations.
+//
+// Caller acquires ownership of the returned WeightedGraph pointer
+// (heap-allocated).
+WeightedGraph<int>* CreateSchurComplementGraph(
+ const std::vector<std::set<int>>& visibility);
+
+} // namespace internal
+} // namespace ceres
+
+#endif // CERES_INTERNAL_VISIBILITY_H_