7,706 research outputs found
Exhaustive and Efficient Constraint Propagation: A Semi-Supervised Learning Perspective and Its Applications
This paper presents a novel pairwise constraint propagation approach by
decomposing the challenging constraint propagation problem into a set of
independent semi-supervised learning subproblems which can be solved in
quadratic time using label propagation based on k-nearest neighbor graphs.
Considering that this time cost is proportional to the number of all possible
pairwise constraints, our approach actually provides an efficient solution for
exhaustively propagating pairwise constraints throughout the entire dataset.
The resulting exhaustive set of propagated pairwise constraints are further
used to adjust the similarity matrix for constrained spectral clustering. Other
than the traditional constraint propagation on single-source data, our approach
is also extended to more challenging constraint propagation on multi-source
data where each pairwise constraint is defined over a pair of data points from
different sources. This multi-source constraint propagation has an important
application to cross-modal multimedia retrieval. Extensive results have shown
the superior performance of our approach.Comment: The short version of this paper appears as oral paper in ECCV 201
SHREC'16: partial matching of deformable shapes
Matching deformable 3D shapes under partiality transformations is a challenging problem that has received limited focus in the computer vision and graphics communities. With this benchmark, we explore and thoroughly investigate the robustness of existing matching methods in this challenging task. Participants are asked to provide a point-to-point correspondence (either sparse or dense) between deformable shapes undergoing different kinds of partiality transformations, resulting in a total of 400 matching problems to be solved for each method - making this benchmark the biggest and most challenging of its kind. Five matching algorithms were evaluated in the contest; this paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods
Efficient Deformable Shape Correspondence via Kernel Matching
We present a method to match three dimensional shapes under non-isometric
deformations, topology changes and partiality. We formulate the problem as
matching between a set of pair-wise and point-wise descriptors, imposing a
continuity prior on the mapping, and propose a projected descent optimization
procedure inspired by difference of convex functions (DC) programming.
Surprisingly, in spite of the highly non-convex nature of the resulting
quadratic assignment problem, our method converges to a semantically meaningful
and continuous mapping in most of our experiments, and scales well. We provide
preliminary theoretical analysis and several interpretations of the method.Comment: Accepted for oral presentation at 3DV 2017, including supplementary
materia
Graph edit distance from spectral seriation
This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graph-matching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems
Higher-order Projected Power Iterations for Scalable Multi-Matching
The matching of multiple objects (e.g. shapes or images) is a fundamental
problem in vision and graphics. In order to robustly handle ambiguities, noise
and repetitive patterns in challenging real-world settings, it is essential to
take geometric consistency between points into account. Computationally, the
multi-matching problem is difficult. It can be phrased as simultaneously
solving multiple (NP-hard) quadratic assignment problems (QAPs) that are
coupled via cycle-consistency constraints. The main limitations of existing
multi-matching methods are that they either ignore geometric consistency and
thus have limited robustness, or they are restricted to small-scale problems
due to their (relatively) high computational cost. We address these
shortcomings by introducing a Higher-order Projected Power Iteration method,
which is (i) efficient and scales to tens of thousands of points, (ii)
straightforward to implement, (iii) able to incorporate geometric consistency,
(iv) guarantees cycle-consistent multi-matchings, and (iv) comes with
theoretical convergence guarantees. Experimentally we show that our approach is
superior to existing methods
Elastic Registration of Geodesic Vascular Graphs
Vascular graphs can embed a number of high-level features, from morphological
parameters, to functional biomarkers, and represent an invaluable tool for
longitudinal and cross-sectional clinical inference. This, however, is only
feasible when graphs are co-registered together, allowing coherent multiple
comparisons. The robust registration of vascular topologies stands therefore as
key enabling technology for group-wise analyses. In this work, we present an
end-to-end vascular graph registration approach, that aligns networks with
non-linear geometries and topological deformations, by introducing a novel
overconnected geodesic vascular graph formulation, and without enforcing any
anatomical prior constraint. The 3D elastic graph registration is then
performed with state-of-the-art graph matching methods used in computer vision.
Promising results of vascular matching are found using graphs from synthetic
and real angiographies. Observations and future designs are discussed towards
potential clinical applications
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