38 research outputs found
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
Formulations linéaires en nombres entiers pour des problèmes d'isomorphisme exact et inexact
Pas de résumé
Subgraph spotting in graph representations of comic book images
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record Graph-based representations are the most powerful data structures for extracting, representing and preserving the structural information of underlying data. Subgraph spotting is an interesting research problem, especially for studying and investigating the structural information based content-based image retrieval (CBIR) and query by example (QBE) in image databases. In this paper we address the problem of lack of freely available ground-truthed datasets for subgraph spotting and present a new dataset for subgraph spotting in graph representations of comic book images (SSGCI) with its ground-truth and evaluation protocol. Experimental results of two state-of-the-art methods of subgraph spotting are presented on the new SSGCI dataset.University of La Rochelle (France
A path following algorithm for the graph matching problem
We propose a convex-concave programming approach for the labeled weighted
graph matching problem. The convex-concave programming formulation is obtained
by rewriting the weighted graph matching problem as a least-square problem on
the set of permutation matrices and relaxing it to two different optimization
problems: a quadratic convex and a quadratic concave optimization problem on
the set of doubly stochastic matrices. The concave relaxation has the same
global minimum as the initial graph matching problem, but the search for its
global minimum is also a hard combinatorial problem. We therefore construct an
approximation of the concave problem solution by following a solution path of a
convex-concave problem obtained by linear interpolation of the convex and
concave formulations, starting from the convex relaxation. This method allows
to easily integrate the information on graph label similarities into the
optimization problem, and therefore to perform labeled weighted graph matching.
The algorithm is compared with some of the best performing graph matching
methods on four datasets: simulated graphs, QAPLib, retina vessel images and
handwritten chinese characters. In all cases, the results are competitive with
the state-of-the-art.Comment: 23 pages, 13 figures,typo correction, new results in sections 4,5,
Towards Quantifying Vertex Similarity in Networks
Vertex similarity is a major problem in network science with a wide range of
applications. In this work we provide novel perspectives on finding
(dis)similar vertices within a network and across two networks with the same
number of vertices (graph matching). With respect to the former problem, we
propose to optimize a geometric objective which allows us to express each
vertex uniquely as a convex combination of a few extreme types of vertices. Our
method has the important advantage of supporting efficiently several types of
queries such as "which other vertices are most similar to this vertex?" by the
use of the appropriate data structures and of mining interesting patterns in
the network. With respect to the latter problem (graph matching), we propose
the generalized condition number --a quantity widely used in numerical
analysis-- of the Laplacian matrix representations of
as a measure of graph similarity, where are the graphs of interest. We
show that this objective has a solid theoretical basis and propose a
deterministic and a randomized graph alignment algorithm. We evaluate our
algorithms on both synthetic and real data. We observe that our proposed
methods achieve high-quality results and provide us with significant insights
into the network structure.Comment: 16 papers, 5 figures, 2 table
Deep Reinforcement Learning of Graph Matching
Graph matching (GM) under node and pairwise constraints has been a building
block in areas from combinatorial optimization, data mining to computer vision,
for effective structural representation and association. We present a
reinforcement learning solver for GM i.e. RGM that seeks the node
correspondence between pairwise graphs, whereby the node embedding model on the
association graph is learned to sequentially find the node-to-node matching.
Our method differs from the previous deep graph matching model in the sense
that they are focused on the front-end feature extraction and affinity function
learning, while our method aims to learn the back-end decision making given the
affinity objective function whether obtained by learning or not. Such an
objective function maximization setting naturally fits with the reinforcement
learning mechanism, of which the learning procedure is label-free. These
features make it more suitable for practical usage. Extensive experimental
results on both synthetic datasets, Willow Object dataset, Pascal VOC dataset,
and QAPLIB showcase superior performance regarding both matching accuracy and
efficiency. To our best knowledge, this is the first deep reinforcement
learning solver for graph matching
Large-scale Binary Quadratic Optimization Using Semidefinite Relaxation and Applications
In computer vision, many problems such as image segmentation, pixel
labelling, and scene parsing can be formulated as binary quadratic programs
(BQPs). For submodular problems, cuts based methods can be employed to
efficiently solve large-scale problems. However, general nonsubmodular problems
are significantly more challenging to solve. Finding a solution when the
problem is of large size to be of practical interest, however, typically
requires relaxation. Two standard relaxation methods are widely used for
solving general BQPs--spectral methods and semidefinite programming (SDP), each
with their own advantages and disadvantages. Spectral relaxation is simple and
easy to implement, but its bound is loose. Semidefinite relaxation has a
tighter bound, but its computational complexity is high, especially for large
scale problems. In this work, we present a new SDP formulation for BQPs, with
two desirable properties. First, it has a similar relaxation bound to
conventional SDP formulations. Second, compared with conventional SDP methods,
the new SDP formulation leads to a significantly more efficient and scalable
dual optimization approach, which has the same degree of complexity as spectral
methods. We then propose two solvers, namely, quasi-Newton and smoothing Newton
methods, for the dual problem. Both of them are significantly more efficiently
than standard interior-point methods. In practice, the smoothing Newton solver
is faster than the quasi-Newton solver for dense or medium-sized problems,
while the quasi-Newton solver is preferable for large sparse/structured
problems. Our experiments on a few computer vision applications including
clustering, image segmentation, co-segmentation and registration show the
potential of our SDP formulation for solving large-scale BQPs.Comment: Fixed some typos. 18 pages. Accepted to IEEE Transactions on Pattern
Analysis and Machine Intelligenc