Visual reconstruction
An Eigendecomposition Approach to Weighted Graph Matching Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Constrained nets for graph matching and other quadratic assignment problems
Neural Computation
Parallel and Deterministic Algorithms from MRFs: Surface Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
A common framework for image segmentation
International Journal of Computer Vision
A new lower bound via projection for the quadratic assignment problem
Mathematics of Operations Research
A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
A New Algorithm for Error-Tolerant Subgraph Isomorphism Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Deterministic Annealing Approach for Parsimonious Design of Piecewise Regression Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Matching With a Dual-Step EM Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Error Correcting Graph Matching: On the Influence of the Underlying Cost Function
IEEE Transactions on Pattern Analysis and Machine Intelligence
P-Complete Approximation Problems
Journal of the ACM (JACM)
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convergence properties of the softassign quadratic assignment algorithm
Neural Computation
Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
On Lagrangian Relaxation of Quadratic Matrix Constraints
SIAM Journal on Matrix Analysis and Applications
QAPLIB – A Quadratic Assignment ProblemLibrary
Journal of Global Optimization
A Linear Programming Approach for the Weighted Graph Matching Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
Structural Matching in Computer Vision Using Probabilistic Relaxation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pairwise Data Clustering by Deterministic Annealing
IEEE Transactions on Pattern Analysis and Machine Intelligence
A New Genetic Algorithm for the Quadratic Assignment Problem
INFORMS Journal on Computing
Modelling Convex Shape Priors and Matching Based on the Gromov-Wasserstein Distance
Journal of Mathematical Imaging and Vision
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We introduce a convex relaxation approach for the quadratic assignment problem to the field of computer vision. Due to convexity, a favourable property of this approach is the absence of any tuning parameters and the computation of high-quality combinatorial solutions by solving a mathematically simple optimization problem. Furthermore, the relaxation step always computes a tight lower bound of the objective function and thus can additionally be used as an efficient subroutine of an exact search algorithm. We report the results of both established benchmark experiments from combinatorial mathematics and random ground-truth experiments using computer-generated graphs. For comparison, a deterministic annealing approach is investigated as well. Both approaches show similarly good performance. In contrast to the convex approach, however, the annealing approach yields no problem relaxation, and four parameters have to be tuned by hand for the annealing algorithm to become competitive.