A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated non-convexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational complexity [O(lm), where l and m are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching, and attributed relational graph matching. To illustrate the performance of the algorithm, attributed relational graphs derived from objects are matched. Then, results from twenty-five thousand experiments conducted on 100 node random graphs of varying types (graphs with only zero-one links, weighted graphs, and graphs with node attributes and multiple link types) are reported. No comparable results have...

A fundamental open problem in computer vision---determining pose and correspondence between two sets of points in space---is solved with a novel, fast [O(nm)], robust and easily implementable algorithm. The technique works on noisy 2D or 3D point sets that may be of unequal sizes and may differ by non-rigid transformations. Using a combination of optimization techniques such as deterministic annealing and the softassign, which have recently emerged out of the recurrent neural network/statistical physics framework, analog objective functions describing the problems are minimized. Over thirty thousand experiments, on randomly generated points sets with varying amounts of noise and missing and spurious points, and on hand-written character sets demonstrate the robustness of the algorithm. Keywords: Point-matching, pose estimation, correspondence, neural networks, optimization, softassign, deterministic annealing, affine. 1 Introduction Matching the representations of two images has long...

We exhibit a systematic way to derive neural nets for vision problems. It involves formulating a vision problem as Bayesian inference or decision on a comprehensive model of the visual domain given by a probabilistic grammar. A key feature of this grammar is the way in which it eliminates model information, such as object labels, as it produces an image; correspondance problems and other noise removal tasks result. The neural nets that arise most directly are generalized assignment networks. Also there are transformations which naturally yield improved algorithms such as correlation matching in scale space and the Frameville neural nets for high-level vision. Networks derived this way generally have objective functions with spurious local minima; such minima may commonly be avoided by dynamics that include deterministic annealing, for example recent improvements to Mean Field Theory dynamics. The grammatical method of neural net design allows domain knowledge to enter from all levels o...

A new technique termed softassign is applied to three combinatorial optimization problems - weighted graph matching, the travelling salesman problem and graph partitioning. Softassign, which has emerged from the recurrent neural network/ statistical physics framework, enforces two-way (assignment) constraints without the use of penalty terms in the energy functions. The softassign can also be generalised from two-way winner-take-all constraints to multiple membership constraints which are required for graph partitioning. The softassign technique is compared to softmax (Potts glass) dynamics. Within the statistical physics framework, softmax and a penalty term has been a widely used method for enforcing the two-way constraints common to many combinatorial optimization problems. The benchmarks present evidence that softassign has clear advantages in accuracy, speed, parallelizability and algorithmic simplicity over softmax and a penalty term in optimization problems with two-way constraints.

The softassign quadratic assignment algoithm is a discrete time, continuous state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching and graph partitioning in thousands of simulations, there was no associated study of its convergence properties. Here, we construct discrete time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction which can be used to show convergence to a fixed point. The combination of good convergence properties and experimental success make the softassign algorithm the technique of choice for neural QAP optimization. 1 Introduction Discrete time optimizing neural networks are a well honed topic in neural computation. Beginning with the discrete state Hopfield model (Hopfield, 1982), considerable effort has been spent in analyzing the convergence properties of discrete time networks, especially along the dimensions of continuous versu...

Deterministic annealing and relaxation labeling algorithms for classification and matching are presented and discussed. A new approach---self annealing---is introduced to bring deterministic annealing and relaxation labeling into accord. Self annealing results in an emergent linear schedule for winner-take-all and linear assignment problems. Self annihilation, a generalization of self annealing is capable of performing the useful function of symmetry breaking. The original relaxation labeling algorithm is then shown to arise from an approximation to either the self annealing energy function or the corresponding dynamical system. With this relationship in place, self annihilation can be introduced into the relaxation labeling framework. Experimental results on synthetic matching and labeling problems clearly demonstrate the three-way relationship between deterministic annealing, relaxation labeling and self annealing. Keywords: Deterministic annealing, relaxation labeling, self anneal...

A Lagrange multiplier and Hopfield-type barrier function method is proposed for approximating a solution...

. Deterministic annealing and relaxation labeling algorithms for classification and matching are presented and discussed. A new approach ---self annealing---is introduced to bring deterministic annealing and relaxation labeling into accord. Self annealing results in an emergent linear schedule for winner-take-all and assignment problems. Also, the relaxation labeling algorithm can be seen as an approximation to the self annealing algorithm for matching and labeling problems. 1 Introduction Labeling and matching problems abound in computer vision and pattern recognition (CVPR). It is not an exaggeration to state that some form or the other of the basic problems of template matching or data clustering has remained central to the CVPR and neural networks communities for about three decades. Due to the somewhat disparate natures of these communities, different frameworks for formulating and solving these two problems have emerged and it is not immediately obvious how to go about reconcili...