We investigate two ways of solving the correspondence problem for motion using the assumptions of minimal mapping and rigidity. Massively parallel analog networks are designed to implement these theories. Their effectiveness is demonstrated with mathematical proofs and computer simulations. We discuss relevant psychophysical experiments.

This paper describes attempts to model the modules of early vision in terms of minimizing energy functions, in particular energy functions allowing discontinuities in the solution. It examines the success of using Hopfield-style analog networks for solving such problems. Finally it discusses the limitations of the energy function approach.

Image smoothing and segmentation algorithms are frequently formulatedsas optimization problems. Linear and nonlinear (reciprocal) resistivesnetworks have solutions characterized by an extremum principle. Thus,sappropriately designed networks can automatically solve certainssmoothing and segmentation problems in robot vision. This papersconsiders switched linear resistive networks and nonlinear resistivesnetworks for such tasks. The latter network type is derived from thesformer via an intermediate stochastic formulation, and a new resultsrelating the solution sets of the two is given for the "zerostermperature'' limit. We then present simulation studies of severalscontinuation methods that can be gracefully implemented in analog VLSIsand that seem to give "good'' results for these non-convexsoptimization problems.

[pt] Neste trabalho desenvolveu-se um método para análise simbólica de redes analógicas lineares, invariantes no tempo, incluindo fontes controladas, transformadores e giradores. O algoritmo determina funções de transferência em forma simbólica analisando um modelo de grafo de fluxo de sinal (GFS) da rede. Este procedimento é baseado em método de análise de filtros digitais, anteriormente desenvolvido, enfatizando a geração de um modelo apropriado de GFS do circuito. O modelo de GFS adotado é gerado a partir de uma descrição pro equações de estado da rede. O método foi implementado, apresentando, em alguns casos, eficiência comparável à dos processos numéricos. São apresentados resultados de testes para redes típicas. / [en] In this paper a method for symbolic analysis of linear time invariant circuits, including controled sources, transformers and gyrators, is presented. The procedure determines transfer functions in symbolic form by analysing a signal flow graph (SFG) model of network. The approach is based on a previews digital filter symbolic analysis method, emphasizing the generation of an appropriate circuit SFG model. The SFG model results from a graph approach to the state space description of the network. The method was implemented with performance comparable or even faster than numerical methods. The tests results for some typical strutures are presented.

Many problems in early vision can be formulated in terms of minimizing an energy or cost function. Examples are shape-from-shading, edge detection, motion analysis, structure from motion and surface interpolation (Poggio, Torre and Koch, 1985). It has been shown that all quadratic variational problems, an important subset of early vision tasks, can be "solved" by linear, analog electrical or chemical networks (Poggio and Koch, 1985). IN a variety of situateions the cost function is non-quadratic, however, for instance in the presence of discontinuities. The use of non-quadratic cost functions raises the question of designing efficient algorithms for computing the optimal solution. Recently, Hopfield and Tank (1985) have shown that networks of nonlinear analog "neurons" can be effective in computing the solution of optimization problems. In this paper, we show how these networks can be generalized to solve the non-convex energy functionals of early vision. We illustrate this approach by implementing a specific network solving the problem of reconstructing a smooth surface while preserving its discontinuities from sparsely sampled data (Geman and Geman, 1984; Marroquin 1984; Terzopoulos 1984). These results suggest a novel computational strategy for solving such problems for both biological and artificial vision systems.