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.