This paper presents a probabilistic approach to solving ill-posed problems in computational vision, particularly in early vision. The authors formulate early vision problems as inverse problems and propose new stochastic techniques, such as Bayesian methods based on Markov Random Field (MRF) models, to address the limitations of standard regularization methods. They discuss efficient algorithms and parallel implementations on digital parallel SIMD architectures and new hybrid computers combining digital and analog components. The paper begins by introducing computational vision as a field that aims to develop image understanding systems and understand biological vision. It emphasizes the theoretical study of vision as an information processing task. The first part of vision, from images to surfaces, is termed early vision. The authors argue that early vision processes are generic and can be studied as independent modules. However, the correctness of this approach is still to be proven, and the nature of the 2-1/2-D sketch representation and the interaction between visual modules remain unclear. The paper then discusses the ill-posed nature of early vision problems, which are defined by Hadamard as problems that fail to satisfy the criteria of existence, uniqueness, and continuous dependence on initial data. The authors show that several problems in early vision have this ill-posed structure and suggest using regularization methods developed in mathematics and physics to solve them. Standard regularization methods, such as Tikhonov regularization, are discussed, and their limitations are identified, particularly in handling discontinuities and fusing information from multiple modules. The authors propose a stochastic approach based on Bayesian estimation and MRF models to overcome the limitations of standard regularization. This approach represents a priori knowledge as a probability distribution and uses Bayes' theorem to compute the posterior distribution, which allows for the maximum a posteriori (MAP) estimate or the minimization of an expected error function. This method is more flexible and can handle discontinuities and information fusion more effectively. The paper also discusses probabilistic models for early vision, focusing on surface reconstruction. It introduces MRFs on finite lattices and their use in modeling piecewise constant functions. The authors present a Gibbs distribution and show how it can be used to model the posterior distribution of the field given observations. They also discuss cost functionals for reconstruction problems, including segmentation and surface reconstruction, and propose Bayesian approaches for estimating these. The paper outlines algorithms based on the Metropolis or Gibbs Sampler methods to simulate the equilibrium behavior of the coupled MRF. These algorithms are used to approximate the posterior marginals and the mean of the posterior distribution. The authors also discuss the use of hybrid parallel computers to implement these algorithms efficiently. The paper concludes with examples of applications in vision, including the reconstruction of piecewise constant functions and piecewise continuous functions. It discusses the use of Bayesian methods for parameter estimation and the development of efficient algorithms for these tasks. The authors also present a hybrid parallel computer for surface reconstruction, which combines digital and analog components to solve the problem efficiently. The paper highlights the importance of probabilistic modelsThis paper presents a probabilistic approach to solving ill-posed problems in computational vision, particularly in early vision. The authors formulate early vision problems as inverse problems and propose new stochastic techniques, such as Bayesian methods based on Markov Random Field (MRF) models, to address the limitations of standard regularization methods. They discuss efficient algorithms and parallel implementations on digital parallel SIMD architectures and new hybrid computers combining digital and analog components. The paper begins by introducing computational vision as a field that aims to develop image understanding systems and understand biological vision. It emphasizes the theoretical study of vision as an information processing task. The first part of vision, from images to surfaces, is termed early vision. The authors argue that early vision processes are generic and can be studied as independent modules. However, the correctness of this approach is still to be proven, and the nature of the 2-1/2-D sketch representation and the interaction between visual modules remain unclear. The paper then discusses the ill-posed nature of early vision problems, which are defined by Hadamard as problems that fail to satisfy the criteria of existence, uniqueness, and continuous dependence on initial data. The authors show that several problems in early vision have this ill-posed structure and suggest using regularization methods developed in mathematics and physics to solve them. Standard regularization methods, such as Tikhonov regularization, are discussed, and their limitations are identified, particularly in handling discontinuities and fusing information from multiple modules. The authors propose a stochastic approach based on Bayesian estimation and MRF models to overcome the limitations of standard regularization. This approach represents a priori knowledge as a probability distribution and uses Bayes' theorem to compute the posterior distribution, which allows for the maximum a posteriori (MAP) estimate or the minimization of an expected error function. This method is more flexible and can handle discontinuities and information fusion more effectively. The paper also discusses probabilistic models for early vision, focusing on surface reconstruction. It introduces MRFs on finite lattices and their use in modeling piecewise constant functions. The authors present a Gibbs distribution and show how it can be used to model the posterior distribution of the field given observations. They also discuss cost functionals for reconstruction problems, including segmentation and surface reconstruction, and propose Bayesian approaches for estimating these. The paper outlines algorithms based on the Metropolis or Gibbs Sampler methods to simulate the equilibrium behavior of the coupled MRF. These algorithms are used to approximate the posterior marginals and the mean of the posterior distribution. The authors also discuss the use of hybrid parallel computers to implement these algorithms efficiently. The paper concludes with examples of applications in vision, including the reconstruction of piecewise constant functions and piecewise continuous functions. It discusses the use of Bayesian methods for parameter estimation and the development of efficient algorithms for these tasks. The authors also present a hybrid parallel computer for surface reconstruction, which combines digital and analog components to solve the problem efficiently. The paper highlights the importance of probabilistic models