A new noniterative approach to determine displacement vector fields with discontinuities is described. In order to overcome the limitations of current methods, the problem is regarded as a general modelling problem. Starting from a family of regularized estimates, by measuring the difference in description length the compatibility between different levels of regularization is determined. This gives local but noisy evidence of possible model boundaries at multiple scales. With the two constraints of continous lines of discontinuities and the spatial coincidence assumption consistent boundary evidence is found. Based on this combined evidence the model is updated, now describing homogeneous regions with sharp discontinuities.

The low-level interpretation of images provides constraints on 3D surface shape at multiple resolutions, but typically only at scattered locations over the visual field. Subsequent visual processing can be facilitated substantially if the scattered shape constraints are immediately transformed into visible-surface representations that unambiguously specify surface shape at every image point. The required transformation is shown to lead to an ill-posed surface reconstruction problem. A well-posed variational principle formulation is obtained by invoking 'controlled continuity,' a physically nonrestrictive (generic) assumption about surfaces which is nonetheless strong enough to guarantee unique solutions. The variational principle, which admits an appealing physical interpretation, is locally discretized by applying the finite element method to a piecewise, finite element representation of surfaces. This forms the mathematical basis of a unified and general framework for computing visible-surface representations. The computational framework unifies formal solutions to the key problems of (i) integrating multiscale constraints on surface depth and orientation from multiple visual sources, (ii) interpolating these scattered constraints into dense, piecewise smooth surfaces, (iii) discovering surface depth and orientation discontinuities and allowing them to restrict interpolation appropriately, and (iv) overcoming the immense computational burden of fine resolution surface reconstruction. An efficient surface reconstruction algorithm is developed. It exploits multiresolution hierarchies of cooperative relaxation processes and is suitable for implementation on massively parallel networks of simple, locally interconnected processors. The algorithm is evaluated empirically in a diversity of applications.