We propose an approach to determine the occurrence of low-parametric qualitative models from images by a hypothesis-and-test approach based on the coincidence of multiple cues, thereby avoiding complete reconstruction of the scene. A system is presented which applies the approach to finding instances of planar surfaces, as it is important in many tasks for mobile or manipulating robots. The system uses monocularly determined L-junctions and binocular disparities. A notable feature of the approach is that it finds the most conspicuous exemplar of the model first. This property seems quite relevant for an agent using vision to guide its behaviors, since the simplest solution becomes available early on.

A unified differential geometric framework for estimation of local surface shape and orientation from projective texture distortion is proposed, based on a differential version of the texture stationarity assumption introduced by Malik and Rosenholtz. This framework allows the information content of the gradient of any texture descriptor defined in a local coordinate frame to be characterized in a very compact form. The analysis encompasses both full affine texture descriptors and the classical "texture gradients". For estimation of local surface orientation and curvature from uncertain observations of affine texture distortion, the proposed framework allows the dimensionality of the search space to be reduced from five to one.>

The problem of scale in shape from texture is addressed. The need for two scale parameters is emphasized: a local scale, for describing the amount of smoothing used for suppressing noise and irrelevant details when computing primitive texture descriptors from image data; and an integration scale, for describing the size of the region in space over which the statistics of the local descriptors is accummulated. The proposed computational model is expressed completely in terms of different invariants defined from Gaussian derivatives at multiple scales in scale-space. The resulting texture description can be combined with various assumptions about surface texture to estimate local surface orientation. Two specific assumptions, weak isotropy and constant area, are explored in more detail. Results from experiments on real and synthetic reference data with known geometry that demonstrate the viability of the approach are presented.>

Witkin (1981) has proposed a maximum likelihood (ML) estimator of surface orientation based on the observed directional bias of projected texture elements. However, a drawback of this procedure is that the estimate is only defined indirectly in terms of a set of nonlinear equations. An alternative method is proposed, which allows an estimate of the surface orientation to be computed directly in a single step from certain simple statistics of the image data. We also show that this direct estimate allows Witkin's ML estimate to be computed to within 0.05 degrees in only two or three iterative steps. The performance of the new estimator is demonstrated experimentally and compared to that of the ML estimator, using both synthetic data and real gray-level images.>

The authors present a unified framework for shape from texture and contour. The framework is based on a concept called weak isotropy and contains as a special case A.P. Witkin's (1987) maximum-likelihood algorithm for shape from texture. The method is based on analysis of the directional statistics of the input data. It can be applied to both smooth curves and polygons, open or closed curves, symmetric figures, and scattered texture edges; thus, it appears to have wider applicability than previous methods. The weak isotropy heuristic captures many important properties (such as various types of symmetry) of both random and regular planar shape, and it also leads to a computationally efficient estimation algorithm based on observables in the image which are direct correlates of the surface orientation. These correlates make it possible to compute an approximate estimate of surface orientation in a single step. In certain simple cases this first estimate is exactly right, and in experiments with natural images it is typically within 5 degrees of the final estimate.>