Rotationally symmetric operations in the image domain may give rise to shape distortions. This article describes a way of reducing this effect for a general class of methods for deriving 3-D shape cues from 2-D image data, which are based on the estimation of locally linearized distortion of brightness patterns. By extending the linear scale-space concept into an affine scale-space representation and performing affine shape adaption of the smoothing kernels, the accuracy of surface orientation estimates derived from texture and disparity cues can be improved by typically one order of magnitude. The reason for this is that the image descriptors, on which the methods are based, will be relative invariant under a ne transformations, and the error will thus be confined to the higher-order terms in the locally linearized perspective mapping.

We address the problem of texture segmentation by using a novel affine invariant model. The introduction of affine invariance as a requirement for texture analysis goes beyond what is known of the human performance and also beyond the psychophysical theories. We propose to compute texture features using affine invariant intrinsic neighborhoods and affine invariant intrinsic orientation matrices. We discuss several possibilities for the definition of the channels and give comparative experimental results where an affine invariant Mumford-Shah type energy functional is used to compute the multichannel affine invariant segmentation. We prove that the method is able to retrieve faithfully the texture regions and to recover the shape from texture information in images where several textures are present. The numerical algorithm is multiscale.

Abstract. This paper addresses the problem of computing cues to the three-dimensional structure of surfaces in the world directly from the local structure of the brightness pattern of a binocular image pair. The geometric information content of the gradient of binocular disparity is analyzed for the general case of a xating system with symmetric or asymmetric vergence, and with either known or unknown viewing geometry. A computationally inexpensive technique which exploits this analysis is proposed. This technique allows a local estimate of surface orientation to be computed directly from the local statistics of the left and right image brightness gradients, without iterations or search. The viability of the approach is demonstrated with experimental results for both synthetic and natural gray-level images. 1