Shape-adapted smoothing in estimation of 3-D shape cues from affine deformations of local 2-D brightness structure

This article describes a method for reducing the shape distortions due to scale space smoothing that arise in the computation of 3-D shape cues using operators (derivatives) defined from scale-space representation. More precisely, we are concerned with a general class of methods for deriving 3-D shape cues from a 2-D image data based on the estimation of locally linearized deformations of brightness patterns. This class constitutes a common framework for describing several problems in computer vision (such as shape-from-texture, shape-from disparity-gradients, and motion estimation) and for expressing different algorithms in terms of similar types of visual front-end-operations. It is explained how surface orientation estimates will be biased due to the use of rotationally symmetric smoothing in the image domain. These effects can be reduced by extending the linear scale-space concept into an affine Gaussian scale-space representation and by performing affine shape adaptation of the smoothing kernels. This improves the accuracy of the surface orientation estimates, since the image descriptors, on which the methods are based, will be relative invariant under affine transformations, and the error thus confined to the higher-order terms in the locally linearized perspective transformation. A straightforward algorithm is presented for performing shape adaptation in practice. Experiments on real and synthetic images with known orientation demonstrate that in the presence of moderately high noise levels the accuracy is improved by typically one order of magnitude.