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Image flow is the velocity field in the image plane caused by the motion of the observer, objects in the scene, or apparent motion. The image flow velocity field is an important intrinsic image and many algorithms that use the image flow velocity field have already been described. The image flow velocity field can contain discontinuities due to object occlusion in the scene. An algorithm that can estimate the image flow velocity field when there are discontinuities due to occlusion is described. Experimental results on a demanding synthetic test case and a real image are presented. Some error analysis that explains the performance of the algorithm is provided. The velocity field estimate can be improved using surface reconstruction between velocity field boundaries. A new surface approximation algorithm that does not blur sharp boundaries is presented.

The first step is the analysis of oriented texture consists of the extraction of an orientation field. The orientation field is comprised of the angle and coherence images, which describe at each point the dominant local orientation and degree of anisotropy, respectively. A new algorithm for computing the orientation field for a flow-like texture is presented. The basic idea behind the algorithm is to use an oriented filter, namely the gradient of Gaussian, and perform manipulations on the resulting gradient vector field. The most important aspect of the new algorithm is that it is provably optimal in estimating the local orientation of an oriented texture. An added strength of the algorithm is that it is simpler and has a better signal-to-noise ratio than previous approaches, because it employs fewer derivative operations. We also propose a new measure of coherence, which works better than previous measures. The estimates for orientation and coherence are related to measures in the statistical theory of directional data. We advocate the use of the angle and coherence images as intrinsic images. An analysis of oriented textures will require the computation of these intrinsic images as a first step. In this sense, the computation of the orientation field, resulting in the intrinsic images, is mdispensible in the analysis of oriented textures. We provide results from several experiments to indicate the usefulness of the angle and coherence intrinsic images. These results show that the notion of scale plays an important role in the interpretation of textures. Further, measures defined on these intrinsic images are useful for the inspection of surfaces. 8 1991 Academic pless, b.