We introduce adaptive multi-scale filtering, a general method for deriving shape from texture under perspective projection without recourse to prior segmentation of the image into geometric texture elements (texels), and without any form of thresholding of filtered images. If texels on a given surface can be identified in an image then the orientation of that surface can be obtained . Unfortunately there is no known procedure for identifying texels for arbitrary textures. Even if the size and shape of texels on the surface is invariant with regard to position, perspective projection ensures that the size and shape of the corresponding image texels will vary by orders of magnitude. Commencing with an initial set, Fo, of identical image filters, iterative filtering derives an ordered set, Fn, which contains a unique filter for each image position. Each element of Fn is tuned to the three-dimensional structure of the surface; that is, each filter projects to an identical shape on the surface. Thus image texels of various sizes, but associated with a single spatial scale on the surface, can be identified in different parts of the image. When combined with a conventional shape from texture method FN provides accurate estimates of surface orientation. Results for planar surfaces are presented.
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