# Adaptive Scale Filtering: A General Method for Obtaining Shape From Texture

James V. Stone and Stephen Isard

We introduce \underline{adaptive scale filtering}\footnote{In \cite{STONE_BMVC90,sto,STONE_BMVC92,STONE_ROY_SOC} this method was referred to as adaptive {\em multi}-scale filtering. We have changed the name to avoid confusion with methods which simultaneosuly filter each image point with multiple filters.} 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 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 \cite{oht}. However, there is no general characterization of texels for arbitrary textures. Furthermore, 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 vary by orders of magnitude. Commencing with an initial set, $F_{0}$, of identical image filters, adaptive scale filtering derives a set, $F_{N}$, which contains a unique filter for each image position. Each element of $F_{N}$ is tuned to the three-dimensional structure of the surface; that is, each filter projects to an identical shape on the surface. Thus \underline{image texels} of various sizes, but associated with a single spatial scale \underline{on the surface}, can be identified in different parts of the image. When combined with a conventional shape from texture method $F_{N}$ provides accurate estimates of surface orientation. Results for planar surfaces are presented.

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