Shape from Regular Patterns

niis paper describes an aigoritlitr1 to obtaitl local surface orierltatiorr frofti the apparetlt surface-pattertl distortion in an image. We propose a spherical projection to model perspctiue imaging. A trtappitlg is debtled based of1 the measurement of the local distortions of a repeated known rexture pattern due Io the image projection. 77tis mapping maps an apparent shape on the image sphere lo a locus of possible surface orienrations on the Gaussian sphere. A n ireratiw constraint propagation algorithm with the orientations at occluding boundaries reduces possible surface orientations to a unique orientation. 7 l i s algorithm can recover local surface orientation as well as interpolate surjace orientations where no information is auailable. ?Xis algorithm is applied to a real image ro demonstrate its perfontlance. 0. Introduction Information about surface within boundaries comes from various sources such as stereopsis, shading, high-light and texture gradient. This information is converted into local surface orientation, often referred to as a 2-1/2 D sketch [2,3], or a needle map 141. This paper concentrates on making this 2-1/2 D sketch from texture gradient . This domain, referred to as the shape-from-texture problem, has been studied extensively [5-121. Historically, Gibson pointed out the role of texture as a basis for the recovery of surface orientation [5 ] . He proposed the density gradient as the primary basis for surface perception by humans. Formalizing the shape-from-texture problem requires modeling the imageforming system. Mainly two kinds of projections have been commonly used: the orthographic projection and the perspective projection. Kender [7], Kanade [SI, and Witkin [ 101 explorzd the domain under the orthographic projection. Kender formalizes the relationship between local surface orientation and two perpendicular texture elements assumed to have the same Artificial Intelligence 22 (1984) 49-75 0004.3702/84/$3.00 @ 1984. Elsevier Science Publishers B.V. (North-Holland)