Shape from texture without boundaries

We describe a shape from texture method that constructs a maximum a posteriori estimate of surface coefficients using only the deformation of individual texture elements. Our method does not need to use either the boundary of the observed surface or any assumption about the overall distribution of elements. The method assumes that texture elements are of a limited number of types of fixed shape. We show that, with this assumption and assuming generic view and texture, each texture element yields the surface gradient unique up to a two-fold ambiguity. Furthermore, texture elements that are not from one of the types can be identified and ignored. An EM-like procedure yields a surface reconstruction from the data. The method is defined for othographic views — an extension to perspective views appears to be complex, but possible. Examples of reconstructions for synthetic images of surfaces are provided, and compared with ground truth. We also provide examples of reconstructions for images of real scenes. We show that our method for recovering local texture imaging transformations can be used to retexture objects in images of real scenes.