Shape from texture without boundaries

We describe a shape from texture method that constructs an estimate of surface geometry 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 surface texture elements are drawn from a number of different types, each of fixed shape. Neither the shape of the elements nor the number of types need be known in advance. We show that, with this assumption and assuming a generic, scaled orthographic view and texture, each type of texture element can be reconstructed in a frontal coordinate system from image instances. Interest-point methods supply a method of simultaneously obtaining instances of each texture element automatically and defining each type of element. Furthermore, image instances that have been marked in error can be identified and ignored using the Expectation-Maximization algorithm. A further EM procedure yields a surface reconstruction and a relative irradiance map from the data. We provide numerous examples of reconstructions for images of real scenes, show a comparison between our reconstruction and range maps, and demonstrate that the reconstructions display geometric and irradiance phenomena that can be observed in the original image.