Recovering Surface Curvature and Orientation from Texture Distortion: A Least Squares Algorithm and Sensitivity Analysis

Abstract

Shape from texture is best analyzed in two stages, analogous to stereopsis and structure from motion: (a) Computing the ‘texture distortion’, and (b) Interpreting the ‘texture distortion’ to infer the orientation and shape of the surface. We model the texture distortion for a given point and direction on the image plane as an affine transformation and derive the relationship between the parameters of this transformation and the shape parameters. We use non-linear minimization of a least squares error criterion to estimate the shape parameters from the affine transformations, using a simple linear algorithm to obtain an initial guess. Under the assumption that the measurement errors in the affine parameters are independent and normally distributed, we can find error bounds on the shape parameter estimates. We present results on images of planar and curved surfaces under perspective projection. We find all five local shape and orientation parameters with no a priori assumptions about the shape of the surface.