Surface orientation and curvature from differential texture distortion

A unified differential geometric framework for estimation of local surface shape and orientation from projective texture distortion is proposed, based on a differential version of the texture stationarity assumption introduced by Malik and Rosenholtz. This framework allows the information content of the gradient of any texture descriptor defined in a local coordinate frame to be characterized in a very compact form. The analysis encompasses both full affine texture descriptors and the classical “texture gradients”. For estimation of local surface orientation and curvature from uncertain observations of affine texture distortion, the proposed framework allows the dimensionality of the search space to be reduced from five to one