Shape from periodic texture using the eigenvectors of local affine distortion

This paper shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly, without the need for iterative n umerical optimization, We work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks. Th e key theoretical contribution is to show that the directions of the eigenv ectors of the affine distortion matrices can be used to estimate local slan t and tilt angles of tangent planes to curved surfaces. In particular, the leading eigenvector points in the tilt direction. Although not as geometric ally transparent, the direction of the second eigenvector can be used to es timate the slant direction. The required affine distortion matrices are com puted using the correspondences between spectral peaks, established on the basis of their energy ordering. We apply the method to a variety of real-wo rld and synthetic imagery.