Shape-from-Texture from Eigenvectors of Spectral Distortion
This paper presents a simple approach to the recovery of dense orientation estimates for curved textured surfaces. We make two contributions. Firstly, we show how pairs of spectral peaks can be used to make direct estimates of the slant and tilt angles for local tangent planes to the textured surface. We commence by computing the affine distortion matrices for pairs of corresponding spectral peaks. The key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles. In particular, the leading eigenvector points in the tilt direction. Although not as geometrically transparent, the direction of the second eigenvector can be used to estimate the slant direction. The main practical benefit furnished by our analysis is that it allows us to estimate the orientation angles in closed form without recourse to numerical optimisation. Based on these theoretical properties we present an algorithm for the analysis of curved regularly textured surfaces. The second contribution of the paper is to show how initial orientation estimates delivered by the eigen-analysis can be refined using a process of robust smoothing. We apply the method to a variety of real-world and synthetic imagery. We show that the new shape-from-texture method can reliably estimate surface topography.
KeywordsTilt Angle Spectral Peak Surface Orientation Frequency Vector Spectral Distortion
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