Shape from periodic texture using the eigenvectors of local affine distortion

Abstract

AbstractÐThis paper shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly, without the need for iterative numerical optimization. We work in the frequency domain and measure texture distortion using the affine distortion of the pattern of 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 of tangent planes to curved surfaces. 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 required affine distortion matrices are computed using the correspondences between spectral peaks, established on the basis of their energy ordering. We apply the method to a variety of real-world and synthetic imagery.

Detecting multiple texture planes using local spectral distortion

“…This analysis applies under the assumption that the underlying texture satisfies local constancy. In our previously published work we have exploited the closed form expressions for the slant and tilt angles in the analysis of curved surfaces [13]. The novel contribution of the current paper is twofold.…”

“…To do this we draw on our recently reported work where we have shown how to make closed form estimates of the local slant and tilt angles for points on regularly textured surfaces [13]. The method follows Krumm and Shafer [12] by assuming that the local texture variations due to the perspectivity can be approximated in an affine manner.…”

“…First, we provide a full derivation of the closed form expressions for the slant and tilt angles (Ref. [13] only provides a sketch). Second, we exploit the results of the analysis to develop an algorithm for texture plane segmentation.…”

An affine Invariant hyperspectral texture descriptor based upon heavy-tailed distributions and fourier analysis

“…This provides a principled link between statistical approaches, signal processing methods for texture recognition and shape modeling approaches based upon measures of spectral distortion [12,15]. Hence, this is a means to both, a compact representation of the hyperspectral texture based upon its statistical characterisation and affine invariance via the estimation of the transformation parameters on a locally planar texture plane.…”

Local image structures and optic flow estimation

“…Sub-domains of Computer Vision have extracted and analyzed such structures in edge detection (see, e.g., [6]), junction classification (see, e.g., [34]) and texture interpretation (see, e.g., [40,33]). There exists evidence that also in human vision such structures are processed (see, e.g., [17,37]) and that they play distinguishable roles in the information processing (see, e.g., [21]).…”