title: Analysis of superimposed oriented patterns.
abstract: Estimation of local orientation in images may be posed as the problem of finding the minimum gray-level variance axis in a local neighborhood. In bivariate images, the solution is given by the eigenvector corresponding to the smaller eigenvalue of a 2 x 2 tensor. For an ideal single orientation, the tensor is rank-deficient, i.e., the smaller eigenvalue vanishes. A large minimal eigenvalue signals the presence of more than one local orientation, what may be caused by non-opaque additive or opaque occluding objects, crossings, bifurcations, or corners. We describe a framework for estimating such superimposed orientations. Our analysis is based on the eigensystem analysis of suitably extended tensors for both additive and occluding superpositions. Unlike in the single-orientation case, the eigensystem analysis does not directly yield the orientations, rather, it provides so-called mixed-orientation parameters (MOPs). We, therefore, show how to decompose the MOPs into the individual orientations. We also show how to use tensor invariants to increase efficiency, and derive a new feature for describing local neighborhoods which is invariant to rigid transformations. Applications are, e.g., in texture analysis, directional filtering and interpolation, feature extraction for corners and crossings, tracking, and signal separation.
authors.affiliation: Institute of Imaging and Computer Vision, RWTH Aachen University, 52062 Aachen, Germany. til.aach@lfb.rwth-aachen.de
authors.forename: Til
authors.initials: T
authors.lastname: Aach
authors.forename: Cicero
authors.initials: C
authors.lastname: Mota
authors.forename: Ingo
authors.initials: I
authors.lastname: Stuke
authors.forename: Matthias
authors.initials: M
authors.lastname: Mühlich
authors.forename: Erhard
authors.initials: E
authors.lastname: Barth
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique