Estimation Of Multiple Local Orientations In Image Signals

Local orientation estimation can be posed as the problem of finding the minimum grey level variance axis within a local neighbourhood. In 2D image signals, this corresponds to the eigensystem analysis of a 22-tensor, which yields valid results for single orientations. We describe extensions to multiple overlaid orientations, which may be caused by transparent objects, crossings, bifurcations, corners etc. Multiple orientation detection is based on the eigensystem analysis of an appropriately extended tensor, yielding so-called mixed orientation parameters. These mixed orientation parameters can be regarded as another tensor built from the sought individual orientation parameters. We show how the mixed orientation tensor can be decomposed into the individual orientations by finding the roots of a polynomial. Applications are, e.g., in directional filtering and interpolation, feature extraction for corners or crossings, and signal separation

Estimation of multiple orientations and multiple motions in multi-dimensional signals

The estimation of multiple orientations in multidimensional signals is a strongly non-linear problem to which a two-step solution is here presented. First, the problem is linearized by introducing the so-called mixed-orientation parameters as a unique, albeit implicit, descriptor of the orientations. Second, the non-linearities are decomposed such as to find the individual orientations. For two-dimensional signals, e.g., images, this decomposition step is solved by simply determining the roots of a polynomial. For multi-dimensional signals, the nD decomposition problem is solved by reducing it to a cascade of 2D decomposition problems. In this way, a full solution for the estimation of any number of orientations in any dimension is achieved for the first time

Daily News, 1958-12-06

The Daily News was published in St. John's from 15 February 1894 to 4 June 1984, daily except Sunday

Analytic Solutions For Multiple Motions

A novel framework for single and multiple motion estimation is presented. It is based on a generalized structure tensor that contains blurred products of directional derivatives. The order of differentiation increases with the number of motions but more general linear filters can be used instead of derivatives. From the general framework, a hierarchical algorithm for motion estimation is derived and its performance is demonstrated on a synthetic sequence

Institute for Signal Processing, University of Lübeck,

Estimation of local orientation in images is often posed as the task of finding the minimum variance axis in a local neighborhood. The solution is given as the eigenvector belonging to the smaller eigenvalue of a 2 × 2 tensor. Ideally, the tensor is rank-deficient, i.e., the smaller eigenvalue is zero. A large minimal eigenvalue signals the presence of more than one local orientation. We describe a framework for estimating such superimposed orientations. Our analysis of superimposed orientations is based on the eigensystem analysis of a suitably extended tensor. We show how to efficiently carry out the eigensystem analysis using tensor invariants. Unlike in the single orientation case, the eigensystem analysis does not directly yield the orientations, rather, it provides so-called mixed orientation parameters. We therefore show how to decompose the mixed orientation parameters into the individual orientations. These, in turn, allow to separate the superimposed patterns. 1

Analysis of Motion and Curvature in Image Sequences

We briefly review a recent development in the area of computer vision and multidimensional signal processing. Image sequences are regarded as hypersurfaces and useful properties are derived from the geometry of that hypersurface. Besides demonstrating the uniqueness of curvature, new methods for the analysis of single and multiple motions are presented including the case of occluded motions