Low-Level Image Processing with the Structure Multivector

The present thesis deals with two-dimensional signal processing for computer vi-sion. The main topic is the development of a sophisticated generalization of the one-dimensional analytic signal to two dimensions. Motivated by the fundamental property of the latter, the invariance – equivariance constraint, and by its relation to complex analysis and potential theory, a two-dimensional approach is derived. This method is called the monogenic signal and it is based on the Riesz transform instead of the Hilbert transform. By means of this linear approach it is possible to estimate the local orientation and the local phase of signals which are projections of one-dimensional functions to two dimensions. For general two-dimensional signals, however, the monogenic signal has to be further extended, yielding the structure multivector. The latter approach combines the ideas of the structure tensor and the quaternionic analytic signal. A rich feature set can be extracted from the structure multivector, which contains measures for local amplitudes, the local anisotropy, the local orientation, and two local phases. Both, the monogenic signal and the struc

The Use of Tree Transducers to Compute Translations Between Graph Algebras

. The power of top-down tree transducers and tree-to-graphto -tree transducers (tgt transducers) to compute translations between hyperedge-replacement algebras is investigated. It turns out that topdown tree transducers are too weak in many cases. Tgt transducers are shown to be more powerful. 1 Introduction Using the notion of hyperedge replacement a hypergraph H may be understood as an operation on hypergraphs (see [Cou91]). If H contains hyperedges e 1 ; : : : ; e n it represents an operation that takes n argument graphs H 1 ; : : : ; H n and yields the hypergraph obtained by the substitution of H i for e i (i = 1; : : : ; n). Roughly speaking, this means a term over these hyperedge-replacement operations corresponds to a derivation tree in a hyperedge-replacement grammar, where operation symbols correspond to right-hand sides of production rules. Every finite set of such hyperedge-replacement operations yields an algebra called a hyperedge-replacement algebra, or HR algebra, for s..