000K utf8 1100 $c2009 1500 eng 2050 urn:nbn:de:101:1-201203133325 3000 Fleischmann, Oliver 4000 The Hilbert transform on the two-sphere$dA spectral characterization [Fleischmann, Oliver] 4209 The analytic signal is an important representation in one dimensional signal processing. Its generalization to two dimensions is the monogenic signal. The properties of the analytic and the monogenic signal in the Fourier domain are well known. A generalization to the sphere is given by the Hilbert transform on the sphere known from Clifford analysis. Nonetheless no spectral characterization exists and therefore prohibits an interpretation. We derive the spherical harmonic coefficients of the Hilbert transform on the sphere and give a series expansion. It will turn out that it acts as a differential operator on the spherical harmonic basis functions of the Laplace equation solution, analogously to the Riesz transform in two dimensions. This allows an interpretation of the Hilbert transform suitable for signal processing of signals naturally arising on the two-sphere. We show that the scale space naturally arising is a Poisson scale space in the unit ball. In addition the obtained interpretation of the Hilbert transform is used for orientation analysis of plane waves. This representation is justified as a novel signal model on the sphere which can be used to construct intensity and rotation invariant feature detectors in a scale-space concept. 4950 https://nbn-resolving.org/urn:nbn:de:101:1-201203133325$xR$3Volltext$534 4961 https://macau.uni-kiel.de/receive/macau_mods_00001837 5051 004