Generalized multidimensional Hilbert transforms in Clifford analysis

Generalized multidimensional Hilbert transforms in Clifford analysis

During the last fifty years, Clifford analysis has gradually developed to a comprehensive theory offering a direct, elegant, and powerful generalization to higher dimension of the theory of holomorphic functions in the complex plane. In its most simple but still useful setting, flat m-dimensional Euclidean space, Clifford analysis focusses on the so-called monogenic functions, that is, null sol...

2D Image Analysis by Generalized Hilbert Transforms in Conformal Space

This work presents a novel rotational invariant quadrature filter approach called the conformal monogenic signal for analyzing i(ntrinsic)1D and i2D local features of any curved 2D signal such as lines, edges, corners and junctions without the use of steering. The conformal monogenic signal contains the monogenic signal as a special case for i1D signals and combines monogenic scale space, phase...

Extending coherent state transforms to Clifford analysis

Segal-Bargmann coherent state transforms can be viewed as unitary maps from L2 spaces of functions (or sections of an appropriate line bundle) on a manifoldX to spaces of square integrable holomorphic functions (or sections) onXC. It is natural to consider higher dimensional extensions of X based on Clifford algebras as they could be useful in studying quantum systems with internal, discrete, d...

Generalized Frames in Hilbert Spaces

Local Structure Analysis by Isotropic Hilbert Transforms

This work presents the isotropic and orthogonal decomposition of 2D signals into local geometrical and structural components. We will present the solution for 2D image signals in four steps: signal modeling in scale space, signal extension by higher order generalized Hilbert transforms, signal representation in classical matrix form, followed by the most important step, in which the matrixvalue...