Paper Info
Title
The Signal Multi-Vector
Abstract
This work covers a fundamental problem of local phase based image analysis: the isotropic generalization of the classical 1D analytic signal to two dimensions. The analytic signal enables the analysis of local phase and amplitude information of 1D signals. Local phase, amplitude and additional orientation information can be extracted by the 2D monogenic signal with the restriction to intrinsically 1D signals. In case of 2D image signals the monogenic signal enables the rotationally invariant analysis of lines and edges. In this work we present the 2D analytic signal as a novel generalization of both the analytic signal and the 2D monogenic signal. In case of 2D image signals the 2D analytic signal enables the isotropic analysis of lines, edges, corners and junctions in one unified framework. Furthermore, we show that 2D signals are defined on a 3D projective subspace of the homogeneous conformal space which delivers a descriptive geometric interpretation of signals providing new insights on the relation of geometry and 2D image signals. Finally, we will introduce a novel algebraic signal representation, which can be regarded as an alternative and fully isomorphic representation to classical matrices and tensors. We will show the solution of isotropic intrinsically 2D image analysis without the need of steering techniques.
Year
DOI
Venue
2010
10.1007/s10851-010-0197-3
Journal of Mathematical Imaging and Vision
Keywords
DocType
Volume
Algebraic image analysis,Isotropic local phase based signal processing,Analytic signal,Monogenic signal,Weyl-projection,Structure multi-vector,Geometric algebra,Clifford analysis,Generalized Hilbert transform,Riesz transform,Conformal space,Projective/homogeneous space,Hybrid matrix geometric algebra,Poisson scale space,Rotational invariance,Radon transform
Journal
37
Issue
ISSN
Citations 
2
0924-9907
7
PageRank 
References 
Authors
0.51
19
2
Name
Order
Citations
PageRank
Lennart Wietzke116311.40
Gerald Sommer270.51