The Conformal Monogenic Signal of Image Sequences

  title={The Conformal Monogenic Signal of Image Sequences},
  author={Lennart Wietzke and Gerald Sommer and Oliver Fleischmann and Christian Schmaltz},
  booktitle={Statistical and Geometrical Approaches to Visual Motion Analysis},
Based on the research results of the Kiel University Cognitive Systems Group in the field of multidimensional signal processing and Computer Vision, this book chapter presents new ideas in 2D/3D and multidimensional signal theory. The novel approach, called the conformal monogenic signal, is a rotationally invariant quadrature filter for extracting i(ntrinsic)1D and i2D local features of any curved 2D signal - such as lines, edges, corners and circles - without the use of any heuristics or… 
Fast Empirical Mode Decompositions of Multivariate Data Based on Adaptive spline-Wavelets and a Generalization of the Hilbert-Huang-Transformation (HHT) to Arbitrary Space Dimensions
This paper extends the Hilbert–Huang-Transform method to multivariate data sets in arbitrary space dimensions and considers the Riesz transformation and an embedding into Clifford-algebra valued functions, from which instantaneous amplitudes, phases and orientations can be derived.
Kompression, Pose-Tracking und Halftoning
An image compression algorithm which saves only a small set of the points in the image and reconstructs the remainder of the image using a partial differential equation (PDE), an algorithm to follow the so-called poses of moving objects within a video sequence, and a number of extensions to this simple and flexible approach to handle specific applications.
Generalised Hilbert Transforms for the Estimation of Growth Direction in Coral Cores
  • R. Marchant, P. Jackway
  • Geology
    2011 International Conference on Digital Image Computing: Techniques and Applications
  • 2011
An objective estimation of major growth axis, growth band location, and off axis extension compensation is now possible, and shows the usefulness of 2D analytic signal based image analysis.
Optimizing Shape Particle Filters for the Detection and Segmentation of Medical Images
Two novel approaches for the generation of the region map are proposed, namely automatic region maps and per-pixel region maps, where the optimal distribution and number of template regions is derived from a set of training images, adapts to complex data and finds consistent features in the training examples without manual interaction.


2D Image Analysis by Generalized Hilbert Transforms in Conformal Space
The main idea is to lift up 2D signals to the higher dimensional conformal space where the signal features can be analyzed with more degrees of freedom and the low computational time complexity, the easy implementation into existing Computer Vision applications and the numerical robustness of determining curvature without the need of any derivatives.
The Conformal Monogenic Signal
The conformal monogenic signal is a novel rotational invariant approach for analyzing i(ntrinsic)1D and i2D local features of two-dimensional signals without the use of any heuristics and shows that isophote curvature can be calculated in a purely algebraic framework without the need of any derivatives.
Low-level image processing with the structure multivector
The two-dimensional generalization of the analytic signal turns out to provide a whole new framework for low-level vision, including methods for orientation estimation, edge and corner detection, stereo correspondence and disparity estimation, and adaptive smoothing.
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
In this paper, edge detection by a new approach to phase congruency and its relation to amplitude based methods, reconstruction from local amplitude and local phase, and the evaluation of the local frequency are discussed.
Differential Geometry of Monogenic Signal Representations
The fusion of monogenic signal processing and differential geometry is presented to enable monogenic analyzing of local intrinsic 2D features of low level image data that are invariant against local and global illumination changes and result from one unique framework within the monogenic scale-space.
Detecting Intrinsically Two-Dimensional Image Structures Using Local Phase
This paper presents a novel approach towards detecting intrinsically two-dimensional (i2D) image structures using local phase information that outperforms Harris and Susan detectors under the illumination change and noise contamination.
The Structure Multivector
The structure multivector is derived from the Laplace equation, which also introduces a new viewpoint on scale space and a phase approach for intrinsically 2D structures is derived and applications are presented which make use of the 2D part of the new operator.
The Radon Transform - Theory and Implementation
The subject of this Ph D thesis is the mathematical Radon transform which is well suited for curve detection in digital images and for reconstruction of tomography images The thesis is divided into
A 3D isotropic quadrature filter for motion estimation problems
Quadrature filters are a well known means for local spectral analysis of images and to extract relevant structure. Recently, there has been the discovering of an isotropic quadrature filter for