Fundamentals of digital image processing
Fundamentals of digital image processing
The “parallel vectors” operator: a vector field visualization primitive
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Non-commutative hypercomplex Fourier tranforms of multidimensional signals
Geometric computing with Clifford algebras
A novel approach to vortex core region detection
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Signal Processing for Computer Vision
Signal Processing for Computer Vision
Geometric verification of swirling features in flow fields
Proceedings of the conference on Visualization '02
Visualizing Nonlinear Vector Field Topology
IEEE Transactions on Visualization and Computer Graphics
Clifford Convolution And Pattern Matching On Vector Fields
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Three-dimensional flow characterization using vector pattern matching
IEEE Transactions on Visualization and Computer Graphics
Computationally attractive reconstruction of bandlimited images from irregular samples
IEEE Transactions on Image Processing
The Two-Dimensional Clifford-Fourier Transform
Journal of Mathematical Imaging and Vision
Moment Invariants for the Analysis of 2D Flow Fields
IEEE Transactions on Visualization and Computer Graphics
CFD visualisation: challenges of complex 3D and 4D data fields
International Journal of Computational Fluid Dynamics - CFD 2006 Held at Queens University at Kingston, Ontario, Canada, 1519 July 2006
The Color Monogenic Signal: Application to Color Edge Detection and Color Optical Flow
Journal of Mathematical Imaging and Vision
Segmentation of flow fields using pattern matching
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Data-intensive spatial filtering in large numerical simulation datasets
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Pattern forced geophysical vector field segmentation based on Clifford FFT
Computers & Geosciences
Convolution Products for Hypercomplex Fourier Transforms
Journal of Mathematical Imaging and Vision
| Hi-index | 0.00 |
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.