Clifford fourier transform on vector fields

IEEE Transactions on Visualization and Computer Graphics

Volumn 11, Issue 4, 2005, Pages 469-479

  Ebling, Julia ^a   Scheuermann, Gerik ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Clifford algebra; Convolution; Flow visualization; Fourier transform; Vector fields

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTER VISION; CONVOLUTION; CORRELATION METHODS; FEATURE EXTRACTION; FLOW VISUALIZATION; TOPOLOGY;

CLIFFORD ALGEBRA; GENERALIZATIONS; SCALAR FIELDS; VECTOR FIELDS;

FOURIER TRANSFORMS;

ALGORITHM; ARTICLE; COMPUTER ASSISTED DIAGNOSIS; COMPUTER GRAPHICS; COMPUTER INTERFACE; COMPUTER SIMULATION; EVALUATION; FLOW KINETICS; FOURIER ANALYSIS; IMAGE ENHANCEMENT; MATHEMATICAL COMPUTING; METHODOLOGY; ONLINE SYSTEM; THEORETICAL MODEL;

ALGORITHMS; COMPUTER GRAPHICS; COMPUTER SIMULATION; FOURIER ANALYSIS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MODELS, THEORETICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; ONLINE SYSTEMS; RHEOLOGY; USER-COMPUTER INTERFACE;

EID: 22944476484     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/TVCG.2005.54     Document Type: Conference Paper

References (16)

1. R. Bracewell, The Fourier Transform and Its Applications. New York: McGraw-Hill Book Company, 1965.
2. T. Bülow, M. Felsberg, and G. Sommer, "Non-Commutative Hypercomplex Fourier Transforms of Multidimensional Signals," Geometric Computing with Clifford Algebra, G. Sommer, ed., Berlin: Springer-Verlag, 2001.
3. J. Ebling and G. Scheuermann, "Clifford Convolution and Pattern Matching on Vector Fields," Proc. IEEE Visualization '03, pp. 193-200, 2003.
4. M. Felsberg, "Low-Level Image Processing with the Structure Multivector," doctoral dissertation, Univ. of Kiel, Germany, 2002.
5. G.H. Granlund and H. Knutsson, Signal Processing for Computer Vision. Dordrecht, The Netherlands: Kluwer, 1995.
6. E.B. Heiberg, T. Ebbers, L. Wigström, and M. Karlsson, "Three Dimensional Flow Characterization Using Vector Pattern Matching," IEEE Trans. Visualization and Computer Graphics, vol. 9, no. 3, pp. 313-319, July-Sept. 2003.
7. D. Hestenes, New Foundations for Classical Mechanics. Dordrecht, The Netherlands: Kluwer Academic, 1986.
8. B. Jähne, Digital Image Processing. Berlin: Springer Verlag, 2001.
9. A.K. Jain, Fundamentals of Digital Image Processing. Englewood Cliffs, N.J.: Prentice Hall, 1989.
10. M. Jiang, R. Machiraju, and D. Thompson, "A Novel Approach to Vortex Core Region Detection," Proc. Joint Eurographics-IEEE TVCG Symp. Visualization, pp. 217-225, May 2002.
11. M. Jiang, R. Machiraju, and D. Thompson, "Geometric Verification of Swirling Features in Flow Fields," Proc. IEEE Visualization 2002, pp. 307-314, 2002.
12. D.N. Kenwright, C. Henze, and C. Levit, "Feature Extraction of Separation and Attachment Lines," IEEE Trans. Visualization and Computer Graphics, vol. 6, no. 2, pp. 151-158, Apr.-June 2000.
13. F.H. Post, B. Vrolijk, H. Hauser, R.S. Laramee, and H. Doleitsch, "Feature Extraction and Visualization of Flow Fields," Eurographics 2002 State of the Art Reports, D. Fellner and R. Scopigno, eds., pp. 69-100, 2002.
14. M. Roth and R Peikert, "The Parallel Vectors Operator-A Vector Field Visualization Primitive," Proc. IEEE Visualization 1999, pp. 263-270, 1999.
15. G. Scheuermann, H. Krüger, M. Menzel, and A. Rockwood, "Visualizing Nonlinear Vector Field Topology," IEEE Trans. Visualization and Computer Graphics, vol. 4, no. 2, pp. 109-116, Apr.-June 1998.
16. T. Strohmer, "Computationally Attractive Reconstruction of Band-Limited Images from Irregular Samples," IEEE Trans. Image Processing, vol. 6, no. 4, pp. 540-548, 1997.