Publications

University of Waterloo Links

The University of Waterloo
In Waterloo, Ontario, Canada
The Faculty of Mathematics
At the University of Waterloo
The Department of Applied Math
At the University of Waterloo
The Vision and Image Processing Lab
At the Unviversity of Waterloo

Some External Links

The International Conference on Image Analysis and Recognition
An annual conference that brings together researchers in the fields of Image Processing, Image Analysis and Pattern Recognition
USC Image Database
An Image Database Administered by the Signal and Image Processing Institute at The University of Southern California
Fractals
A scientific journal published by World Scientific
Fractal Artwork
On DeviantART

List of Publications (Waterloo Group Only)

This page is still under construction, but below is a list of some of our publications (not meant to be a complete list, yet) from the research group at the University of Waterloo only. For a list of publications from members of our group at other institutions, please visit their respective web pages, listed here.

2001 - Current

G.S. Mayer and E.R. Vrscay. Self-similarity of Fourier Domain Data. Nonlinear Analysis (in press).
G.S. Mayer, E.R. Vrscay, M.L. Lauzon, B.G. Goodyear and J.R. Mitchell. Self-similarity of images in the Fourier domain, with applications. ICIAR 2008, LCNS 5112, Springer-Verlag, Berlin Heidelberg, pages 43 - 52, 2008.
G.S. Mayer and E.R. Vrscay. Iterated Fourier Transform Systems: A Method for Frequency Extrapolation. ICIAR 2007, LNCS 4633, Springer-Verlag, Berlin Heidelberg, 2007.
H.E. Kunze, D. La Torre and E.R. Vrscay, Contractive multifunctions, fixed-pont inclusions and iterated multifunction systems, J. Math. Anal. Appl.330, 159-173 (2007).
H.E. Kunze, D. La Torre and E.R. Vrscay, Random fixed point equations and inverse problems by collage theorem, J. Math. Anal. Appl. 334, 1116-1129 (2007).
D. La Torre, F. Mendivil and E.R. Vrscay, Iterated function systems on multifunctions, in Math Everywhere (Springer-Verlag, Heidelberg, 2006).
E.R. Vrscay, Continuous evolution of fractal transforms and nonlocal PDE imaging, in Image Analysis and Recognition, ICIAR 2006, Lecture Notes in Computer Science, Vol. 4141, pp. 82-93 (2006).
M. Ebrahimi and E.R. Vrscay, Fractal image coding as projection onto convex sets, in Image Analysis and Recognition, ICIAR 2006, ibid., pp. 493-506 (2006).
M. Ghazel, G. Freeman and E.R. Vrscay, "Fractal-wavelet image denoising revisited, IEEE Trans. Image Proc. 15(9), 2669-2675 (2006).
J. Bona and E.R. Vrscay, Continuous evolution of functions and measures toward fixed points of contraction mappings, in Fractals in Engineering: New Trends in Theory and Applications, edited by J. Levy-Vehel and E. Lutton (Springer Verlag, London 2005), pp. 237-253.
H. Kunze, J. Hicken and E.R. Vrscay, Inverse problems for ODEs using contraction maps: Suboptimality of the `Collage Method', Inverse Problems 20, 977-991 (2004).
M. Ghazel, G. Freeman and E.R. Vrscay, Fractal image denoising, IEEE Trans. Image Proc. 12(12), 1560-1578 (2003).
F. Mendivil and E.R Vrscay, Fractal vector measures and vector calculus on planar fractal domains, Chaos, Solitons and Fractals 14, No. 8, 1239-1254 (2002).
E.R. Vrscay, From Fractal Image Compression to Fractal-Based Methods in Mathematics, in Fractals in Multimedia, edited by M.F. Barnsley, D. Saupe and E.R. Vrscay (Springer-Verlag, New York, 2002).

1990 - 2000

B. Forte, F. Mendivil and E.R. Vrscay (1999), IFS-Type Operators on Integral Transforms, in Fractals: Theory and Applications in Engineering, edited by M. Dekking, J. Levy-Vehel, E. Lutton and C. Tricot (Springer Verlag, London), pp. 125-138 (1999).
E.R. Vrscay and D. Saupe Can One Break the "Collage Barrier" in Fractal Image Coding?" in Fractals: Theory and Applications in Engineering, edited by M. Dekking, J. Levy-Vehel, E. Lutton and C. Tricot, (Springer Verlag, London) pp. 307-323 (1999).
H.E. Kunze and E.R. Vrscay, Solving Inverse Problems for ODEs Using the Picard Contraction Mapping , Inverse Problems 15, 745-770 (1999).
B. Forte and F. Mendivil, A classical ergodic property for IFS: A simple proof, Ergodic Theory and Dynamical Systems 18, xx-xx (1998). (Note: This is the original manuscript. The year "2000" appears in it because the file was regenerated from the original source file that year.)
B. Forte and E.R. Vrscay, Theory of Generalized Fractal Transforms, in Fractal Image Encoding and Analysis, edited by Y. Fisher (Springer Verlag, Heidelberg, 1998).
B. Forte and E.R. Vrscay, Inverse Problem Methods for Generalized Fractal Transforms, in Fractal Image Encoding and Analysis, ibid.
E.R. Vrscay, A Generalized Class of Fractal-Wavelet Transforms for Image Representation and Compression, Canadian Journal of Electrical and Computer Engineering, Vol. 23, Nos. 1-2, pp. 69-83 (1998).
B. Forte and E.R. Vrscay, Theory of Generalized Fractal Transforms, in Fractal Image Encoding and Analysis, edited by Y. Fisher (Springer Verlag, Heidelberg, 1998).
R.A. Wannamaker and E.R. Vrscay, Fractal Wavelet Compression of Audio Signals, J. Audio Engineering Society, Vol. 45, Nos. 7-8, pp. 540-553 (1997).
F. Mendivil and E.R. Vrscay, Correspondence Between Fractal-Wavelet Transforms and Iterated Function Systems With Grey-Level Maps, in Fractals in Engineering: From Theory to Industrial Applications,, edited by J. Levy Vehel, E. Lutton and C. Tricot (Springer Verlag, London, 1997).
B. Forte and E.R. Vrscay, Solving the inverse problem for measures using iterated function systems: A new approach, Adv. Appl. Prob., 27, 800-820 (1995).
B. Forte and E.R. Vrscay, Solving the inverse problem for function and image approximation using iterated function systems Dyn. Cont. Disc. Imp. Sys. 1, 177-231 (1995).
C.A. Cabrelli, B. Forte, U.M. Molter and E.R. Vrscay, Iterated Fuzzy Set Systems: A New Approach to the Inverse Problem for Fractals and Other Sets, J. Math. Anal. Appl. 171, 79-100 (1992).