A Brief History of Our Group Members

The "Waterloo Fractal Compression Project" began in 1996 as a part of an international collaborative project involving the University of Waterloo (E.R. Vrscay), the Ecole Polytechnique de l'Universite de Montreal (C. Tricot, now at the University of Clermont-Ferrand, France) and the Groupe Fractales (J. Levy-Vehel) of the INRIA labs at Rocquencourt, France. This project was made possible with funding from the Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of a Collaborative Research Grant. One of the primary goals of this collaboration was to develop a new generation of image and signal compression methods which incorporate "fractal based" methods.

But let's step back a bit and see how fractal coding and analysis first arrived at Waterloo:

1985

Ed Vrscay, who defended his Ph.D. in Applied Mathematics at Waterloo in December 1984 (subject area: mathematical physics/quantum mechanics), takes an NSERC Postdoctoral Fellowship to the School of Mathematics, Georgia Institute of Technology, to work with Michael Barnsley on fractal analysis and dynamical systems. Here, Ed obviously became "infected" with the fractal virus. In 1986, Ed taught the first course on fractal geometry offered by Georgia Tech's School of Math (MATH 4806).

1986

Ed returns to the Department of Applied Mathematics, U Waterloo, as an NSERC University Research Fellow. The Chairman of the Department at that time was Bruno Forte, whose expertise included analysis, functional equations and information theory.

1987

Ed teaches a graduate course on topics in dynamical systems/fractal geometry at Waterloo. At some point, Bruno Forte, who originally said that Ed's work was #$*%, gets very interested in fractals, in particular, in the inverse problem. The Forte-Vrscay collaboration is born.

1993

Bruno Forte retires from Waterloo and assumes a position at the University of Lecce in Italy. (This was made possible by a program instituted by the Italian government to attract senior Italian academics back to their home country.) In 1995, Bruno moves to the University of Verona. While there he meets a young mathematics student, Davide La Torre, from the University of Milan. Bruno supervises Davide's Master's thesis on the subject of the inverse problem for IFS. Bruno also visits Waterloo at least once a year.

1994

John Kominek, an undergraduate student in Computer Science at Waterloo who is interested in fractal image compression, suggests to Ed that he should consider having a website for the Waterloo fractal work. John sets up such a website, to which he also launches his "brainchild" - the Waterloo "BragZone", a repository of images, papers and software for fractal image compression.

1997

Franklin Mendivil, a recent Ph.D. graduate in topology from the School of Mathematics, Georgia Tech, comes to Waterloo to work as a postdoctoral researcher with Ed. Franklin's position is funded by the NSERC Collaborative Grant mentioned earlier. We mention that during Franklin's graduate student days at Georgia Tech, he worked one summer with Ron Shonkwiler from the School of Math on the inverse problem for fractal construction using moments.

1998(?)

Franklin Mendivil assumes a position in the Department of Mathematics, Acadia University, Nova Scotia.

1998(?)

Herb Kunze, after finishing his Ph.D. in Applied Mathematics at Waterloo in the area of differential equations, works for four months with Ed. The goal of their research was to devise a method of solving the inverse problem for differential equations using the contractive Picard integral operator and the "collage theorem". In 2xxx, Herb moves to the Dept. of Mathematics and Statistics, University of Guelph, to eventually become a faculty member there.

2001(?)

Simon Alexander comes to Waterloo to begin an M.Math. programme. Having graduated from U. Victoria several years earlier, Simon spent a couple of years working in medical imaging at the firm xxxxxx in Silicon Valley, California. Simon changes his original plan to do his Master's thesis work in quantum mechanics and works with Ed on problems in mathematical imaging. His M.Math. thesis was on the subject of fractal and fractal-wavelet image coding.

Simon stays at Waterloo to do his Ph.D. work in mathematical imaging. His thesis work, which could be classified under the heading of multiscale methods in imaging, had two major components: (a) fractal-based methods and (b) a hierarchical/multiscale method of simulated annealing.

Bruno Forte passes away in Florence, Italy.

2006

Davide La Torre spends a six-month sabbatical at Waterloo (Feb-July). During this time, he establishes a very active collaboration with Ed, Herb and Franklin (sometimes all at once, as evidenced by the photo on the main page).