A Brief History of Our Group Members
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:
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).
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.
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.
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.
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
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.
Franklin Mendivil assumes a position in the Department
of Mathematics, Acadia University, Nova Scotia.
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.
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
Bruno Forte passes away in Florence, Italy.
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