Karel Culik
Karel Culik's Home Page
Left: original
Middle: WFA compression 50:1, 27.07 dB
Right: JPEG compression 50:1, 24.70 dB
For more examles of image compression see
Examples
History
M.Math: Mathematics, Charles
University. (Prague) 1957
Ph.D: Theoretical Comp. Science, Czechoslovak Acad.of Sciences,
(Prague) 1966
RNDr: Mathematical Logic, Charles Univ. (Prague) 1967
Dr.h.c.: Philosophy, Univ. of Turku, Finland 1995
Research Interests:
Formal Languages and Automata Theory
Parallel Computing
CellularAutomata
Image Generation, Compresion and Manipulation
Cellular Automata as Models of Complex Systems
I study various properties
of the global behavior of CA and other problems motivated by applications
in Physics. An example is the investigation of limit sets of CA which
formalize in this model the notion of the attractor of a dynamical system.
Cellular automata and other parallel architectures are also studied as
models for highly parallel computation.
Methods for Image Description, Generation and Compression
In
recent years, Mandelbrot's fractal geometry has drawn considerable attention
of scientists and mathematicians, as it provides method for a concise
description of many of the seemingly complex forms and patterns in
nature and in the sciences. An important application to graphics is to
develop methods based on fractal geometry that allow us to give a concise
mathematical description of a wide range of images. We are working on
the design of new methods that have two purposes:
1) to give a convenient
tool for the design of various types of
images,
2) to develop and implement methods for concise automatic
encoding of images and regeneration
with minimal degrading.
Our Mutual Recursive Function Systems (MRFS) are an example of the former,
our Weighted Finite Automata (WFA) and Generalized Finite Autmata
(GFA) of the latter.
WFA constitue an excellent tool for compression of grayscale and color images.
The image data compression software based on WFA developed
in cooperation with Jarkko Kari has been acquired by industry.
GFA developed with V. Valenta serve as a tool for
generation of bilevel images and for the compression of silhouette-like
bilevel images.
Weighted Finite Transducers (WFT) developed with I. Fris and J. Kari
give a powerful tool for manipulation of images both in pixel form
and in WFA representation. They can be also used for computer
assisted design of WFA.
The following systems are available by anonymous
ftp
BW includes programs for GFA based compressuon of silhouette-like
bilevel images and for decoding of arbitrary GFA (both coputer
encoded and human designed).
WFTX, imlemented by P. Rajcani, is a comprhensive menu driven system
that includes WFA decoder, implements WFT and various operations
on WFA, WFT and images in pixel form (both grayscale and color).
XALL, designed by S. Dube and other students, implements several
image generation methods: deterministic and probabilistic
MRFS (a generalization of Barnsley's IFS, D0L systems in turtle
geometry interpretation and matrix substitution systems.
For user guides see REDME files in the appropriate places.
By GFA
you reach an applet that allows to draw a diagram of an automaton
and immediately shows the images corresponding to each state.
Currently, it works for deterministic finite automata with all
states both initial and final only, the quadrant transformations
have not yet been implemented.
Classical problems in Automata and Language Theory
Theoretical
computer science and in particular Automata and Language theory is
my primary research area and I continue to be interested in finding
new methods for solving different classical problems in this area, and
applying automata in other areas. An excellent example is the construction
of small aperiodic sets of Wang tiles and cubes in cooperation with Jarkko Kari.
For more see the list of publications.
List of
Publications
Some of them are available via
ftp. Please read README file first.
List of former Ph.D. students at the University of Waterloo:
List of former Ph.D. students at USC:
List of former Postdoctoral assistents at the University of Waterloo:
