Imaging The primary
purpose of my research is to enhance the mathematical and scientific
foundations of "predictive" modeling,
so that mathematical modeling results can conform more accurately
to physical experiments. Starting in 1980 with a series of applications
in computer graphics, the intent is to extend generic modeling
approaches beyond mere picturemaking, to the point that reconfigurable
models will have great predictive power.
The work includes computational methods that incorporate error
bounds, such as Interval Analysis, as well as general purpose
modeling methods for deriving reliable equations for mathematical
modeling, rendering, simulation, scientific visualization and
human/computer interaction. The intent is to develop methods
for constructing, simulating, rendering, and perceiving the shape
and behavior of a broad range of physical objects.
A source of motivation and long term goal for the research is
the creation of tools for simulation and behavioral prediction
of mechanical and biophysical structures. The methods are intended
to eventually be applied to simulating the behavior of cellular
organelles, but also to selfassembling robotic structures as
potentially needed for human colonization of space; the same
modeling technology can be used for both applications.
One consequence of my research, together with the efforts of
a few other researchers (including Profs. Arvo and Schröder),
is that the field of computer graphics has undergone a transformation,
towards an increasing reliance on robust mathematical methods.
This is a significant change; computer graphics in the past had
a much greater reliance on heuristic and adhoc methods. In this
context, a number of paradigm shifts have been enabled, such
as methods for modeling flexible objects and deformations, and
methods for dynamic constraints and inverse dynamics, mechanics
and goalbased models. For this work in computer graphics modeling,
I was awarded the sixth ACM Siggraph computer graphics achievement
award.
Subsequently, with my students, I have applied my efforts towards
a number of mathematicallybased applications, such as computer
graphics splining methods in nonlinear spaces, cellbased "developmental
models," new types of computer graphics hardware, reducing geometric
distortion in wide angle scenes, and, in collaboration with the
Caltech Biological Imaging Center in the Beckman Institute, scientific
visualization methods and goaldirected MRI acquisition. The
plan is to continue (1) the development of the basic methods,
extending the state of the art in computer graphics and scientific
visualization, but also (2) to work more with JPL and use the
methods to study macroscopic selfassembling mechanical structures
and (3) work with with Caltech Biology to study the behavior
of cellular organelles and other biophysical systems.
