Signals, Images, ..., What's Next in Scientific Visualization
S. Allen Broughton
Abstract
"A picture is worth a thousand words." That is the principle
that scientists have been using for centuries to convey information about
scientific concepts, data, and models. With the availability of cheap computers
and the ability to gather enormous amounts of data about scientific objects
of study, scientists today have very effective tools to help them in their
quest for knowledge. Indeed, the computer has become a laboratory itself
as theories are tested by computer simulation. This blessing poses
its own challenges. The enormous amounts of data require increasingly sophisticated
tools to analyze, refine and understand this data. The disciplines of computer
science, mathematics, electrical engineering and optics, as well as practitioners
from other sciences have all contributed to this understanding, resulting
in an emerging discipline of Imaging Science. In this talk we will
explore this area, mostly through examples. The talk is intended
for a general audience.
Lecture

Lecture slides in pdf format  printout of power point file: (24 pages
 536K)
sciviz.pdf

Pictures for some of the examples (not in the PDF)

Example
1  Fourier methods pictures

Example
2  Colour histograms and feature analysis by vector quantization.

Example
3  Dyadic multiresolution of fingerprint image by wavelet analysis.
(see Ref 2 below)
Answer to questions after the lecture

Dimension of signal. This usually refers to the dimension of the set on
which the signal is defined, audio signal is defined on a 1D rectangle,
an image is defined in a 2D rectangle. Volumetric data such as the entire
CAT scan of an part of a body is a 3D signal. The non flat geometric shapes
are all really complex two dimensional objects embedded in three dimensional
space. One should distinguish by using terms such as "embedding dimension"
and "intrinsic dimension".
Scripts
Most of the scripts use the MATLAB image processing toolbox and the some
use the wavelet tool box.

analsynDCTsx.m,
dctsmoothdemo.m:
show the analysis of a wave form into periodic components and smoothing
by eliminating noise frequencies

darhist.m,
hist2D.m,
imagehist1D.m,
imagehist2D.m
scripts to illustrate 1D and 2D color histogram

darvect.m,
colourfeature.m,
hist3D.m,
imagehist3D.m:
scripts to extract a feature on the basis of colour.

dwt2stagesnorm.m,
dwt2stagesunnorm.m:
illustrates the wavelet transform and dyadic resolution of a fingerprint
file, require detfinger.mat

jpg2rgb.m,
RGBOpic.m:
converts jpeg files to their constituent R, G and B components.

SigmaXipics.mws:
generates maple pictures shown in the lecture.
References and Links

Caltech geometric
modeling group

C. Brislawn's publications
web page (fingerprint compression)

An Imaging Science Conference

Transform
Methods in Image Processing, Mathematics Faculty Seminar, Mount Holyoke
College, Spring 2001
Email: allen.broughton@rosehulman.edu
Webpage: http://www.rosehulman.edu/~brought/
This page last updated on 7 May 01.