The goal of this project is to create
high-resolution computer models and images
of anatomical structures in the human head, thorax, and abdomen.
The anatomical accuracy of the models is insured
by digitizing data points
lying on actual specimens of the relevant organs.
This process leads inevitably to much larger data sets (of raw data points)
than are strictly necessary to model the structure.
Of fundamental interest therefore is
the efficient extraction of features
and the encoding of both 2 and 3-dimensional data
in three-space for model generation and display.
Multi-dimensional spline techniques, contour extraction,
triangulation methods, and geometric filtering and smoothing
are the primary subjects of study.<p>

This project is funded by Glaxo, Inc. and is entitled
"Glaxo Virtual Anatomy"
The Glaxo Virtual Anatomy project is devoted to the creation of
a ``computerized atlas'' of human and animal anatomy,
especially suitable for educational purposes.
It is being developed jointly by professors
in the Departments of Anatomy (Prof. Tom Spurgeon),
Mathematics (Prof. Rick Miranda), and
Mechanical Engineering (Prof. David Alciatore),
and is also utilizing the expertise of
Tom McCracken of Biographics, Inc.
The technical aspect of the project is to create
accurate computer models of human and animal organs,
which are flexible enough to be used
both in the teaching of basic anatomy to undergraduate students,
and by professional physicians, clinicians, and anatomists in their work.
Many applications would be forthcoming both in basic education of
professionals in health care and in patient education.
By using current techniques in computer graphics and surface reconstruction,
it will be possible to provide on a desktop platform
an ``electronic Gray's Anatomy'',
which would duplicate most of the benefits of an actual dissection,
without any of the associated medical, financial, and ethical costs.
A computerized anatomical atlas will make it possible to create
realistic, vivid 3-dimensional images
which the user may interactively rotate, view from any angle,
and "electronically dissect",
by removing structures in turn from a picture
with simple keyboard, joystick, or mouse commands.
Moreover, this material presented on a graphics terminal
can be tailored to meet the needs of the specific audience,
and students can learn the fundamentals of anatomy
either through a guided design approach or by a self-paced system.<p>

Click <A HREF="http://www.vis.colostate.edu/library/gva/gva.html">here</A>
for the Glaxo Virtual Anatomy page at the Colorado State University
Visualization Laboratory; some sample images are available there.<p>

Professor Miranda's part in this project at Colorado State University
is in the design and implementation of algorithms and software
to accurately and quickly produce the 3-dimensional images
of anatomical structures from the raw data.
The basic problems can be summarized into three areas:
raw data acquisition, surface reconstruction, and image display.
Each of these will be addressed briefly below.

<h3>Raw data acquisition:</h3>
For simplicity, let us assume that the anatomical structure
to be put into the computer atlas is a single volume,
bounded by its exterior surface.
For example, the structure at hand may be a vertebra in the spine.
Currently, the thorax is frozen,
and successive slices of the thorax are photographed,
forming a series of parallel contours,
each representing a cross-section of the thorax at varying heights.
These contours in the photographs are now digitized by hand,
using a pen tablet.
(We are developing an automatic scan with edge detection procedure
to digitize the contours.)
Professor Miranda has been involved
in the data acquisition phase of the project
by helping to develop the registration algorithms
to properly align the digitized contours.
He will be involved in the effort to proceed automatically with this step,
by developing and testing the appropriate edge detection algorithms.
The process is naturally complicated by the existence,
in any one area of the body,
of many different anatomically distinct volumes
(e.g., bone, muscle, skin, nerves, veins, etc.)
and these must all be properly distinguished in the detection procedure.
Standard thresholding and filtering techniques
typically produce poor results in the contouring phase with medical images,
and we are investigating new techniques using wavelet analysis and 
neural networks to aid in the contour generation.

<h3>Surface Reconstruction</h3>
Upon acquiring the parallel contours for any one structure,
the contours must be "assembled",
producing the surface exterior of the volume.
This process can be viewed as "joining" two adjacent contours,
by a sequence of triangles,
thereby producing a "ribbon" in between two contours,
which represents a horizontal section of the surface.
The joining process is the "triangulation" of the surface,
and Prof. Miranda's primary duty in the project
is to oversee the design and implementation of the triangulation algorithms.
The purpose of these algorithms is to find optimal triangulations,
where optimality can be defined in various ways:
minimal area, minimal edge length, and minimal curvature
are several possible definitions.
There are many triangulation methods in print,
but virtually all of them fail on complicated structures
which bifurcate and re-combine from one level to the next.
Our raw data contours are currently taken at 1 millimeter distance apart,
and for many small structures or small features of structures
this causes large variations in the topology from level to level,
resulting in highly non-standard problems for the triangulation process.
We are currently developing algorithms
both in the spirit of combinatorial geometry
and using ideas from differential geometry and minimal surface theory.

<h3>Image Display:</h3>
Once the anatomical structure has been triangulated,
the triangles must be rendered on the screen to produce the final image.
This of course involves hidden surface removal,
smooth shading techniques, texture mapping, and filtering algorithms.
Many of these operations can now be automatically performed in hardware,
and the problem becomes one of data representation:
how can the triangle data sets be optimally organized
to take advantage of the particular graphics engine
being used to produce images?