A key problem in medical computation is reconstruction of shapes (of
organs, bones, tumors etc) from lower dimensional information such as
CAT scans and sonograms. The CAT scan information is originally
one-dimensional, but is transformed into two-dimensional slices by signal processing techniques. However the
reconstruction of three-dimensional shapes from slices becomes a more
geometric problem, which can be abstracted as that of finding a surface
connecting a collection of contour lines or data points. A different
problem relates to compression of medical images for transmission and
storage; this differs from most other applications of image compression
in that little or no loss of information can be tolerated.
reconstruction home page, NASA Ames Biocomputation Center.
- Analysis of
metaphase chromosomes. D. Sudar et al. use medial axes to map
locations along images of chromosome structures.
- Anatomical modeling research, Rick Miranda, Colorado State.
Miranda's part in this study is finding optimal triangulations
to reconstruct surfaces by joining parallel contours.
- Annotated bibliography on medical imaging, H.-G. Park, Air Force Inst. Tech.
- Central path
algorithm. Y.R. Ge and D. Stelts use medial axes to find paths
along the central line of the intestinal system as part of a
virtual endoscopy system
for non-invasive medical diagnosis.
- Computer Aided Geometric Design, special
issue on Medical Visualization, call for papers. Deadline is Jan 31, 1997.
- Fractal analysis of trabecular bone.
M. L Richardson and T. Gillesby discuss algorithms
for automatically estimating fractal dimension,
and their use in modeling bone tissue.
Geiger of INRIA works on problems of surface reconstruction in
Human organs in polygonal slice format,
Gil Barequet, Tel Aviv U.
- Level set
methods for following the evolution of interfaces, J. Sethian,
Berkeley. The basic idea is to solve various "advancing front" type problems
such as finding shortest paths around obstacles, by evolving a surface
in one higher dimension that describes the dynamics of the front.
Includes movies and Java applets describing applications to
VLSI design, medical image processing, noise removal from images, and
robot motion planning.
- Medical Image Volume Visualization Software FAQ.
- Medical imaging links, M. Joppe, Bremen.
and tuberculosis diagnosis. Jason Everhart of Los
Alamos uses convex hulls as part of a heuristic for estimating the
percentage of lung volume occupied by a pneumonea infection.
This initial guess of the lung contour is then iteratively refined
to a more accurate representation.
Processing and display of medical three dimensional arrays of numerical
data using octree encoding, Amans and Darrier, Proc. SPIE, 1985.
Shape-Based 4D Left Ventricular Myocardial Function Analysis.
P. Shi, A. Amini, G. Robinson, A. Sinusas, C.T. Constable, and J. Duncan,
Yale U. Reconstructs heart membranes by triangulation of contours.
Their version of the problem is complicated by the extra dimension
of time-varying data.
Nina Amenta's CG software directory.
- Skeleton and
boundary extraction. Glynn Robinson of Yale overlays the Delaunay
triangulation and Voronoi diagram of points sampled from a surface
(the boundary between different features in a medical image) and
somehow extracts from them subsets representing the surface itself and
its medial axis.
Patent 5463721 describes the use of convex hulls in a method for finding a
path for a radiation-beam scanner so it can get enough data
to reconstruct object shapes. Patents
also use convex hulls for computerized tomography.
directory of Medical Imaging resources.
Geometry in Action,
a collection of applications of computational geometry.
from a common source file.