May 2001
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Applications
Computer Vision
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Basic representation for object recognition.
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Provides initial geometric structure to permit the robust
extraction of ridges, edges, vertices.
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Shape transforms acting on the MA permit simplifications
while preserving the most significant structures of the original object.
Computer Graphics
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The MA representation permits to implicitly find the distance
from a point to a complex polygonal shape. Distance permits prediction,
use of coherence and dynamic path modification, of particular interest
for rendering of surfaces and volumes, collision prevention, tolerance
verification, visibility computations, accurate motion dynamics and 3D
path planning, self-intersection detection.
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Also, the MA shape description can be used for manipulation
in animation (automated skeleton production), shape simplifications and
shape morphing, surface meshing (polygonal mesh from unorganized or partially
connected clouds of samples).
Computer Aided Design
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The MA is particularly relevant to define offsets and self-intersection
in 3D.
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3D skeletons and Voronoi diagrams for shape modeling and
object tesselation (for meshing, finite element analysis).
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The MA is also of benefit in reverse engineering and virtual
prototyping to permit to automatically for from 3D data to CAD files to
3D printers.
Robotics and Numerical Control
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Precise path-planning in 3D, for manufacturing tasks, such
as milling, turning, punching and drilling.
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Offsets
Computational Chemistry and Crystallography
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In Molecular Design, the MA can be used to construct a molecular
graph, which recovers the network of chemical bonds, based on the quantum
theory for atoms.
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In Drug design, the MA permits to build Molecular surfaces
and molecular volume, models of receptor sites, dockings of ligands inside
protein cavities, and geometric invariants among different molecules that
exhibit similar activity.
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The MA embeds the Critical net crystal structure and can
be used for its construction and visualization.
Medical Imaging and Biology
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Fast volume rendering
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Morphometry of nerve, bones, cross-sections, etc., 3D organ
shape representation
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Registration of MR images, e.g. for brains (sulci)
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Camera path-planning in virtual endoscopy
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Characterizing dental articulations (modeling contact of
complex objects)
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Tracking live cell pseudopod dynamics, studying growth and
morphogenesis
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3D distribution of chromosomes.
Archaeology, Architecture, Cultural Heritage
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Free-form shape modeling
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Object reconstruction from sherds: stitching fragments together
automatically.
Multimedia - Datamining
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Recently considered as a viable representation for complex
object queries in large 2D and 3D databases.
Meshing -
Design