Applications

Computer Vision

• Basic representation for object recognition.
• Provides initial geometric structure to permit the robust extraction of ridges, edges, vertices.
• Shape transforms acting on the MA permit simplifications while preserving the most significant structures of the original object.

Computer Graphics

• 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.

• 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

• The MA is particularly relevant to define offsets and self-intersection in 3D.
• 3D skeletons and Voronoi diagrams for shape modeling and object tesselation (for meshing, finite element analysis).
• 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

• Precise path-planning in 3D, for manufacturing tasks, such as milling, turning, punching and drilling.
• Offsets

Computational Chemistry and Crystallography

• 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.
• 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.
• The MA embeds the Critical net crystal structure and can be used for its construction and visualization.

Medical Imaging and Biology

• Fast volume rendering
• Morphometry of nerve, bones, cross-sections, etc., 3D organ shape representation
• Registration of MR images, e.g. for brains (sulci)
• Camera path-planning in virtual endoscopy
• Characterizing dental articulations (modeling contact of complex objects)
• Tracking live cell pseudopod dynamics, studying growth and morphogenesis
• 3D distribution of chromosomes.

Archaeology, Architecture, Cultural Heritage

• Free-form shape modeling
• Object reconstruction from sherds: stitching fragments together automatically.

Multimedia - Datamining

• Recently considered as a viable representation for complex object queries in large 2D and 3D databases.