Construction and optimization of CSG representations
Computer-Aided Design - Beyond solid modelling
Separation for boundary to CSG conversion
ACM Transactions on Graphics (TOG)
Computation of the Medial Axis Transform of 3-D polyhedra
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
An approach to systematic part design
GMCAD '96 Proceedings of the fifth IFIP TC5/WG5.2 international workshop on geometric modeling in computer aided design on Product modeling for computer integrated design and manufacture
Shock Graphs and Shape Matching
International Journal of Computer Vision
Convex Decomposition of Simple Polygons
ACM Transactions on Graphics (TOG)
An efficient algorithm for finding the CSG representation of a simple polygon
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
The Role of Propagation and Medial Geometry in Human Vision
BMCV '02 Proceedings of the Second International Workshop on Biologically Motivated Computer Vision
Any open bounded subset of Rn has the same homotopy type than its medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Automating the CAD/CAE dimensional reduction process
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Representation and Self-Similarity of Shapes
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Multiscale Medial Loci and Their Properties
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
Recognition of Shapes by Editing Their Shock Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stability and Finiteness Properties of Medial Axis and Skeleton
Journal of Dynamical and Control Systems
Determining the Geometry of Boundaries of Objects from Medial Data
International Journal of Computer Vision
Canonical Skeletons for Shape Matching
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 02
Medial axis based solid representation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Shape and topology optimization of compliant mechanisms using a parameterization level set method
Journal of Computational Physics
Strategies for shape matching using skeletons
Computer Vision and Image Understanding
Gray skeletons and segmentation of shapes
Computer Vision and Image Understanding
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
Eigenmodes of surface energies for shape analysis
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
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The popularity of medial axis in shape modeling and analysis comes from several of its well known fundamental properties. For example, medial axis captures the connectivity of the domain, has a lower dimension than the space itself, and is closely related to the distance function constructed over the same domain. We propose the new concept of a medial zone of an n-dimensional semi-analytic domain @W that subsumes the medial axis MA(@W) of the same domain as a special case, and can be thought of as a 'thick' skeleton having the same dimension as that of @W. We show that by transforming the exact, non-differentiable, distance function of domain @W into approximate but differentiable distance functions, and by controlling the geodesic distance to the crests of the approximate distance functions of domain @W, one obtains families of medial zones of @W that are homeomorphic to the domain and are supersets of MA(@W). We present a set of natural properties for the medial zones MZ(@W) of @W and discuss practical approaches to compute both medial axes and medial zones for 3-dimensional semi-analytic sets with rigid or evolving boundaries. Due to the fact that the medial zones fuse some of the critical geometric and topological properties of both the domain itself and of its medial axis, re-formulating problems in terms of medial zones affords the 'best of both worlds' in applications such as geometric reasoning, robotic and autonomous navigation, and design automation.