Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Continuous skeleton computation by Voronoi diagram
CVGIP: Image Understanding
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Generating skeletons and centerlines from the distance transform
CVGIP: Graphical Models and Image Processing
Triangulating topological spaces
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Convergence and continuity criteria for discrete approximations of the continuous planar skeleton
CVGIP: Image Understanding
Automatic reconstruction of surfaces and scalar fields from 3D scans
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Piecewise-linear interpolation between polygonal slices
Computer Vision and Image Understanding
Approximating polyhedra with spheres for time-critical collision detection
ACM Transactions on Graphics (TOG)
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Arbitrary topology shape reconstruction from planar cross sections
Graphical Models and Image Processing
Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
Skeleton-based modeling operations on solids
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Assisted articulation of closed polygonal models
ACM SIGGRAPH 98 Conference abstracts and applications
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Proceedings of the sixth ACM symposium on Solid modeling and applications
Detecting undersampling in surface reconstruction
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
Shape Description By Medial Surface Construction
IEEE Transactions on Visualization and Computer Graphics
Shape Reconstruction with Delaunay Complex
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Approximating the Medial Axis from the Voronoi Diagram with a Convergence Guarantee
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Free-form skeleton-driven mesh deformations
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
A Formal Classification of 3D Medial Axis Points and Their Local Geometry
IEEE Transactions on Pattern Analysis and Machine Intelligence
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Shape Simplification Based on the Medial Axis Transform
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Graphical Models
Simultaneous shape decomposition and skeletonization
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Skeleton based solid representation with topology preservation
Graphical Models - Special issue on SPM 05
Efficient and robust computation of an approximated medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Medial axis extraction and shape manipulation of solid objects using parabolic PDEs
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Medial axis based solid representation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
An effective condition for sampling surfaces with guarantees
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Stability and homotopy of a subset of the medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Computing a family of skeletons of volumetric models for shape description
Computer-Aided Design
The voronoi diagram of three lines
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Topology Repair of Solid Models Using Skeletons
IEEE Transactions on Visualization and Computer Graphics
Approximating the pathway axis and the persistence diagram of a collection of balls in 3-space
Proceedings of the twenty-fourth annual symposium on Computational geometry
3D reconstruction of large tubular geometries from CT data
IS4TM'03 Proceedings of the 2003 international conference on Surgery simulation and soft tissue modeling
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
Graph-based representations of point clouds
Graphical Models
Extended grassfire transform on medial axes of 2D shapes
Computer-Aided Design
Computing a family of skeletons of volumetric models for shape description
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Non-manifold medial surface reconstruction from volumetric data
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Research on 3D medial axis transform via the saddle point programming method
Computer-Aided Design
Polygonization of volumetric skeletons with junctions
Computer-Aided Design
Skeletal representations of orthogonal shapes
Graphical Models
Intensity-Based Skeletonization of CryoEM Gray-Scale Images Using a True Segmentation-Free Algorithm
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Medial axis as a compact representation of shapes has evolved as an essential geometric structure in a number of applications involving 3D geometric shapes. Since exact computation of the medial axis is difficult in general, efforts continue to approximate them. One line of research considers the point cloud representation of the boundary surface of a solid and then attempts to compute an approximate medial axis from this point sample. It is known that the Voronoi vertices converge to the medial axis for a curve in 2D as the sample density approaches infinity. Unfortunately, the same is not true in 3D. Recently, it is discovered that a subset of Voronoi vertices called poles converge to the medial axis in 3D. However, in practice, a continuous approximation as opposed to a discrete one is sought. Recently few algorithms have been proposed which use the Voronoi diagram and its derivatives to compute this continuous approximation. These algorithms are scale or density dependent. Most of them do not have convergence guarantees, and one of them computes it indirectly from the power diagram of the poles. In this paper we present a new algorithm that approximates the medial axis straight from the Voronoi diagram in a scale and density independent manner with convergence guarantees. The advantage is that, unlike for others, one does not need to fine tune any parameter for this algorithm. We present extensive experimental evidences in support of our claims.