Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Accurate and efficient unions of balls
Proceedings of the sixteenth annual symposium on Computational geometry
Proceedings of the sixth ACM symposium on Solid modeling and applications
Digital Image Processing
Image-based surface modeling: a multi-resolution approach
Signal Processing
Reconstruction with Voronoi centered radial basis functions
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
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This paper describes an innovative extension of morphological operators to the analysis and processing of three dimensional images represented by voxels. In particular, the morphological skeleton well approximates the Medial Axis of a 3D object rendered using a net of Kinect devices: it has proven to be a really effective tool to obtain a compact representation of the object surface that is accurate and very inexpensive in terms of computational time. The reconstructed surface is representable either as a union of balls or as an iso-surface of a 3D function defined as a linear combination of elementary functions with radial support. Furthermore, the representation is easily processable and hierarchically interpretable. The morphological operators neither require any prior information on the reconstructed volume, nor impose any resolution requirement on the object under analysis. The only input for morphological operators is a volume of voxels. Information on the volume nature or resolution requirements are related only to the particular application to which the morphological operators are applied, but do not limit the applicability of any of the proposed morphological operators.