Hybridization in Digital Geometry

Digital Geometry and Khalimsky Spaces

Melin, E. 2008. Digital Geometry and Khalimsky Spaces (Digital geometri och Khalimskyrum). Uppsala Dissertations in Mathematics 54. vii+47 pp. Uppsala. ISBN 978-91-506-1983-6 Digital geometry is the geometry of digital images. Compared to Euclid’s geometry, which has been studied for more than two thousand years, this field is very young. Efim Khalimsky’s topology on the integers, invented in t...

Generalised Triangular Grids in Digital Geometry

The hexagonal and the triangular grids are duals of each other. These two grids are the first and second ones in the family of triangular grids (we can call them as oneand two-planes triangular grids). This family comes from the mapping their points to Z3. Their symmetric properties are triangular. The next grid is the three-planes triangular grid, which looks like the mix of them. In this pape...

Integral Based Curvature Estimators in Digital Geometry

In many geometry processing applications, the estimation of differential geometric quantities such as curvature or normal vector field is an essential step. In this paper, we investigate a new class of estimators on digital shape boundaries based on Integral Invariants. More precisely, we provide both proofs of multigrid convergence of curvature estimators and a complete experimental evaluation...

Collaborating with an Artist in Digital Geometry

In this invited paper, we are going to present an ongoing collaboration with a local artist, Aurélie Mourier. The artist works with voxel shapes and this led our digital geometry team to develop new shape modeling tools and explore a particular class of unfolding problems.

Digital geometry - geometric methods for digital picture analysis