
...classical digital geometry deals with sets of cubical voxels (or square pixels) that can sharefaces, edges, or vertices; but basic parts of digital geometry can be generalized to sets s ofconvex voxels (or pixels) that can have...

...the paper presents a new set of axioms of digital topology, which are easily
understandable for application developers. they define a class of locally
finite (lf) topological spaces. an important property of lf spaces satisfying
the axioms is that the neighborhood relation is antisymmetric and...

...image analysis. early work in the preservation of an object’s
topology to brain imaging involved generating digital reconstructions of the cerebral cortex, which is known...in this chapter, we present the core principles of digital topology and describe their
use in several fundamental tools for topologypreserving image analysis. we further...

...the paper presents a new set of axioms of digital topology, which are easily understandable for application developers. they define a class of locally finite (lf) topological spaces. an important property of lf spaces satisfying the axioms is that the neighborhood relation is antisymmetric and...
Published in 2010.

...is usually modeled either by the set of points of a discrete grid, or by the set of ncells in a convex cell complex whose union isrn...on very general axiomatic definitions of “wellbehaved digital spaces”. this approach gives the possibility of stating and proving results of digital topology as single theorems which apply...

...is usually modeled either by the set of points of a discrete grid, or by the set of ncells in a convex cell complex whose union is...on very general axiomatic definitions of “wellbehaved digital spaces.” this approach gives the possibility of stating and proving results of digital topology as single theorems which apply...

...moreover, we will show that the surface of the original object is homeomorphic to the result of the marching cubes algorithm. this is...construct a smooth isosurface from the digital image that has the same topology as the original surface. finally we give a surprisingly simple topology preserving reconstruction method by using...

...moreover, we will show that the surface of the original object is homeomorphic to the result of the marching cubes algorithm. this is...construct a smooth isosurface from the digital image that has the same topology as the original surface. finally, we give a surprisingly simple topology preserving reconstruction method by using...

...ko valevsky as a means of solving certain connectivity paradoxes in graph
theoretic digital topology,and to this extent provide an improved the oretical basis for image analysis...are a very nat ural setting for digital convexity,to the extent that their use permits simple,almost trivial formulations
of major convexity results such as caratheodory’s, helly’s...

...object, as it is in the case of curves and hypersurfaces,in the euclidean space. relying on the obtained,properties of digital hypersurfaces, we propose a uniform...we also discuss possible applications of the presented definitions and results. index terms digital geometry, digital topology, discrete dimension, digital manifold, digital curve, digital hypersurface, good pair....