21 research outputs found
On the spine of a PDE surface
yesThe spine of an object is an entity that can characterise the
objectÂżs topology and describes the object by a lower dimension. It has
an intuitive appeal for supporting geometric modelling operations.
The aim of this paper is to show how a spine for a PDE surface can
be generated. For the purpose of the work presented here an analytic
solution form for the chosen PDE is utilised. It is shown that the spine
of the PDE surface is then computed as a by-product of this analytic
solution.
This paper also discusses how the of a PDE surface can be used to manipulate
the shape. The solution technique adopted here caters for periodic
surfaces with general boundary conditions allowing the possibility of the
spine based shape manipulation for a wide variety of free-form PDE surface
shapes
The simplified solution procedure for the EOQ model under cash discount and trade credit
Directional 3D thinning using 8 subiterations
Thinning of a binary object is an iterative layer by layer erosion to extract an approximation to its skeleton. In order to provide topology preservation, different thinning techniques have been proposed. One of them is the directional (or border sequential) approach in which each iteration step is subdivided into subiterations where only border points of certain kind are deleted in each subiteration. There are six kinds of border points in 3D images, therefore, 6–subiteration parallel thinning algorithms were generally proposed. In this paper, we present two 8–subiteration algorithms for extracting “surface skeletons” and “curve skeletons”, respectively. Both algorithms work in cubic grid for (26,6) images. Deletable points are given by templates that makes easy implementation possible
Fully parallel 3D thinning algorithms based on sufficient conditions for topology preservation
This paper presents a family of parallel thinning algorithms for extracting medial surfaces from 3D binary pictures. The proposed algorithms are based on sufficient conditions for 3D parallel reduction operators to preserve topology for (26, 6) pictures. Hence it is self-evident that our algorithms are topology preserving. Their efficient implementation on conventional sequential computers is also presented
A Discrete Homotopic Deformable Model Dealing with Objects with Different Local Dimensions
3D Parallel Thinning Algorithms Based on Isthmuses
Abstract. Thinning is a widely used technique to obtain skeleton-like shape features (i.e., centerlines and medial surfaces) from digital binary objects. Conventional thinning algorithms preserve endpoints to provide important geometric information relative to the object to be represented. An alternative strategy is also proposed that preserves isthmuses (i.e., generalization of curve/surface interior points). In this paper we present ten 3D parallel isthmus-based thinning algorithm variants that are derived from some sufficient conditions for topology preserving reductions