1,262 research outputs found
Subset Warping: Rubber Sheeting with Cuts
Image warping, often referred to as "rubber sheeting" represents the deformation of a domain image space into a range image space. In this paper, a technique is described which extends the definition of a rubber-sheet transformation to allow a polygonal region to be warped into one or more subsets of itself, where the subsets may be multiply connected. To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities in the range image, using a technique based on generalized Voronoi diagrams. The concept of medial axis is extended to describe inner and outer medial contours of a polygon. Polygonal regions are decomposed into annular subregions, and path homotopies are introduced to describe the annular subregions. These constructions motivate the definition of a ladder, which guides the construction of grid point pairs necessary to effect the warp itself
The divider set of explicit parametric geometry
In this paper we describe a novel concept for classification
of complex parametric geometry based on the concept
of the Divider Set. The Divider Set is an alternative concept
to maximal disks, Voronoi sets and cut loci. The Divider
Set is based on a formal definition relating to topology
and differential geometry. In this paper firstly we discuss
the formal definition of the Divider Set for complex
3-dimensional geometry. This is then followed by the introduction
of a computationally feasible algorithm for computing
the Divider Set for geometry which can be defined
in explicit parametric form. Thus, an explicit solution form
taking advantage of the special form of the parametric geometry
is presented. We also show how the Divider Set can
be computed for various complex parametric geometry by
means of illustrating our concept through a number of example
An Unified Multiscale Framework for Planar, Surface, and Curve Skeletonization
Computing skeletons of 2D shapes, and medial surface and curve skeletons of 3D shapes, is a challenging task. In particular, there is no unified framework that detects all types of skeletons using a single model, and also produces a multiscale representation which allows to progressively simplify, or regularize, all skeleton types. In this paper, we present such a framework. We model skeleton detection and regularization by a conservative mass transport process from a shape's boundary to its surface skeleton, next to its curve skeleton, and finally to the shape center. The resulting density field can be thresholded to obtain a multiscale representation of progressively simplified surface, or curve, skeletons. We detail a numerical implementation of our framework which is demonstrably stable and has high computational efficiency. We demonstrate our framework on several complex 2D and 3D shapes
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