Search results for "Medial axis"
showing 8 items of 8 documents
An Alternative to Medial Axis for the 3D Reconstruction of Unorganized Set of Points Using Implicit Surfaces
2006
Rebuilding three-dimensional objects represented by a set of points is a classical problem in computer graphics. Multiple applications like medical imaging or industrial techniques require finding shape from scattered data. Therefore, the reconstruction of a set of points that represents a shape has been widely studied, depending on data source and reconstruction's objectives. This purpose of this paper is to provide an automatic reconstruction from an unorganized cloud describing an unknown shape in order to provide a solution that will allow to compute the object's volume and to deform it with constant volume. The main idea in this paper consists in filling the object's interior with an e…
Topology guaranteeing manifold reconstruction using distance function to noisy data
2006
Given a smooth compact codimension one submanifold S of Rk and a compact approximation K of S, we prove that it is possible to reconstruct S and to approximate the medial axis of S with topological guarantees using unions of balls centered on K. We consider two notions of noisy-approximation that generalize sampling conditions introduced by Amenta & al. and Dey & al. Our results are based upon critical point theory for distance functions. For the two approximation conditions, we prove that the connected components of the boundary of unions of balls centered on K are isotopic to S. Our results allow to consider balls of different radii. For the first approximation condition, we also prove th…
Soft Computing and Image Analysis
2000
The paper describes a soft approach to solve image analysis problems. Theory of fuzzy-sets has been used to implement most of the algorithms described in the paper. Soft approaches can be useful to extend mathematical morphology operators on gray level images and to describe the shape of dotted objects. Examples on real data are also provided.
The “λ-medial axis”
2005
Medial axis is known to be unstable for nonsmooth objects. For an open set O, we define the weak feature size, wfs, minimum distance between Oc and the critical points of the function distance to Oc. We introduce the "lambda-medial axis" Mλ of O, a subset of the medial axis of O which captures the homotopy type of O when λ < wfs. We show that, at least for some "regular" values of λ, Mλ remains stable under Hausdorff distance perturbations of Oc.
Stability and Finiteness Properties of Medial Axis and Skeleton
2004
The medial axis is a geometric object associated with any bounded open set in \Bbb R^n which has various applications in computer science. We study it from a mathematical point of view. We give some results about its geometrical structure when the open set is subanalytic and we prove that it is stable under C2-perturbations when the open set is bounded by a hypersurface with positive local feature size.
Real and Complex Singularities
2016
In this paper a Minkowski analogue of the Euclidean medial axis of a closed and smooth plane curve is introduced. Its generic local configurations are studied and the types of shocks that occur on these are also determined.
Compression of binary images based on covering
1995
The paper describes a new technique to compress binary images based on an image covering algorithm. The idea is that binary images can be always covered by rectangles, univocally described by a vertex and two adjacent edges (L-shape). Some optimisations are necessary to consider degenerate configurations. The method has been tested on several images representing drawings and typed texts. The comparison with existing image file compression techniques shows a good performance of our approach. Further optimisations are under development.
Skeleton-Based Multiview Reconstruction
2016
International audience; The advantage of skeleton-based 3D reconstruction is to completely generate a single 3D object from well chosen views. Having numerous views is necessary for a reliable reconstruction but projections of skeletons lead to different topologies. We reconstruct 3D objects with curved medial axis (whose topology is a tree) from the perspective skeletons on an arbitrary number of calibrated acquisitions. The main contribution is to estimate the 3D skeleton, from multiple images: its topology is chosen as the closest to those of the perspective skeletons on the set of images, which means that the number of topology changes to map the 3D skeleton topology to topologies on im…