Browse Proceedings

The main objective in content-based image retrieval is to find images similar to a query image in an image collection. Matching using descriptors computed from regions centered at local invariant interest points (key points) have become popular because ...

We show how to localize the Delaunay triangulation of a given planar point set, namely, bound the set of points which are possible Delaunay neighbors of a given point. We then exploit this observation in an algorithm for constructing the Delaunay ...

We have previously established delicate connections between the Voronoi diagram of polynomial roots and their basins of attraction with respect to the Basic Family of iteration functions. We have also previously defined polynomiography, visualization ...

In order to enjoy a digital version of the Jordan Curve Theorem, it is common to use the closed topology for the foreground and the open topology for the background of a 2-dimensional binary image. In this paper, we introduce a single topology that ...

We present structural properties of the farthest line-segment Voronoi diagram in the piecewise linear L_infinity and L_1 metrics, which are computationally simpler than the standard Euclidean distance and very well suited for VLSI applications. We ...

Given a region $R$ in a Euclidean space and a distinguished point $p \in R$, the \emph{forbidden zone}, $F(R,p)$, is the union of all open balls with center in $R$, having $p$ as a common boundary point. For a polytope, the forbidden zone is the union ...

The nearest neighbor transform of a binary image assigns to each pixel the index of the nearest black pixel--it is the discrete analog of the Voronoi diagram. Implementations that compute the transform use numerical calculations to perform geometric ...

A ball-polyhedron is the intersection with non-empty interior of finitely many (closed) unit balls in Euclidean 3-space. A new result of this paper is a Cauchy-type rigidity theorem for ball-polyhedra. Its proof presented here is based on the underlying ...

Consider a given space, e.g., the Euclidean plane, and its decomposition into Voronoi regions induced by given sites. It seems intuitively clear that each point in the space belongs to at least one of the regions, i.e., no neutral region can exist. ...

This paper studies adaptive point location in Delaunaytriangulations with $o(n^{1/3})$ (and practically $O(1)$) preprocessing and storage. Given $n$ pseudo-random points in a compact convex set $C$ with unit area in two dimensions (2D) and the ...

We raise and investigate the following problems that one can regard as very close relatives of the densest sphere packing problem. If the Euclidean 3-space is partitioned into convex cells each containing a unit ball, how should the shapes of the cells ...

A simple formalism is proposed for a quantitative analysis of interatomic voids inside and outside of a molecule in solution. It can be applied for the interpretation of volumetric data, obtained in studies of protein folding in water. The method is ...

Continuing the investigations of Harborth (1974) and the author (2002) we study the following basic problem on sphere packings. Recall that the contact graph of an arbitrary finite packing of unit balls (i.e., of an arbitrary finite family of non-...

This paper presents a Voronoi-based algorithm to extract the medial axis through labeling sample points. A major issue of the medial axis is its inherent instability under small perturbations. The medial axis is very sensitive to small changes of the ...

Motivated by an application to nanotechnology, Voronoi diagrams on ($\ell_1$-embeddable) periodic graphs and a motion planning problem on those graphs have been investigated by Fu, Hashikura, Imai and Moriyama. In this paper, through the investigations ...

We describe the structure of the Voronoi diagram of lines for a set of points in the plane, thereby making use of an extra dimension. In contrast to previous results in this respect, which were based on the dual representation of the Voronoi diagram ...

For a given meromorphic function $g:\mathbb C\to \mathbb C$, we study the locus of points $z$ that are {\it collinear} with their two iterations $g(z)$ and $g(g(z))$. Such points form a {\it collinearity curve}. Generally, this curve is reducible: it ...

We introduce a new concept of constructing a generalized Voronoi inverse (GVI) of a given tessellation ${\cal T}$ of the plane. Our objective is to place a set $S_i$ of one or more sites in each convex region (cell) $t_i \in {\cal T}$, such that all the ...

Molecular external structure is important in understanding molecular interaction with its solvent environment and is useful in developing drugs. Important examples of external structures are tunnels, pockets, caves, clefts, voids, etc. This paper ...

We present a computational method to create a new illusionary solid sign inspired by two kinds of illusions, fighollow mask illusionfih and figcrater illusionfih. The three dimensional vertices of the illusionary solid sign are obtained by the straight line ...