Given a large set of irregularly spaced points in the plane, an algorithm for partitioning the points into subsets and fitting a parametric curve to each subset is described. The points could be measurements from a physical phenomenon, and the objective in this process could be to find patterns among the points and describe the phenomenon analytically. The points could be measurements from a ge...

We consider an n-ary random Boolean function f such that Pr[f(α̃) = 1] = p for α̃ ∈ {0, 1} and study its geometric model, the so called interval graph. The interval graph of a Boolean function was introduced by Sapozhenko and has been used in construction of schemes realizing Boolean functions. Using this model, we estimate the number of maximal intervals intersecting a given maximal interval of ...

We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives rise to a complex valued geometry consistent with both the hyperbolic and de Sitter space. Such a construction shed a light and inspires a new insight for the ...

Multiresolution analysis has received considerable attention in recent years by researchers in the fields of computer graphics, geometric modeling and visualization. They are now considered a powerful tool for efficiently representing functions at multiple levels-of-detail with many inherent advantages, including compression, Level-Of-Details (LOD) display, progressive transmission and LOD edit...

Determining point-to-point correspondence in multiple images is a complex problem because of the multiple geometric and photometric transformations and/or occlusions that the same point can undergo in corresponding images. This paper presents a method of pointto-point correspondence analysis based on the combination of two techniques: (1) correspondence analysis through similarity of invariant ...

The social context of an agent can have a profound influence upon their decisions and actions, where their attitudes and ideologies frequently change the interpretation given to a specific body of knowledge. However, attitudes and ideologies themselves result from groups of agents as they communicate and respond to information. This paper proposes a geometric model of an agent in context, where...

Bensmail, Celeux, Raftery and Robert (1997) introduced a new approach to cluster analysis based on geometric modeling based on the within-group covariance in a mixture of multivariate normal distributions using a fully Bayesian framework. This is a model-based methodology, where the covariance matrix structure is involved. Previously, similar structures were used (using a maximum likelihood app...

In this paper, we present a new geometry compression technique particularly suitable for 3D mesh models of engineering class – architectural models, machine plants, factories, etc. We observe that such models have a number of repeating features at various levels of granularity. In most of the widely available models in this class, the geometric description of such features are also repeated. A ...

Birds flying across a region containing a windfarm risk death from turbine encounters. This paper describes a geometric model that helps estimate that risk and a spreadsheet that implements the model.

Texture mapping on scanned objects, that is, the method to map current color images on a 3D geometric model measured by a range sensor, is a key technique of photometric modeling for virtual reality. Usually range and color images are obtained from different viewing positions, through two independent range and color sensors. Thus, in order to map those color images on the geometric model, it is...