This work presents a methodology for 3D modeling of lip motion in speech production and its application to lip tracking and visual speech animation. Firstly, a geometric modeling allows to create a 3D lip model from 30 control points for any lip shape. Secondly, a statistical analysis, performed on a set of 10 key shapes, generates a lip gesture coding with three articulatory-oriented parameter...

A generalization of the exponentiated Weibull geometric model called the transmuted exponentiated Weibull geometric distribution is proposed and studied. It includes as special cases at least ten models. Some of its structural properties including order statistics, explicit expressions for the ordinary and incomplete moments and generating function are derived. The estimation of the model param...

We described in [M1] a monoid b G, the face monoid, acting on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid whose unit group is a Kac-Moody group G. We found in [M5] two natural extensions of the action of the Kac-Moody group G on its building Ω to actions of the face monoid b G on the building Ω....

We have developed a model for representing the image of segments of blood vessels in x-ray angiograms, and a software package for generating the model from digitized angiograms. The model is based on projections of linearly tapering cylinders and is suitable for the analysis of vessel lumen position, size and shape. This is of interest for research into the disease atherosclerosis. The system h...

Modeling complex organs, such as the human heart, requires a detailed understanding of the geometric and mechanical properties of that organ. Similarly, the model is only as accurate as the precision of the underlying properties allow. Hence, it is of great importance that accurate measurements of the geometric configuration are available. This paper describes the different steps that are neces...

We present a method for recovering the structure of a plant directly from a small set of widely-spaced images for automated analysis of phenotype. Structure recovery is more complex than shape estimation, but the resulting structure estimate is more closely related to phenotype than is a 3D geometric model. The method we propose is applicable to a wide variety of plants, but is demonstrated on ...

This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties. In particular, we explain the relation between linear precision and a particular linear projection we call the algebraic moment map.

A proof of the Ending Laminations Theorem is given which uses Teichmüller geodesics directly, restricted, for simplicity to the case when the ending laminations data is a pair of minimal laminations.