In this paper, we propose a new approach to the problem of degree reduction of Bézier curves based on the given endpoint constraints. A differential term is added for the purpose of controlling the smoothness to a certain extent. Considering the adjustment of second derivative in curve design, a modified objective function including two parts is constructed here. One part is a kind of measure o...

This paper presents a method to selectively elevate the degree of an S-Patch of arbitrary dimension. We consider not only S-Patches with 2D domains but 3D and higher-dimensional domains as well, of which volumetric cage deformations are a subset. We show how to selectively insert control points of a higher degree patch into a lower degree patch while maintaining the polynomial reproduction orde...

Traditionally schematized maps make extensive use of curves. However, automated methods for schematization are mostly restricted to straight lines. We present a generic framework for topology-preserving curved schematization that allows a choice of quality measures and curve types. Our fully-automated approach does not need critical points or salient features. We illustrate our framework with B...

Article history: Received 21 May 2009 Received in revised form 25 June 2010 Accepted 22 August 2010 Available online 16 September 2010

In this paper, we present our approach of face and lip detection, lip modeling, and tracking. A new lip model based on Bézier Curves is used to capture the dynamics of the lips efficiently. The model is defined only through few points which are modeled using the Active Shape Model (ASM). Accurate detection of lip details is implemented using multiple independent feature templates. The method de...

[AinAD11] Bernstein-Bézier finite elements of arbitrary order and optimal assembly procedures, SIAM J. Scient.

We present a model for the lips using the Active Shape Model (ASM) based on Bézier Curves which can capture the dynamics of the lips efficiently. The curves are defined only by a few points that can be used as visual speech features. Using some measured feature points, we can recover the full model of the lips especially for those features which are difficult to be detected. Accurate detection ...