Ternary shape-preserving subdivision schemes

We analyze the shape-preserving properties of ternary subdivision schemes generated by bell-shaped masks. We prove that any bell-shaped mask, satisfying the basic sum rules, gives rise to a convergent monotonicity preserving subdivision scheme, but convexity preservation is not guaranteed. We show that to reach convexity preservation the first order divided difference scheme needs to be bell-shaped, too. Finally, we show that ternary subdivision schemes associated with certain refinable functions with dilation 3 have shape-preserving properties of higher order

Polynomial cubic splines with tension properties

In this paper we present a new class of spline functions with tension properties. These splines are composed by polynomial cubic pieces and therefore are conformal to the standard, NURBS based CAD/CAM systems

Information hiding through variance of the parametric orientation underlying a B-rep face

Watermarking technologies have been proposed for many different,types of digital media. However, to this date, no viable watermarking techniques have yet emerged for the high value B-rep (i.e. Boundary Representation) models used in 3D mechanical CAD systems. In this paper, the authors propose a new approach (PO-Watermarking) that subtly changes a model's geometric representation to incorporate a 'transparent' signature. This scheme enables software applications to create fragile, or robust watermarks without changing the size of the file, or shape of the CAD model. Also discussed is the amount of information the proposed method could transparently embed into a B-rep model. The results presented demonstrate the embedding and retrieval of text strings and investigate the robustness of the approach after a variety of transformation and modifications have been carried out on the data

Data-driven quasi-interpolant spline surfaces for point cloud approximation

In this paper we investigate a local surface approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), specifically designed for large and noisy point clouds. We briefly describe the properties of the wQISA representation and introduce a novel data-driven implementation, which combines prediction capability and complexity efficiency. We provide an extended comparative analysis with other continuous approximations on real data, including different types of surfaces and levels of noise, such as 3D models, terrain data and digital environmental data

Monotonicity preserving approximation of multivariate scattered data

This paper describes a new method of monotone interpolation and smoothing of multivariate scattered data. It is based on the assumption that the function to be approximated is Lipschitz continuous. The method provides the optimal approximation in the worst case scenario and tight error bounds. Smoothing of noisy data subject to monotonicity constraints is converted into a quadratic programming problem. Estimation of the unknown Lipschitz constant from the data by sample splitting and cross-validation is described. Extension of the method for locally Lipschitz functions is presented.<br /

On the Assessment of Stability and Patterning of Speech Movements

Speech requires the control of complex movements of orofacial structures to produce dynamic variations in the vocal tract transfer function. The nature of the underlying motor control processes has traditionally been investigated by employing measures of articulatory movements, including movement amplitude, velocity, and duration, at selected points in time. An alternative approach, first used in the study of limb motion, is to examine the entire movement trajectory over time. A new approach to speech movement trajectory analysis was introduced in earlier work from this laboratory. In this method, trajectories from multiple movement sequences are time- and amplitude-normalized, and the STI (spatiotemporal index) is computed to capture the degree of convergence of a set of trajectories onto a single, underlying movement template. This research note describes the rationale for this analysis and provides a detailed description of the signal processing involved. Alternative interpolation procedures for time-normalization of kinematic data are also considered