vVe discuss procedures based on non parametric regression for estimating the dominant Lyapunov exponent Al from time-series data generated by a system xt =f(xt _l' x t _2' ... xt_d)+o-et , where XtEIR, and {et } is an iid sequence of random variables. For systems with bounded fluctuations in x t ' '\1 >0 is the defining feature of chaos. vVe show that any consistent estimator of the partial of/...

In this paper, we propose a novel technique to address motion estimation and tracking. Such technique represents the motion field using a regular grid of thin-plate splines, and the moving objects using an implicit function on the image plane that is a cubic interpolation of a ”level set function” defined on this grid. Optical flow is determined through the deformation of the grid and consequen...

A common motif in the expositions of spline-based methods in statistical smoothing or numerical interpolation is an allusion to mechanical analogies—motivated perhaps by a desire to provide some explanation why the resulting shapes ought to be regarded as “natural”. The univariate case has its Oxford English Dictionary reference to draftsman spline as “a flexible strip of wood or hard rubber us...

This paper attempts to solve a basic problem in distributed statistical inference: how many machines can we use in parallel computing? In kernel ridge regression, we address this question in two important settings: nonparametric estimation and hypothesis testing. Specifically, we find a range for the number of machines under which optimal estimation/testing is achievable. The employed empirical...

In the last years the need to numerically define color by its coordinates in n-dimensional space has increased strongly. Colorimetric calibration is fundamental in food processing and other biological disciplines to quantitatively compare samples' color during workflow with many devices. Several software programmes are available to perform standardized colorimetric procedures, but they are ofte...

Autism is a severe developmental disorder whose neurological basis is largely unknown. The aim of this study was to identify the shape differences of the corpus callosum between patients with autism and control subjects. Anatomical landmarks were collected from midsagittal magnetic resonance images of 25 patients and 18 controls. Euclidean distance matrix analysis and thin-plate spline analyses...

Morphometrics, a new branch of statistics, combines tools from geometry, computer graphics and biometrics in techniques for the multivariate analysis of biological shape variation. Although medical image analysts typically prefer to represent scenes by way of curving outlines or surfaces, the most recent developments in this associated statistical methodology have emphasized the domain of landm...

Craniofacial registration is used to establish the point-to-point correspondence in a unified coordinate system among human craniofacial models. It is the foundation of craniofacial reconstruction and other craniofacial statistical analysis research. In this paper, a non-rigid 3D craniofacial registration method using thin-plate spline transform and cylindrical surface projection is proposed. F...