In this paper we propose a smoothing method for non smooth signals, which control the geometry of a sampled signal. The signal is considered as a geometric object and the smoothing is done using a smoothing kernel function that controls the curvature of the obtained smooth signal in a close neighborhood of a metric curvature measure of the original signal.

The paper evaluates the properties of nonparametric estimators of the expected shortfall, an increasingly popular risk measure in financial risk management. It is found that the existing kernel estimator based on a single bandwidth does not offer variance reduction, which is surprising considering that kernel smoothing reduces the variance of estimators for the value at risk and the distributio...

A new potential smoothing method, the shifted-tophat (or stophat) is presented. This method uses a tophat function as the smoothing kernel, instead of the gaussian used in conventional methods. Stophat smoothing is applied, as part of the Potential Smoothing and Search (PSS) procedure for global optimization, to several biomolecular problems, including polyalanine helices, united-atom and all-a...

Multi-view stereo reconstruction techniques yield inherently multi-scale point data typically fed into surface reconstruction algorithms. Following the intuition of scale space we assume that sample points originate from smoothed versions of the original surface. The smoothing can be characterized by a smoothing kernel that suppresses fine-scale structures. In this paper, we propose a surface r...

It has been known even since relatively few structures had been solved that longer protein chains often contain multiple domains, which may fold separately and play the role of reusable functional modules found in many contexts. In many structural biology tasks, in particular structure prediction, it is of great use to be able to identify domains within the structure and analyze these regions s...

We present a novel data smoothing and analysis framework for cortical thickness data defined on the brain cortical manifold. Gaussian kernel smoothing, which weights neighboring observations according to their 3D Euclidean distance, has been widely used in 3D brain images to increase the signal-to-noise ratio. When the observations lie on a convoluted brain surface, however, it is more natural ...

Statistical data contains noise. Smoothing is used to smooth out these noises and present the data as a meaningful one. Kernel methods are nonparametric smoothing tools that can reveal structural features in the data which may not be possible with a parametric approach. This paper applies Epanechnikov kernel method of data smoothing to smooth out the dropout rates of the children with disabilit...

Diffusion tensor magnetic resonance imaging (DT-MRI) is a non-invasive imaging method for assessing the characteristics and organization of tissue microstructure. The diffusion tensor provides information about the magnitude, anisotropy, and orientation of water diffusion in biological tissues. In brain white matter, the direction of greatest diffusivity is typically assumed to be parallel to t...