In this paper, we present a new approach to scale-space which is derived from the 3D Laplace equation instead of the heat equation. The resulting lowpass and bandpass filters are discussed and they are related to the monogenic signal. As an application, we present a scale adaptive filtering which is used for denoising images. The adaptivity is based on the local energy of spherical quadrature f...

In this article, the Tobit Kalman filtering problem is investigated for a class of discrete time-varying fractional-order systems in presence measurement censoring and stochastic nonlinearities under Round-Robin protocol (RRP). The dynamic model described by Grunwald–Letnikov difference equation, statistical means are utilized to characterize that include state-dependent disturbances as special...

Exploratory projection pursuit is a method for finding interesting projections of highdimensional multivariate data sets. Typically interesting projections are found by numerically optimizing a measure of non-normality over projection direction. In general, explicit computation of a projection index is impossible although for certain restricted situations an index may be computed analytically. ...

Projection pursuit learning networks (PPLNs) have been used in many elds of research but have not been widely used in image processing. In this paper we demonstrate how this highly promising technique may be used to connect edges and produce continuous boundaries. We also propose the application of PPLN to deblurring a degraded image when little or no apriori information about the blur is avail...

Learning from data with complex non-local relations and multimodal class distribution for widely used classification algorithms is still very hard. Even if accurate solution is found the resulting model may be too complex for a given data and will not generalize well. New types of learning algorithms are needed to extend capabilities of standard machine learning systems. Projection pursuit meth...

Evoked response potentials (ERPs) to brief flashes of light were analyzed for constituent features that could be used to distinguish individuals with Alzheimer's disease (AD, n = 15) from matched control subjects (n = 17). Statistical k nearest-neighbor methods distinguished AD from control with a maximum sensitivity of 29% and false alarm rate of 12%. The comparable sensitivity/false-alarm val...

Different algorithms for principal component analysis (PCA) based on the idea of projection pursuit are proposed. We show how the algorithms are constructed, and compare the new algorithms with standard algorithms. With the R implementation pcaPP we demonstrate the usefulness at real data examples. Finally, it will be outlined how the algorithms can be used for robustifying other multivariate m...

Projection pursuit was originally introduced to identify structures in multivariate data clouds (Huber, 1985). The idea of projecting data to a lowdimensional subspace can also be applied to multivariate statistical methods. The robustness of the methods can be achieved by applying robust estimators to the lower-dimensional space. Robust estimation in high dimensions can thus be avoided which u...

Consider a de ned density on a set of very large dimension. It is quite di cult to nd an estimate of this density from a data set. However, it is possible through a projection pursuit methodology to solve this problem. In his seminal article, Huber (see "Projection pursuit", Annals of Statistics, 1985) demonstrates the interest of his method in a very simple given case. He considers the factori...