In geographical epidemiology it is often required to produce a map of the risk of disease over a study region, a disease map. This paper reviews a variety of approaches to produce disease maps when individual address locations are observed. These methods vary from kernel based smoothing approaches, e.g. Nadaraya-Watson, local linear and GAMs, to Bayesian partition models. The kernel based metho...

Linear scale-space theory is the fundamental building block for many approaches to image processing like pyramids or scale-selection. However, linear smoothing does not preserve image structures very well and thus non-linear techniques are mostly applied for image enhancement. A different perspective is given in the framework of channelsmoothing, where the feature domain is not considered as a ...

49, 90]. Witkin proposed that the convolution of a signal Visual tasks often require a hierarchical representation of with a Gaussian removes small-scale features, namely, shapes and images in scales ranging from coarse to fine. A zero-crossings, while retaining the more significant ones variety of linear and nonlinear smoothing techniques, such as [88]. Koenderink showed that among the linear ...

The authors propose an algorithm for detection of three-dimensional bundaries in noisy images based on higher-order polynomial surface fitting and directional smoothing. Fitting a polynomial to the local intensities gives the intensity hypersurface. An isointensity surface i s derived from the hyperplane and directional smwthiag is defined as smoothing along this isointensjty surface. The devel...

This paper describes a new approach to low level image processing; in particular, edge and corner detection and structure preserving noise reduction. Non-linear ltering is used to deene which parts of the image are closely related to each individual pixel; each pixel has associated with it a local image region which is of similar brightness to that pixel. The new feature detectors are based on ...

Generalized additive models are useful in finding predictor-response relationships in many kinds of data without using a specific model. They combine the ability to explore many nonparametric relationships simultaneously with the distributional flexibility of generalized linear models. The approach often brings to light nonlinear dependency structures in your data. This paper discusses an examp...

Smoothing splines are one of the most popular approaches to nonparametric regression. Wahba (J. Roy. Statist. Soc. Set. B 40 (1978) 364-372; 45 (1983) 133-150) showed that smoothing splines are also Bayes estimates and used the corresponding prior model to derive interval estimates for the regression function. Although the interval estimates work well on a global basis, they can have poor local...

MSC: 35Q53 35A07 Keywords: Local well posedness Dispersive smoothing Real-analytic solutions Higher-order water-wave models a b s t r a c t Local well posedness for a class of higher-order nonlinear dispersive partial differential equations is obtained in spaces of functions analytic on a strip around the real axis. The proof relies on estimates in space–time norms adapted to the linear part of...