Abstract In this paper, we present new regularized Shannon sampling formulas which use localized with special window functions, namely Gaussian, $$\mathrm B$$ B -spline, and $$\sinh $$ sinh -type functions. contrast to the classical series, possess an exponential decay are numerically robust ...

The first order stable spline (SS-1) kernel is used extensively in regularized system identification. In particular, the stable spline estimator models the impulse response as a zero-mean Gaussian process whose covariance is given by the SS-1 kernel. In this paper, we discuss the maximum entropy properties of this prior. In particular, we formulate the exact maximum entropy problem solved by th...

The cell nucleus is a highly organized structure and plays an important role in gene regulation. Understanding the mechanisms that sustain this organization is therefore essential for understanding genome function. Centromeric regions (CRs) of chromosomes have been known for years to adopt specific nuclear positioning patterns, but the significance of this observation is not yet completely unde...

Landmark-based registration using radial basis functions (RBF) is an efficient and mathematically transparent method for the registration of medical images. To ensure invertibility and diffeomorphism of the RBF-based vector field, various regularization schemes have been suggested. Here, we report a novel analytic method of RBF regularization and demonstrate its power for Gaussian RBF. Our anal...

Image-based fluid motion estimation is of interest to science and engineering. Flow-estimation methods often rely on physics-based or spline-based parametric models, as well as on smoothing regularizers. The calculation of physics models can be involved, and commonly used 2nd-order regularizers can be biased towards lower-order flow fields. In this paper, we propose a local parametric model bas...

Bivariate and trivariate functions for interpolation from scattered data are derived. They are constructed by explicit minimization of a general smoothness functional, and they include a tension parameter that controls the character of the interpolation function (e.g., for bivariate case the surface can be tuned from a `membrane' to a `thin steel plate'). Tension can be applied also in a chosen...

1 Summary The extraction of roof edges requires the reconstruction of the original signal from a lattice of sampled values of grey level (i.e. the sampled image). This is an ill-posed task and therefore, adequate constraints of regularization have to be incorporated. A scheme employing one-dimensional Regularized Cubic B-Spline (RCBS) tting has been used successfully on the task of step edge de...

Edge detection attempts to reconstruct 3-D physical edges from a 2-D image. It is therefore an ill-posed problem, and a regularization procedure is required to convert it into a well-posed problem. This procedure introduces a regularization parameter for adjusting the extent of the regularization eeect: the larger the value of is, the stronger the regularization eeect. Therefore, could be inter...

Regularized Spline with Tension (RST) is an accurate, flexible and efficient method for multivariate interpolation of scattered data. This study evaluates its capabilities to interpolate daily and annual mean precipitation in regions with complex terrain. Tension, smoothing and anisotropy parameters are optimized using the crossvalidation technique. In addition, smoothing and rescaling of the t...