In this paper, we propose and validate a computationally efficient non-iterative domain decomposition procedure for calculating bivariate cubic L1 smoothing splines. This domain decomposition procedure involves calculating local L1 smoothing splines individually on overlapping “extended subdomains” that cover the global domain and then creating the global L1 smoothing spline by patching togethe...

The traditional fuzzy C-means(FCM) algorithm is an optimization algorithm based on gradient descending, it is sensitive to the initial condition and liable to be trapped in a local optimum. Search space smoothing allows a local search heuristics to escape from a poor, local optimum. In this paper, an improved FCM algorithm based on search space smoothing is proposed. By designing a proper smoot...

An approach to multi-dimensional smoothing is introduced which is based on a penalized with a modified The choice of penalty stanaard multi-dim~nsiQnal.Lapladan SQ11aI'e errQrcharacteristics at-least on the interior of hyper-rectangular~omains, which has wide restorationproblems,computar tions are carried out using fast Fourier transforms. Non-linear smoothing is accomplished by iterative appli...

In models using categorical data one may use adjacency relations to justify smoothing to improve upon simple histogram approximations of the probabilities. This is particularly convenient for sparsely observed or rather peaked distributions. Moreover, in a few models, prior knowledge of a marginal distribution is available. We adapt local polynomial estimators to include this partial informatio...

Minimizing a nonlinear functional is presented as a way of obtaining a planar mapping that matches two similar images. A smoothing term is added to the nonlinear functional to penalize discontinuous and irregular solutions. One option for the smoothing term is a quadratic form generated by a linear differential operator. The functional is then minimized using the Fourier representation of the p...

Nonparametric regression techniques such as spline smoothing and local tting depend implicitly on a parametric model. For instance, the cubic smoothing spline estimate of a regression function based on observations ti; Yi is the minimizer of P(Yi (ti))2 + R ( 00)2. Since R ( 00)2 is zero when is a line, the cubic smoothing spline estimate favors the parametric model (t) = 0+ 1t: Here we conside...

facial expressions are the most powerful and direct means of presenting human emotions and feelings and offer a window into a persons’ state of mind. in recent years, the study of facial expression and recognition has gained prominence; as industry and services are keen on expanding on the potential advantages of facial recognition technology. as machine vision and artificial intelligence advan...

In this paper, a primal-dual algorithm for total bounded variation (TV)–type image restoration is analyzed and tested. Analytically it turns out that employing a global Lregularization, with 1 < s ≤ 2, in the dual problem results in a local smoothing of the TVregularization term in the primal problem. The local smoothing can alternatively be obtained as the infimal convolution of the r-norm, wi...