Principal curves are smooth curves that minimize the average squared orthogonal distance to each point in a data set. Fitting a principal curve is a maximum-likelihood technique for nonlinear regression in the presence of Gaussian noise on both x and y. We choose two definitions of principal curves in the literature and then present experimental results to discuss over them.

Background Residual background phase in cardiac phase-contrast (PC) imaging introduces velocity errors that bias quantitative flow measurements [1]. While the bias can be offset using static phantoms [2], improved workflow is realized if self-calibrated correction is performed by fitting the phase of static tissue from the in vivo images. However, the residual phase can be nonlinear in space an...

In a recent paper we showed that the electroweak chiral Lagrangian at leading order is equivalent to the conventional [Formula: see text] formalism used by ATLAS and CMS to test Higgs anomalous couplings. Here we apply this fact to fit the latest Higgs data. The new aspect of our analysis is a systematic interpretation of the fit parameters within an EFT. Concentrating on the processes of Higgs...

Deep nonlinear models pose a challenge for fitting parameters due to lack of knowledge of the hidden layer and the potentially non-affine relation of the initial and observed layers. In the present work we investigate the use of information theoretic measures such as mutual information and Kullback-Leibler (KL) divergence as objective functions for fitting such models without knowledge of the h...

Multi-tracer positron emission tomography (PET) can image two or more tracers in a single scan, characterizing multiple aspects of biological functions to provide new insights into many diseases. The technique uses dynamic imaging, resulting in time-activity curves that contain contributions from each tracer present. The process of separating and recovering separate images and/or imaging measur...

This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a...