Asymptote is widely used in astronomy, mechanics, architecture and relevant subjects. In this paper, by analyzing the Frenet frame and the Darboux frame of a curve on the surface, the necessary and sufficient conditions for a quadrilateral boundary being asymptotic of a surface are derived. This quadrilateral is called asymptotic quadrilateral. Given corner data including positions, tangents an...

Image-based change quantitation has been recognized as a promising tool for accurate assessment of tumor's early response to chemoprevention in cancer research. For example, various changes on breast density and vascularity in glandular tissue are the indicators of early response to treatment. Accurate extraction of glandular tissue from pre- and postcontrast magnetic resonance (MR) images requ...

We extend Schoenberg’s family of polynomial splines with uniform knots to all fractional degrees α > −1. These splines, which involve linear combinations of the one-sided power functions x+ = max(0, x) α, are α-Hölder continuous for α > 0. We construct the corresponding B-splines by taking fractional finite differences and provide an explicit characterization in both time and frequency domains....

Bayesian hierarchical models have been used for smoothing splines, thin-plate splines, and L-splines. In analyzing high dimensional data sets, additive models and backfitting methods are often used. A full Bayesian analysis for such models may include a large number of random effects, many of which are not intuitive, so researchers typically use noninformative improper or nearly improper priors...

Nonrigid registration of 3D tomographic images of di erent modalities (e.g., CT and MR images) is a key issue for neurosurgery and radiotherapy planning. Here, we consider image registration based on a set of corresponding anatomical point landmarks and approximating thin-plate splines. With this approach it is possible to take into account landmark localization errors and thus to control the i...