This paper presents a new approach to computation of geometric continuity for parametric bi-cubic patches, based on a simple mathematical reformulation which leads to simple additional conditions to be applied in the patching computation. The paper presents an Hermite formulation of a bicubic parametric patch, but reformulations can be made also for Bézier and B-Spline patches as well. The pres...

Polyhedral meshes consisting of triangles, quads, and pentagons and polar configurations cover all major sampling and modeling scenarios. We give an algorithm for efficient local, parallel conversion of such meshes to an everywhere smooth surface consisting of low-degree polynomial pieces. Quadrilateral facets with 4-valent vertices are ‘regular’ and are mapped to bi-cubic patches so that adjac...

A new image approximation scheme is proposed. The structural constraints are incorporated in an iterative M -estimator algorithm. As a result, an image modeling method is obtained that is not influenced by outliers and reduces Gaussian and heavy-tailed noise efficiently; and, at the same time it retains important details. The images are modeled as tensor product bicubic B-splines. The smoothing...

We generate a basis of the space of bicubic and biquartic C-smooth geometrically continuous isogeometric functions on bilinear multi-patch domains Ω ⊂ R. The basis functions are obtained by suitably combining C-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains (cf. [16]). They are described by simple explicit formulas for their spline coefficie...

Magnetic resonance image (MRI) in high spatial resolution provides detailed anatomical information and is often necessary for accurate quantitative analysis. However, high spatial resolution typically comes at the expense of longer scan time, less spatial coverage, and lower signal to noise ratio (SNR). Single Image Super-Resolution (SISR), a technique aimed to restore high-resolution (HR) deta...

The main question we try to answer in this work is whether it is feasible to employ super-resolution (SR) algorithms to increase the spatial resolution of endoscopic high-definition (HD) images in order to reveal new details which may have got lost due to the limited endoscope magnification of the HD endoscope used (e.g. mucosal structures). For this purpose we compare the quality achieved of d...

This paper presents a novel method for modifying the shapes of existing uniform bi-cubic B-spline surfaces by interactively editing the curvatures along isoparametric curves. The method allows us to edit the curvatures of the two intersecting isoparametric curves at each knot with specified positions, unit tangents, and unit normals. The user adjusts the radii of circles, representing the radii...

This paper describes a new class of surface patch for use in computational geometry, where fairness is built in at the design stage by using ideas from differential geometry. Principal patches are patches whose sides are lines of curvature, and can be created by making the boundary curves obey two conditions called the frame and position matching equations. lt is shown that surface continuity i...

We present a new approach for reconstructing a smooth surface from a set of scattered points in three-dimensional (3D) space. Our algorithm first decomposes a given point set into a quadtree-like data structure known as a strip tree. The strip tree is used to fit a set of least squares quadratic surfaces to the data points. These quadratic surfaces are then degree-elevated to bi-cubic surfaces ...