Lower bounds, mandating a minimal number and degree of polynomial pieces, represent a major achievement in the theory of geometrically smooth (G) constructions. On one hand, they establish a floor when searching for optimal constructions, on the other they can be used to flag complex constructions for potential flaws. In particular, quadrilateral meshes of arbitrary topology can not in general ...

Based on the local refinement algorithm addressed in [18], we analyze the linear independence of the bi-cubic T-spline blending functions corresponding to particular T-meshes.

In this paper we present a method to optimize the smoothness order of subdivision algorithms generating surfaces of arbitrary topology. In particular we construct a subdivision algorithm with some negative weights producing G 2 {surfaces. These surfaces are piecewise bicubic and are at at their extraordinary points. The underlying ideas can also be used to improve the smoothness order of subdiv...

This paper presents a new fast and local method of 3D surface reconstruction for scattered data. The algorithm makes use of quasiinterpolants to compute the control points from a coarse to fine hierarchy to generate a sequence of bicubic B-spline functions whose sum approaches to the desired interpolation function. Quasi-interpolants gives a procedure for deriving local spline approximation met...

We consider patches that contain any given 3D polynomial curve as a pregeodesic (i.e. geodesic up to reparametrization). A curve is a pregeodesic if and only if its rectifying plane coincides with the tangent plane to the surface, we use this fact to construct ruled cubic patches through pregeodesics and bicubic patches through pairs of pregeodesics. We also discuss the G1 connection of (1, k) ...

A C1 piecewise rational trigonometric cubic function with four shape parameters has been constructed to address the problem of visualizing positive data. Simple data-dependent constraints on shape parameters are derived to preserve positivity and assure smoothness. The method is then extended to positive surface data by rational trigonometric bicubic function. The order of approximation of deve...

In this paper we address the problem of producing an enlarged picture from a given digital image (zooming). We propose a method that tries to take into account information about discontinuities or sharp luminance variations while doubling the input picture. This is realized by a multiple scan of the zoomed image and could hence be implemented with limited computational resources. The algorithm ...

Super-resolution techniques that process multiple images to achieve resolution enhancement for satellite images are very important. This work utilizes Vandewalle method to realize super-resolution for satellite images. Assuming the motions between images are all on the same plane, we estimate and stick images into the high resolution grid. Because of the huge size of satellite images, only part...

Image scaling, fundamental task of numerous image processing and computer vision applications, is the process of resizing an image by pixel interpolation. Image scaling leads to a number of undesirable image artifacts such as aliasing, blurring and moiré. However, with an increase in the number of pixels considered for interpolation, the image quality improves. This poses a quality-time trade o...