International Conference on Curves and Surfaces 

About: International Conference on Curves and Surfaces is an academic conference. The conference publishes majorly in the area(s): Interpolation & Spline (mathematics). Over the lifetime, 191 publications have been published by the conference receiving 4211 citations.

On single image scale-up using sparse-representations

Abstract: This paper deals with the single image scale-up problem using sparse-representation modeling. The goal is to recover an original image from its blurred and down-scaled noisy version. Since this problem is highly ill-posed, a prior is needed in order to regularize it. The literature offers various ways to address this problem, ranging from simple linear space-invariant interpolation schemes (e.g., bicubic interpolation), to spatially-adaptive and non-linear filters of various sorts. We embark from a recently-proposed successful algorithm by Yang et. al. [1,2], and similarly assume a local Sparse-Land model on image patches, serving as regularization. Several important modifications to the above-mentioned solution are introduced, and are shown to lead to improved results. These modifications include a major simplification of the overall process both in terms of the computational complexity and the algorithm architecture, using a different training approach for the dictionary-pair, and introducing the ability to operate without a training-set by boot-strapping the scale-up task from the given low-resolution image. We demonstrate the results on true images, showing both visual and PSNR improvements.

Image separation using wavelets and shearlets

Abstract: In this paper, we present an image separation method for separating images into point- and curvelike parts by employing a combined dictionary consisting of wavelets and compactly supported shearlets utilizing the fact that they sparsely represent point and curvilinear singularities, respectively. Our methodology is based on the very recently introduced mathematical theory of geometric separation, which shows that highly precise separation of the morphologically distinct features of points and curves can be achieved by l1 minimization. Finally, we present some experimental results showing the effectiveness of our algorithm, in particular, the ability to accurately separate points from curves even if the curvature is relatively large due to the excellent localization property of compactly supported shearlets.

OpenFlipper: an open source geometry processing and rendering framework

Abstract: In this paper we present OpenFlipper, an extensible open source geometry processing and rendering framework. OpenFlipper is a free software toolkit and software development platform for geometry processing algorithms. It is mainly developed in the context of various academic research projects. Nevertheless some companies are already using it as a toolkit for commercial applications. This article presents the design goals for OpenFlipper, the central usability considerations and the important steps that were taken to achieve them. We give some examples of commercial applications which illustrate the flexibility of OpenFlipper. Besides software developers, end users also benefit from this common framework since all applications built on top of it share the same basic functionality and interaction metaphors.

Parameterization of contractible domains using sequences of harmonic maps

Abstract: In this paper, we propose a new method for parameterizing a contractible domain (called the computational domain) which is defined by its boundary. Using a sequence of harmonic maps, we first build a mapping from the computational domain to the parameter domain, i.e., the unit square or unit cube. Then we parameterize the original domain by spline approximation of the inverse mapping. Numerical simulations of our method were performed with several shapes in 2D and 3D to demonstrate that our method is suitable for various shapes. The method is particular useful for isogeometric analysis because it provides an extension from a boundary representation of a model to a volume representation.

Surface construction based on variational principles

Abstract: Variational principles have become quite popular in the design of surfaces. The idea is to consider a class of surfaces having more degrees of freedom than are necessary to fullll the constraints (e. g. interpolation or boundary conditions). The remaining degrees of freedom are set by minimizing a fairness functional. The choice of thèright' fairness functional is a crucial step. In this paper we describe a systematic approach for choosing an appropriate fairness functional that produces high quality surfaces and which allows the solution of the optimization problem in a reasonable amount of time. x1. Introduction In diierent areas in CAGD arises the problem of constructing smooth curves or surfaces satisfying certain constraints. Typical examples are (scattered data) interpolation and the construction of blending surfaces. In scattered data interpolation one has to construct a surface which does not oscillate too much and goes through a sampled set of points in the space. Finding a blending surface (i.e. a smooth transition surface between primary surfaces) amounts to the construction of a reasonable surface that satisses certain boundary conditions determined by the primary surfaces. The traditional approach to these problems is the following: Choose an appropriate set of functions that has as many degrees of freedom as are necessary to fullll the constraints. Determination of the degrees of freedom usually is done by solving a system of equations. Recently, a variational approach for solving these problems has got more and more attention. The idea is to start with a class of surfaces having more degrees of freedom than are strictly necessary to fullll the constraints. The remaining degrees of freedom are used to Curves and Surfaces II 1 P.