Modeling on triangulations with geodesic curves

This paper discusses the problem of modeling on triangulated surfaces with geodesic curves. In the first part of the paper we define a new class of curves, called geodesic Bézier curves, that are suitable for modeling on manifold triangulations. As a natural generalization of Bézier curves, the new curves are as smooth as possible. In the second part we discuss the construction of C ⁰ and C ¹ piecewise Bézier splines. We also describe how to perform editing operations, such as trimming, using these curves. Special care is taken to achieve interactive rates for modeling tasks. The third part is devoted to the definition and study of convex sets on triangulated surfaces. We derive the convex hull property of geodesic Bézier curves.

一种基于纹理的SAR图像居民区提取方法

居民区是SAR图像中比较重要的一类地物,它的提取在许多方面有着重要的应用。给出了一种居民区提取方法,根据居民区具有的高亮度和规范的纹理特性,利用Sobel算子和Otsu阈值处理得到居民区离散点图,再用K均值将其分割成块,最后用格雷厄姆方法生成居民区的边界,实现了居民区的自动提取。实验处理结果表明,该方法是一种有效的居民区提取方法。     

3D-line clipping algorithms — a comparative study

Some well-known line-polyhedron intersection methods are summed up and new accelerating modifications presented. Results of comparison of known and newly developed methods are included. New methods use the fact that each line can be described as the intersection of two planes.     

Weighted and extended total variation for image restoration and decomposition

In various information processing tasks obtaining regularized versions of a noisy or corrupted image data is often a prerequisite for successful use of classical image analysis algorithms. Image restoration and decomposition methods need to be robust if they are to be useful in practice. In particular, this property has to be verified in engineering and scientific applications. By robustness, we mean that the performance of an algorithm should not be affected significantly by small deviations from the assumed model. In image processing, total variation (TV) is a powerful tool to increase robustness. In this paper, we define several concepts that are useful in robust restoration and robust decomposition. We propose two extended total variation models, weighted total variation (WTV) and extended total variation (ETV). We state generic approaches. The idea is to replace the TV penalty term with more general terms. The motivation is to increase the robustness of ROF (Rudin, Osher, Fatemi) model and to prevent the staircasing effect due to this method. Moreover, rewriting the non-convex sublinear regularizing terms as WTV, we provide a new approach to perform minimization via the well-known Chambolle's algorithm. The implementation is then more straightforward than the half-quadratic algorithm. The behavior of image decomposition methods is also a challenging problem, which is closely related to anisotropic diffusion. ETV leads to an anisotropic decomposition close to edges improving the robustness. It allows to respect desired geometric properties during the restoration, and to control more precisely the regularization process. We also discuss why compression algorithms can be an objective method to evaluate the image decomposition quality.     

支持向量预选的凸壳顶点法

为减少参训样本数量,加快支持向量机在大规模数据集上的学习速度,提出一种基于凸壳顶点法的支持向量预选算法.该算法基于线性可分样本集凸壳顶点的集合必然是支持向量超集的事实,运用对偶原理将凸壳顶点的求解转化为判断线性规划是否有解,从而求出样本集的凸壳顶点.构造了非线性映射函数,并将该算法推广到非线性可分样本集.基于人工数据集和标准数据集的实验结果验证了算法的有效性.     

H∞ Controller design for spectral MIMO models by convex optimization

A new method for robust fixed-order H_∞ controller design by convex optimization for multivariable systems is investigated. Linear Time-Invariant Multi-Input Multi-Output (LTI-MIMO) systems represented by a set of complex values in the frequency domain are considered. It is shown that the Generalized Nyquist Stability criterion can be approximated by a set of convex constraints with respect to the parameters of a multivariable linearly parameterized controller in the Nyquist diagram. The diagonal elements of the controller are tuned to satisfy the desired performances, while simultaneously, the off-diagonal elements are designed to decouple the system. Multimodel uncertainty can be directly considered in the proposed approach by increasing the number of constraints. The simulation examples illustrate the effectiveness of the proposed approach.     

A certain class of starlike functions

This paper presents a new class of functions analytic in the open unit disc, and closely related to the class of starlike functions. Besides being an introduction to this field, it provides an interesting connections defined class with well known classes. The paper deals with several ideas and techniques used in geometric function theory. The order of starlikeness in the class of convex functions of negative order is also considered here.     

Tangential cover for thick digital curves

The recognition of digital shapes is a deeply studied problem. The arithmetical framework, initiated by Reveillès [Géométrie discrète, calcul en nombres entiers et algorithmique, Thèse d’Etat, 1991], provides a powerful theoretical basis, as well as many algorithms to deal with digital objects. The tangential cover, first presented in Feschet and Tougne [Optimal time computation of the tangent of a discrete curve: application to the curvature, in: G. Bertrand, M. Couprie, L. Perroton (Eds.), 8th Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, vol. 1568, Springer, Berlin, 1999, pp. 31-40] and Feschet [Canonical representations of discrete curves, Pattern Anal. Appl. 8(1-2) (2005) 84-94] is a useful tool for representing geometric digital primitives. It computes the set of all maximal segments of a digital curve and permits either to obtain minimal length polygonalization or asymptotic convergence of tangents estimations. Nevertheless, the arithmetical approach does not tolerate the introduction of irregularities, which are however inherent to the acquisition of digital shapes. The present paper is an extension of Faure and Feschet [Tangential cover for thick digital curves, in: D. Coeurjolly, I. Sivignon, L. Tougne, F. Dupont (Eds.), DGCI 2008, Lecture Notes in Computer Science, vol. 4992, Springer, Berlin, 2008, pp. 358-369], in which we propose a new definition for a class of the so-called “thick digital curves” that applies well to a large class of digital object boundaries. We then propose an extension of the tangential cover to thick digital curves and provide an algorithm with an O(nlogn) time complexity, where n denotes the number of points of specific subparts of the thick digital curve. In order to keep up with this low complexity, some critical points must be taken into account. We describe all required implementation details in this paper.