关键词： 边缘检测   小波变换   形态学梯度运算   小波降噪   融合技术  

摘要： 针对传统的基于小波变换的边缘检测法无法提取低频区域完整连续的边缘,并且会丢弃包含一些重要细节的高频区域,同时受到噪声的影响而导致边缘提取效果不佳的问题,提出了一种基于融合技术的小波变换和数学形态学的边缘检测算法.在小波域中,对低频子图像采用数学形态学进行边缘检测,对高频子图像先进行小波降噪再采用小波模极大值法进行加权边缘检测,最后采用一定的融合规则对高、低频边缘子图像进行融合.实验结果表明,该方法用于图像边缘提取,不但能有效去除噪声干扰,又能突出边缘细节,边缘定位连续准确.

关键词： 高中数学   算法初步   比较   教学建议  

摘要： 通过对人教A、B版数学3的"算法初步"的内容进行比较探讨,以"算法初步"的教研内容为学习对象,具体例题具体分析,对教课书上的章节、组织结构和习题等多方面的内容进行详细的比较研究。

关键词： Nonconvex nonsmooth optimization   Semi-algebraic optimization   Tame optimization   Kurdyka-Lojasiewicz inequality   Descent methods   Relative error   Sufficient decrease   Forward-backward splitting   Alternating minimization   Proximal algorithms   Iterative thresholding   Block-coordinate methods   o-minimal structures  

摘要： In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance. Our result guarantees the convergence of bounded sequences, under the assumption that the function f satisfies the Kurdyka-Aojasiewicz inequality. This assumption allows to cover a wide range of problems, including nonsmooth semi-algebraic (or more generally tame) minimization. The specialization of our result to different kinds of structured problems provides several new convergence results for inexact versions of the gradient method, the proximal method, the forward-backward splitting algorithm, the gradient projection and some proximal regularization of the Gauss-Seidel method in a nonconvex setting. Our results are illustrated through feasibility problems, or iterative thresholding procedures for compressive sensing.

关键词： Evolutionary algorithms   Multi-objective optimization   Global optima   Cluster analysis   Parameter identification   Genetic regulation  

摘要： Based on evolutionary computation techniques, we present a parallel, globally convergent, multi-objective optimization algorithm which extends the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES). This approach enables identifying multiple global optima and multiple discontinuous Pareto set solutions of the optimization problem in a compact search space. After evaluating the algorithm with test functions, we apply our method to the identification of the parameters of a reaction-diffusion model of a genetic regulatory mechanism during Drosophila early development, our simulations being in agreement with the experimental data. Comparisons with a multi-objective version of the CMA-ES (MO-CMA-ES) on this dataset show that our algorithm outperforms largely the speed of convergence of MO-CMA-ES. We have identified an infinite number of accurate solutions of the model equations, associated with the Pareto set of the optimization problem. This non-unicity property of a biological developmental process explains phenotypic plasticity and resilience in biological systems. (C) 2012 Elsevier B.V. All rights reserved.

关键词： “算法多样化”   小学数学教学   优化性   价值   数学课程标准   学生个性化   计算教学   义务教育  

摘要： 提倡“算法多样化”是《义务教育数学课程标准（2011年版）》关于计算教学的亮点。这满足了课堂中学生个性化的学习需求，承载着“要使不同的人在数学上得到不同的发展”的神圣使命，其优点显而易见。但当人们对数学多样化趋之若鹜、纷纷仿效之时，我们应该冷静思考：事物的发展都有一个优化性，数学本身就是一个不断优化的过程，算法多样化不应该停留于此，算法优化才是它的最终目的。

关键词： 图像去噪   复数小波方向窗   维纳滤波   数学形态学  

摘要： 利用小波进行图像去噪是目前图像处理研究的热点。提出了一种结合数学形态学和复数小波方窗维纳滤波的图像去噪算法。该算法同时利用了复数小波的方向特性和图像本身固有的几何特性,首先使用双树复数小波变换对图像进行处理,再在基于复数小波域上进行维纳滤波,接着使用数学形态学把图像分成光滑区域和纹理区域2个部分,然后结合复数小波方向窗去更准确地估计小波域方向子带每一点的信号方差,最后利用维纳滤波器进对含噪图像进行去噪处理。实验结果表明,该算法的去噪效果优于一般的复数小波维纳滤波,并且运算更加简洁。

关键词： Building region   LiDAR   Mathematic morphological   Reversed iterative  

摘要： A new algorithm, called RIMM (Reversed Iterative Mathematic Morphological) algorithm, is proposed for automatic derivation of building region information from LiDAR (Light Detection And Ranging) data. The main contribution of the proposed algorithm is to provide a reliable way for building point detection from airborne LiDAR data, in which the reversed iteration makes that the thresholds can be determined in a simple way, thus guaranteeing the applicability of this algorithm for various complicated real situations. An experimental region with 2.8 million LiDAR points, containing many buildings with various roof structures, various sizes, various orientations, and various roof texture conditions, are selected to validate the effect and applicability of this algorithm. The average values of commission and omission error in building information derivation are 5.7% and 8.7%. respectively. The experimental results indicate that this RIMM algorithm is able to derive building region information effectively. (C) 2012 Elsevier B.V. All rights reserved.

关键词： 点云   数学形态学   开启   闭合   拓扑缺陷   柄体算子   星形算子  

摘要： 针对散乱点云数据在三角剖分过程中产生的拓扑缺陷,提出一种基于数学形态学运算和拓扑规则的网格拓扑修补算法。通过交互的方式选择需要修改的区域,使用自适应分层栅格的缺陷识别技术提取有拓扑缺陷的网格的顶点,从而确定待修复区域的边界,然后利用数学形态学的开启运算和闭合运算去除该修复区域的拓扑缺陷,并利用基于柄体理论的拓扑运算法则对该区域进行局部拓扑修改,生成二维流形的三角网格。应用实例表明,由于不需要对整个点云数据重新进行三角剖分,简化数据处理的过程,该算法具有运算速度快、结果准确性好的优点,并能较好地消除网格中的拓扑缺陷,有效地提高三角网格的显示精度,最终得到具有几何一致性和网格单元拓扑一致性的三角网格模型。