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摘要翻译：
给定一组二维散射点（通常是从边缘检测过程中获得的），椭圆拟合的目的是构造一个最适合于所收集的观测数据的椭圆方程。然而，由于边缘检测的不完善，一些散射点可能包含离群点。针对这一问题，提出了一种基于拉格朗日规划神经网络(LPNN)和局部竞争算法(LCA)的鲁棒实时椭圆拟合方法。首先，为了缓解这些异常值的影响，将拟合问题转化为目标函数为L1范数或L0范数项的非光滑约束优化问题。这是因为与一些传统椭圆拟合模型中的L2范数相比，P<2的LP范数对异常值的敏感性较低。然后，应用LPNN实时求解该优化问题。针对LPNN模型不能处理目标中不可微项的问题，引入了LCA的概念，并将其与LPNN框架相结合。仿真和实验结果表明，本文提出的椭圆拟合方法优于现有的几种算法。
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英文标题：
《Robust Real-time Ellipse Fitting Based on Lagrange Programming Neural
Network and Locally Competitive Algorithm》
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作者：
Hao Wang, Chi-Sing Leung, Hing Cheung So, Junli Liang, Ruibin Feng,
and Zifa Han
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最新提交年份：
2018
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分类信息：
一级分类：Electrical Engineering and Systems Science 电气工程与系统科学
二级分类：Image and Video Processing 图像和视频处理
分类描述：Theory, algorithms, and architectures for the formation, capture, processing, communication, analysis, and display of images, video, and multidimensional signals in a wide variety of applications. Topics of interest include: mathematical, statistical, and perceptual image and video modeling and representation; linear and nonlinear filtering, de-blurring, enhancement, restoration, and reconstruction from degraded, low-resolution or tomographic data; lossless and lossy compression and coding; segmentation, alignment, and recognition; image rendering, visualization, and printing; computational imaging, including ultrasound, tomographic and magnetic resonance imaging; and image and video analysis, synthesis, storage, search and retrieval.
用于图像、视频和多维信号的形成、捕获、处理、通信、分析和显示的理论、算法和体系结构。感兴趣的主题包括：数学，统计，和感知图像和视频建模和表示；线性和非线性滤波、去模糊、增强、恢复和重建退化、低分辨率或层析数据；无损和有损压缩编码；分割、对齐和识别；图像渲染、可视化和打印；计算成像，包括超声、断层和磁共振成像；以及图像和视频的分析、合成、存储、搜索和检索。
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英文摘要：
Given a set of 2-dimensional (2-D) scattering points, which are usually obtained from the edge detection process, the aim of ellipse fitting is to construct an elliptic equation that best fits the collected observations. However, some of the scattering points may contain outliers due to imperfect edge detection. To address this issue, we devise a robust real-time ellipse fitting approach based on two kinds of analog neural network, Lagrange programming neural network (LPNN) and locally competitive algorithm (LCA). First, to alleviate the influence of these outliers, the fitting task is formulated as a nonsmooth constrained optimization problem in which the objective function is either an l1-norm or l0-norm term. It is because compared with the l2-norm in some traditional ellipse fitting models, the lp-norm with p<2 is less sensitive to outliers. Then, to calculate a real-time solution of this optimization problem, LPNN is applied. As the LPNN model cannot handle the non-differentiable term in its objective, the concept of LCA is introduced and combined with the LPNN framework. Simulation and experimental results show that the proposed ellipse fitting approach is superior to several state-of-the-art algorithms.
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PDF链接：
https://arxiv.org/pdf/1806.00004
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