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清华大学学报(自然科学版)  2016, Vol. 56 Issue (6): 640-645    DOI: 10.16511/j.cnki.qhdxxb.2016.22.025
  机械工程 本期目录 | 过刊浏览 | 高级检索 |
圆柱透视投影轮廓的隐式方程描述和拟合方法
谢颖, 杨向东, 芮晓飞, 任书楠, 陈恳
清华大学 机械工程系, 北京 100084
Implicit equation description and fitting method for cylinder perspective contours
XIE Ying, YANG Xiangdong, RUI Xiaofei, REN Shunan, CHEN Ken
Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
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摘要 为了提高从视觉图像中识别并提取圆柱透视投影轮廓的鲁棒性和精度, 将由直线和椭圆组成的投影轮廓曲线用含约束的二元高次隐式方程进行描述。采用该描述方式可将轮廓曲线拟合问题通过线性近似转化为含有非线性约束的非线性优化问题。针对该问题求解时, 先粗略地估计出曲线参数的初值, 再利用初值筛选出内点, 最后采用罚函数法将问题转化为求解无约束问题从而求得该优化问题的解。由于该描述方式引入了轮廓中直线和椭圆的相互约束, 采用该描述方式的轮廓曲线拟合方法比采用独立的直线或椭圆识别方法提取轮廓, 具有更强的抗噪能力。仿真和实物图像的实验结果表明, 该方法能有效提高圆柱投影轮廓曲线拟合的鲁棒性和精度。
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谢颖
杨向东
芮晓飞
任书楠
陈恳
关键词 图像识别轮廓曲线隐式方程曲线拟合非线性优化    
Abstract:A constrained implicit equation is developed to enhance the robustness and precision of perspective contour extraction for cylinders. The contour curve fitting problem is converted to a nonlinear optimization problem containing nonlinear constraints by a linear approximation. The problem is then solved with a rough estimate of the curve parameters and the noisy points filtered to find reasonable points based on the rough estimate of the curve parameters. This constrained problem is then converted to an unconstrained problem using the penalty function method to find the solution. This method takes advantage of the constraint between the lines and the ellipse to give better anti-noise performance for perspective cylinder contour extraction than separate methods using lines or ellipses. Tests of synthetic and real images show that this method effectively improves perspective contour curve fitting for cylinders.
Key wordsimage recognition    contour curve    implicit equation    curve fitting    nonlinear optimization
收稿日期: 2015-05-15      出版日期: 2016-07-01
ZTFLH:  TP391.4  
通讯作者: 杨向东, 副教授, E-mail: yangxd@tsinghua.edu.cn     E-mail: yangxd@tsinghua.edu.cn
引用本文:   
谢颖, 杨向东, 芮晓飞, 任书楠, 陈恳. 圆柱透视投影轮廓的隐式方程描述和拟合方法[J]. 清华大学学报(自然科学版), 2016, 56(6): 640-645.
XIE Ying, YANG Xiangdong, RUI Xiaofei, REN Shunan, CHEN Ken. Implicit equation description and fitting method for cylinder perspective contours. Journal of Tsinghua University(Science and Technology), 2016, 56(6): 640-645.
链接本文:  
http://jst.tsinghuajournals.com/CN/10.16511/j.cnki.qhdxxb.2016.22.025  或          http://jst.tsinghuajournals.com/CN/Y2016/V56/I6/640
  图1 曲线拟合仿真实验结果
  表1 曲线拟合仿真实验数据
  图2 各参数的相对误差
  图3 实物图像中待处理的圆柱
  图4 实物图像曲线拟合结果对比
  表2 实物图像曲线拟合前后圆柱高度重建结果对比
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