霍夫变换在指数函数型曲线检测中的应用  

The Application of Hough Transform in the Detection of Exponent Function Curve

作　　者：曾接贤[1] 张桂梅[1] 储珺[1] 鲁宇明[1] 

机构地区：[1]南昌航空工业学院计算机视觉研究室,南昌330034

出　　处：《中国图象图形学报（A辑）》2005年第2期236-240,共5页Journal of Image and Graphics

基　　金：国家自然科学基金项目(60275037);江西省自然科学基金项目 (0311019);江西省测试技术与控制工程研究中心开放基金项目(2002.007)

摘　　要：利用了霍夫变换抗噪声能力强和能分离出属于不同直线附近点的特性,研究离散数据点集M中xi,yi满足指数函数关系时的曲线检测问题。首先,对离散数据点集M中的数据xi,yi做半对数变换,得到新的数据点集M (x i,y i),此时,x i,y i具有线性关系;其次,用霍夫变换检测M 中的直线,可得直线参数;然后,利用霍夫变换所得的直线参数,计算图像中的点到直线的距离dki,并与给定阈值dk比较,从而将分布在不同直线附近的点分离出来,同时剔除数据点集M 中的干扰点或噪声;最后,用最小二乘法拟合直线,再经过反变换,得到剔除干扰点或噪声后的拟合曲线方程参数a和b。该方法能够很好地检测出数据集中的数据点按指数关系分布时的曲线,特别是能够检测出数据集中存在多条曲线的情况,解决了最小二乘法拟合曲线时存在的3个问题,同时又对霍夫变换的精度要求不高。This paper, by using the strong resistance of Hough transform to noise and its characteristics of extracting points in the vicinity of different lines, studies the curve detection when x i,y i of the discrete data point set M satisfy the exponential function relation. Firstly, the new data points M *( x * i,y * i ) are obtained by logarithmically transforming the discrete data points, and the relation between x * i and y * i becomes linear. Secondly, Hough transform is used to detect the line of M * so that the parameters of lines are obtained. Thirdly, the parameters of lines obtained by Hough transform are used to calculate the distances d ki from the points to the line, and compared d ki with the given threshold d k , so the points in the vicinity of the different lines are extracted and the interferences or noise of data point set M * are deleted. At last, by using the fit line of the least square method and through inverse transform, parameters a and b of the fit curve equation after interferences or noise being deleted are obtained. This paper proposes a new method of detecting the exponential functional curves, which overcomes the three problems existed in the use of the fit curve of the least square method and does not need high accuracy of Hough transform.

关 键 词：霍夫变换 数据点 曲线检测 离散数据 点集 抗噪声能力 精度要求 直线 指数函数 除数 

分 类 号：TB53[理学—物理] TP391[理学—声学]