For circle detection, many researchers have developed the modified HT methods using the parameter decomposition and/or some geometric properties of circles to reduce the complexities. Yuen et al. (1990) have performed a comparative study of several HT-based techniques for circle finding. The parameter decomposition-based approaches usually start with the detection of the centers of the circles, then determine the radii. One of those properties is that the normal to a point on a circle passes through the center of the circle (Davies, 1987a; Illingworth and Kittler, 1987). Yip et al. (1992) used the property that two points on a circle whose tangent lines are parallel are the endpoints of the diameter of the circle. The above approaches require the gradient information of edge contours which are sensitive to noise (Davies, 1987b).许多研究者开发了改良的HT方法,这是通过使用参数分解及/或一些圆弧的几何特性来降低它的复杂性。袁氏与伙伴曾于1990年对多种基于HT的圆弧识别技术进行比较研究。参数分解法的步骤通常是以识别圆弧的中心开始,然后才确定它们的半径。其中的一个几何特性是:在圆弧上一点的法线经过圆弧的中心(Davies, 1987a; Illingworth和Kittler, 1987)。叶氏与伙伴于1992年则使用另一个特性:在圆弧上两点的正切线如果是平行,这两点就是圆弧直径的两个端点。上述两种方法都需要对噪音极度敏感的边缘轮廓的梯度信息 (Davies, 1987b)。The e�ect of noise on the edge direction information is generally larger than that on the edge position. There are several approaches without using the edge direction information. Chan and Siu (1990) proposed a fast ellipse detection based on the horizontal and vertical chord bisectors. Similarly, Ho and Chen (1995) proposed a fast detection algorithm of circles using a global geometric symmetry. It computed the circle center from the symmetrical vertical axis and the symmetrical horizontal axis. 一般来说,边缘方向信息受噪音的影响要大于在边缘的位置;有几种方式可以避免使用边缘方向信息。陈和萧于1990年提出基于水平与垂直平分弦的椭圆识别快速算法。何与陈于1995年也提出通过使用全体几何对称性的类似的圆弧识别快速算法。它是从对称竖轴与横轴计算圆弧的中心。Sheu et al. (1997) used the symmetric axis information throughout the entire process to compute all five parameters. Goneid et al. (1997) developed the chord bisection method using a 1D array. Davies (1999) studied a simple chord bisection method for the rapid accurate location of ellipses. The method of Ioannou et al. (1999) is based on the property that the line perpendicularly bisecting a chord of the circle passes through its center. Lei and Wong (1999) detected the symmetric axes and found pairs of two orthogonal axes whose intersections are the candidates of the centers. Its disadvantage is that straight lines in the image may make the detection of symmetric axes complex.萧氏与伙伴则于1997年在整个过程中使用对称轴的信息来计算全部五个参数。Goneid与伙伴开发了使用一维数组的平分弦方法。Davies于1999年研究一种简单的平分弦方法对椭圆的快速、正确定位。1999年Loannou与伙伴的方法则是基于垂直平分圆弧弦的线会经过其中心点的几何特性。黎与黄于1999年测到对称轴线,并发现多双正交轴线,其交叉点是圆弧的中心。它的缺点是图像里的直线会与对称轴线混淆,导致识别的复杂性。【英语牛人团】