针对图像边缘检测过程中噪声抑制与细节保留不能兼顾的问题, 提出一种基于Bertrand曲面模型的边缘检测算法.在确定像素级边缘的基础上, 选取沿边缘方向的带状域为拟合区域, 利用Bertrand曲面具有沿母线各点的法线与母线共面的性质, 将拟合曲面区域内的像素点信息转化为边缘曲线的活动坐标, 并对转化后的像素点坐标和归一化灰度值进行拟合, 求得亚像素边缘到像素级边缘的法向距离, 实现图像亚像素边缘的检测.用视觉测量系统对量块直线边缘进行实验, 并与改进Facet曲面拟合亚像素边缘检测算法比较, 说明基于Bertrand曲面模型的边缘检测算法具有较高的定位精度, 测得一等量块的直线度误差在1 μm以内, 多次测量的误差平均值为－0.811 μm, 可靠性高.通过机油泵泵体测量实例, 说明本文算法可以应用于机械零件的精密测量, 尤其适用于中心距、孔径等的测量.

Image edge detection process is problematic in that noise suppression and detail retention can not be taken into account, this prompted us to propose an edge detection algorithm based on Bertrand surface model. On the basis of determined pixel edge,selecting strip domain along edge direction as fitting area,with the Bertrand surface characteristic of normal lines at various points along generatrix line are in one plane, transforming the pixel information in fitting surface area into active coordinate of edge curve,and fitting coordinate and normalized gray value to obtain normal distance between sub-pixel edge and pixel edge for sub-pixel edge detection.Adopt the vision measurement system to experiment with the gauge block line edge,andcompared to the improved algorithm of sub-pixel edge detection based on Facet surface fitting, the results show that algorithm of edge detection based on Bertrand surface model has high location accuracy, the first grade gauge blocklinear error is within 1 μm, and the multiple measurement error is －0.811 μm,it also has high reliability. The oil pump body measurement demonstratesthat this algorithm can be applied to precision measurement of mechanical parts, especially suitable for measurement of center distance, bore diameter, and so on.