边缘识别的二维正交多项式拟合及结构变形检测

数字图像中边缘附近的灰度是沿边缘方向和跨边缘方向二维变化的，以前边缘识别的多项式拟合大多采用跨边缘方向的一维拟合。介绍一种采用二维正交多项式进行边缘识别的新方法，由于二维拟合更符合边缘附近小区域内像素灰度二维变化的实际，因此拟合结果优于一维拟合。在进行拟合时，利用正交多项式的正交性将优化方程对角化，避免求逆或解方程，没有多项式拟合优化方程的病态问题，采用高阶多项式拟合可以提高拟合精度。对生成图像的边缘识别结果表明，二维正交多项式拟合识别边缘的精度和稳定性较好。简支梁模型试验表明，采用正交多项式边缘拟合方法检测梁的静变形，图像变形检测精度在0.1像素之内，适当选择图像采集设备和采集范围，点检测精度与传统检测方法的精度相当，边缘检测属线状高密度检测，检测范围远大于传统方法。

Orthogonal Polynomial Fitting for the Edge Detection and BeamDeformation Measurement

The gray-scale digital image is two-dimensional, and most of the previous polynomial fitting methods for edge detection are one-dimensional. The new method of two-dimensional orthogonal polynomial fitting for edge detection is presented. The two-dimensional fitting is actually more suitable for the two-dimensional image, and the fitting results are significantly better than that of the one-dimensional one. Because of the orthogonality of the polynomial function, the fitting coefficients can be determined by simple arithmetic method instead of the solution of algebra equation. So the high-order polynomial function can be used in the data fitting, and the fitting results are significantly better than that of ordinary polynomial. It is shown through the analysis of the synthesis image and the test of simply supported beam that the results of surface fitting and edge identification used of the proposed method are quite good. Within a certain image coverage, the precision of the beam measurement by proposed method is relatively same with dial gage results at the measurement point. Intense deflection data along the beam can be obtained by the proposed method, while only point deflection can be obtained by dial gage measurement.