中文摘要：

进行三维图像边缘检测时，利用Facet模型能够获得较精确的边缘信息，但耗时较多；而利用小波变换可获得较快的检测速度，但得到的边缘依赖于阈值的大小。综合上述两种方法的特点，提出了一种基于小波定位及Facet模型的三维边缘检测方法。首先，对工业CT三维图像进行三维小波变换，设定较小阈值，得到三维粗边缘，即对图像边缘进行粗定位；然后，针对粗边缘点逐个进行三维Facet拟合，得到实际边缘点，从而完成图像边缘的精确定位。该方法通过小波变换粗定位这一前处理过程减少了Facet拟合的体素点数，加快了Facet模型三维边缘检测的速度。实验结果显示，本文方法不仅能得到与直接Facet模型效果相当的边缘，还能使Facet模型三维边缘检测的速度提高3．51～7．39倍，而且图像边缘越简单加速比越高。实验结果表明，基于小波定位和Facet模型的边缘检测方法可满足工业CT三维图像边缘检测对精度和速度的要求。

英文摘要：

In 3D edge detection for an industrial Computed Tomography（CT） image, the Facet model can be used to obtain the relatively precise image edge, but it will cost too much time. Otherwise, the wavelet transform method can be taken to detect 3D image edges in a shorter time, however, the edge information obtained depends on the threshold strongly . In combination with the characteristics of two methods above, a 3D edge detection method based on wavelet transform and Facet model is presented in this paper. Firstly, 3D wavelet transform is used for an industrial CT 3D image , and initial candidates of edge could be obtained by setting a smaller threshold. Through this step, the edge is located roughly. Then, 3D Facet model is used to decide if the candidate is the true edge, and the points in rough edge are fitted one by one to realize the precise location of the image edge. The improved algorithm reduce the number of edge pixel candidates by the preprocessing of 3D wavelet transform, which improves the detection speed of the original 3D Facet model. Experimental results show that the proposed method not only can obtain the same image edge as that by original 3D Facet model but also can improve the image detection speed greatly. Obtained results indicate that the image detection speed has increased by 3.51-7.39 times as compared with that of original 3D Facet model, and the simpler the image edge is, the higher the accelerate ratio is. These results show that the 3D edge detection method based on wavelet transform and Facet model can meet the requirements of the 3D image in an actual industrial CT for high accuracy and high speed.