## 3 Experiment Results  
The data for this experiment came from a wheel defect on-line detection system which includes an X-ray detector as an image intensifier plus a CCD camera. The resolution of the camera is 768 \(\times\) 576, and the power of the ray source is set to 170 kV and 2 mA. Figure 5a shows an X-ray image of a wheel acquired by this system, and Figure 2a shows a part of the image. Given the state-of-the-art wheel hub production, hub defects are generally small. A smoothing operator of size \(r\) about 5% of the long side of the acquired image will satisfy the detection purpose and, in this system, the size is about 39. The ray source by its voltage and current determines the gradation change of the X-ray image. For the combination of 170 kV and 2 mA, the small threshold \(T_{s}\) in step 3 of the segmentation process should be set between 0 and 10, and the large threshold \(T_{b}\) in step 4 should be between 10 and 20. The area s of the hub defect is defined as the number of pixels in the segmented region, and the diameter d is the maximum distance between any two points on the edge of the segmented region. According to the physical fact that a hub defect is typically small, the upper limit \(M_{\rm s}\) of the defect area is generally smaller than 10% of the total number of pixels in the image, and the upper limit \(M_{d}\) of the diameter is generally less than 20% of the shorter side of the entire image. In the acquisition system in question, \(M_{\rm s}\) is 4424 and \(M_{d}\) is 115. In step 6 of the division process, a region having an area smaller than \(M_{\rm s}\) and having a diameter smaller than \(M_{d}\) is retained as the final defect region. Figure 5: Segmentation result of proposed method: (**a**) original image; (**b**) result of \(T_{s}=1\); (**c**) result of \(T_{b}=12\); (**d**) result of reconstruction; (**e**) pseudo-color image of preliminary defects; (**f**) final result of proposed method. Figure 5a is smoothed using a mean smoothing operator with an \(r\) of 39. The segmentation result with the small threshold \(T_{s}\) set to 1 is shown in Figure 5b, and the segmentation result with the large threshold \(T_{b}\) set to 12 is shown in Figure 5c. The morphological reconstruction result is shown in Figure 5d. The reconstruction result includes the sought defect region along with pretty much interference. So, the result is to be analyzed having regard to the area and diameter, as described in step 6 of the segmentation process. Figure 5d is superimposed, in the format of a pseudo-color image, onto the original image Figure 5a, with its diameter displayed and each region numbered, and Figure 5e shows the result. Each defect region is studied for its area and diameter, and the data are shown in Table 1. As can be seen from Table 1, region 2, which meets the requirement that its area shall be smaller than \(M_{s}\) and its diameter shall be smaller than \(M_{d}\), is the true defect region. Performing step 6 of the segmentation process to get the defect region, which is marked on the original image, as shown in Figure 5f, it can be seen that the defect is accurately segmented out while the interference is altogether removed. To verify the performance of the algorithm, testing was conducted on different hub images. Figure 6a is another hub X-ray image with defects, taken from the same acquisition system. Figure 6b shows the segmentation result obtained from the same parameters, that is, the size \(r\) of the mean smoothing operator is 39, the small threshold \(T_{s}\) is 1, the large threshold \(T_{b}\) is set to 12, the defect area is less than 4424, and its diameter is less than 115. It can be seen that the more obvious large defect is extracted with accuracy while the small one, which is less obvious and of a poor contrast, is also extracted. Figure 7a shows still another hub X-ray image with small defects. The defects were segmented using the same parameters as in Figure 6a. The initial segmentation result, produced by step 3, is shown in Figure 7b.