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Repeatability property of the normalized image

4 Experiments and Discussion

4.1 Repeatability property of the normalized image

To demonstrate the repeatability property of the normalized image, the user can place the internal thread on the fixture at any arbitrary orientation. The original sequence of images is reconstructed by rounding the start point of the tapping process of the unwrapped image to the right-hand side. As shown in Figures 17(a)-(c), three unwrapped images were reconstructed in arbitrary orientations. The three images differed only in their relative position. Applying the proposed image normalization procedure normalized all these images in the same manner, as shown in Figure 17(d). This shows that our normalization procedure can successfully normalize the unwrapped image so that the start point of the tapping process is always on the right-hand side. Such image position normalization also provides a uniform inspected image for defect detection.

31 (a)

(b)

(c)

(d)

Figure 17: Demonstration of repeatability: (a) first unwrapped image, (b) second unwrapped image, (c) third unwrapped image, and (d) corresponding normalized image

32 4.2 Sensitivity analysis of parameter settings

As implemented the OTPG algorithm described in section 3.3 has four major parameters that influence the inspection outcome: the structure element size of grayscale closing operator k1, the offset constant k2, the high-energy threshold k3, and the control constant k4.

4.2.1. Effects of the structure element size of grayscale closing operator k1 and the offset constant k2

The parameter k1 is the rectangular size of the structure element of grayscale closing operator that can mend the interrupted crests or roots in the internal thread image. The parameter k2 is an offset constant that can adjust the binary threshold value in Equation (1) to enable the user to reveal the pixels with gray levels between max(G) – k2 and max(G) in Figure 14(a). The bright bands (crests or roots) and gray bands (flanks) in the morphological image of the internal thread can be well mended and totally separated if both k1 and k2 are selected properly. That permits the analysis of the normalization and segmentation procedures in subsections 3.3.1 and 3.3.2 to proceed successfully. As shown in Figures 18(a)-(c), as the value of k1 or k2 increases, there are more and more crests and roots will join into the connected blobs. On the contrary, as the value of k1 or k2 decreases, neither the crest nor the root will be well shaped or well mended. Those blobs will appear as false crests or roots so that the image of the internal thread will be ambiguous and complicated for later processing.

(a)

33 (b)

(c)

Figure 18: Effect of different offset constants: (a) k1 = 10 and k2 = 7,(b) k1 = 50 and k2 = 11, and (c) k1 = 100 and k2 = 15

To obtain reliable values of k1 and k2, a supervised pre-training session was conducted on 22 samples. Figure 19 and Figure 20 showed the curves of the average area of blobs and the average number of blobs after the blob elimination sub-operation described in subsection 3.3.2 was applied for different combinations of k1 and k2. The curves of different k1 in Figure 19 were dramatically inflating when the values of k2 were larger than 25. Meanwhile, in Figure 20, these curves were decreasing when the values of k2 were larger than 14 due to the bright and gray bands have gradually joined together. The intersection of the intervals, (k2

≧ 25) ∩ (k2 ≧ 14), was took the complement which yielded an interested region, k2 < 14, to be following discussed. When k1 was smaller than 5, the average area of blobs were relative low and the averages number of blobs were relative high due to interrupted crests or

34

roots were not well mended and then were partial eliminated. When k1 was in the range of 7-11, the average area of blobs and the average number of blobs were relative stable due to the crests and roots can be well mended and separated from the flanks reliably. When k1 was larger than 13, the average area of blobs were relative high and the average number of blobs were relative low due to some crests or roots have joined together by the large structure element sizes that some blobs will be misinterpreted as false crests, roots, or flanks. In this way, we could get the stable intervals of k1 in the range of 7-11 and k2 less than 14.

Figure 19: Average area of blobs generated for different values of k1 and k2

Figure 20: Average number of blobs generated for different values of k1 and k2

4.2.2. Effect of the high-energy threshold k3

The high-energy threshold of Equation (5) assists in reducing the high-energy frequency

35

components in the spectrum to zero. In general, the smaller the value of k3 is, the greater the numbers of high-energy frequency components are eliminated in the spectrum. A value of k3 that is too large results in an insufficient number the high-energy frequency components of the thread patterns properly to be eliminated and the thread patterns will not be removed completely when the spectrum is converted back to the spatial image. Conversely, when the value of k3 is too small, too many high-energy frequency components that characterize both the thread patterns and defects are eliminated. Thus, the thread patterns and local defects will all be removed in the restored image.

In this experiment, the effect of three different high-energy threshold values on the image in Figures 16(a) was examined; the results are shown in Figures 21(a1)-(a3). Figures 21(b1)-(b3) show the corresponding restored images. In Figure 21(a1) and Figure 21(b1), a smaller value of k3 was selected to eliminate too many high-energy frequency components so that the overall texture and defects were all removed, leaving nothing meaningful. In Figure 21(a2) and Figure 21(b2), an appropriate value of k3 was used to remove the periodic directional texture of the thread pattern while preserving the defects. Note that the eliminated high-energy frequency components were allocated in a direction orthogonal to the thread pattern spread range near the origin of the spectrum image only. In Figure 21(a3) and Figure 21(b3), a large value of k3 was used so that only one high-energy frequency component was eliminated at the origin of the spectrum. Notice that the overall texture was retained in the corresponding restored image.

(a1)

36 (a2)

(a3)

(b1)

(b2)

(b3)

Figure 21: Effect of different high-energy threshold values: (a1)-(a3) show the results of eliminated high-energy frequency components in the spectrum image of Figure 16(a) for k3 =

1, 50, and 150 respectively; (b1)-(b3) are the resulting restored images

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Twenty-two samples were used to calculate the corresponding average angle of the eliminated high-energy frequency components in the DCT domain. The included angles between the angle of thread pattern in the spatial domain and the angle of the eliminated high-energy frequency components in the DCT domain are shown as functions of k3 in Figure 22. The average included angles increased rapidly when k3 was in the range of 1-5. When k3 was in the range of 6-104, the average included angles were approximately orthogonal. When k3 was greater than 105, only one high-energy frequency component was eliminated in the DCT domain so that the corresponding average included angle could not be computed.

Experience from the training samples indicates that a value between 6 and 104, where the average included angles are approximately orthogonal, is the most suitable.

Figure 22: Average included angles for different values of k3

4.2.3. Effect of the control constant k4

Since scratches are brighter, and collapses and flaws are darker than blurred thread patterns in the restored image, the SPC binarization concept shown in Equation (7) was used to distinguish between thread patterns and defects. The value of k4 affects the severity of the lower and upper control limits. In general, smaller values of k4 results in tight limits that the thread patterns might not been fully whitened and more noise appears in the binary image, i.e.

false alarms. Conversely, a value of k4 that is too large results in a very relaxed standard that may white both the thread patterns and defects and produce missed detections.

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In this experiment, the effect of three different values of k4 on the image in Figure 16(e) was examined; the results are shown in Figures 23(a)-(c). Figure 23(a) showed the binarized result of Figure 16(e) for k4 = 2. We could observe that the thread patterns were not fully white when the control constant was too small; much noise appeared in Figure 23(a). Figure 23(b) presents the binarized result of Figure 16(e) for k4 = 5. A proper control constant value could produce white thread patterns and dark defects more precisely. The defects were shown clearly in Figure 23(b). Figure 23(c) presented the binarized result of Figure 16(e) for k4 = 8.

We could observe that both the thread patterns and defects became white when a large control constant was used. The defects were almost eliminated in Figure 23(c).

(a)

(b)

(c)

Figure 23: The effect of different control constants: (a)-(c) show the binarized image of Figure 16(e) for k4 = 2, 5, and 8, respectively

Figure 24 showed the detection outcome based on 22 samples. Given the middle value of

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the recommended range of k3, the false alarm phenomenon decreased gradually as k4 increased, and was the inverse of the missed detection phenomenon. Figure 24 also illustrated that SPC binarization yielded satisfactory limits with the highest number of correct detections and lowest number of false alarms and missed detections when k4 was in the range of 5.0-5.2.

Figure 24: Defect detection results for different values of k4

40 4.3 Experimental results

In this subsection, some experimental results of internal thread inspection were presented to confirm the function of the proposed OTPG. Figures 25(a1)-(a10) showed the inspected images of good or defective internal threads. The parameters generated from 22 training samples were k1 = 9, k2 = 7, k3 = 55, and k4 = 5.1 (To take the middle values of these corresponding recommended intervals). Figures 25(b1)-(b10) showed the corresponding inspection results. A non-defective internal thread image resulted in a clear response;

otherwise defects were clearly indicated in their actual locations. As previously mentioned, a scratch will cause an internal thread to bind with an external one, and a collapse or flaw will decrease the tight fit. The pixels of a scratch were relatively bright and the pixels of a collapse or flaw were relatively dark compared to the blurred thread patterns in the restored image.

Forty-four testing samples (23 non-defective and 21 defective) were tested for evaluating the inspection rate of proposed method. After applying the proposed OTPG algorithm, no any false alarm but only one miss-detection was encountered; this meant that the inspection rate was up to 97.72%. The only miss-detection was due to the scratches on the flanks were small and non-continuous, so they were miss-regarded as small-area noise blobs to be miss-removed.

(a1)

(a2)

41 (a3)

(a4)

(a5)

(a6)

(a7)

42 (a8)

(a9)

(a10)

(b1)

(b2)

43 (b3)

(b4)

(b5)

(b6)

(b7)

44 (b8)

(b9)

(b10)

Figure 25: Experimental test results of the proposed OTPG: (a1)-(a3) good internal thread, (a4)-(a6) defective internal thread with a collapse, (a7)-(a8) defective internal thread with a collapse and flaw, (a9) defective internal thread with a collapse and scratch, (a10) defective internal thread with a scratch and (b1)-(b10) the resulting binary images corresponding to

(a1)-(a10)

For quality assurance purposes, the internal threads could be classified into four categories as listed in Table 3. First, when no blob existed in the final response image, this was classified as a good grade A internal thread. Second, when a blob existed in the final response image and the corresponding gray levels in the restored image were above the upper limit, this was classified as a scratched defective grade B internal thread that should be reworked by thread tapping to sweep away the bulges on the flanks. The third classification was the same as the second, except the gray levels were below the lower limit; this was

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classified as a collapsed or flawed defective grade C internal thread that should be tested for close fit by a human expert. Fourth, when an internal thread with a mixture of defects existed, this was classified as grade D for which both rework and fit testing are required.

Table 3: The classification rule of the OTPG algorithm

Grade Criterion Class Action

A number of blobs = 0 good Seller can dispatch the internal thread to customers.

B number of blobs > 0 gray levels > UCL

scratch defect The internal thread should be reworked by thread tapping to sweep away the bulges on the flanks.

C number of blobs > 0 gray levels < LCL

collapse or flaw defect

The internal thread that should be tested for close fit by a human expert.

D number of blobs > 1

gray levels > UCL and < LCL

mixed-type defects

Both rework and fit testing are required for the internal thread.

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5 Conclusions and Further Researches

5.1 Conclusions

A novel OTPG for the auto-inspection of internal threads was proposed in this dissertation that provides a non-contact and an orientation-free internal thread inspection mechanism. The OTPG system captured a sequence of partial wall 2D images of the internal thread and converted them into a 2D unwrapped image. A preprocessing algorithm was designed to achieve repeatability when segmenting the inspected image. A DCT-based restoration technique was implemented to highlight defects such as scratches, collapses, and flaws in the directional texture image. The proposed OTPG can be used to detect both bulge-shaped scratch and cave-shape collapse or flaw.

47 5.2 Further Researches

The reconstructed 2D image loses the depth information of an internal thread pattern.

Some crucial features, such as the diameter and lead angle of the internal thread, are beyond the scope of this dissertation. The three-dimensional reconstruction of internal threads to improve automated optical measurement remains a subject for further research.

For the developed prototype OTPG, the inspection time includes image grabbing and image processing. The former takes about 10 minutes and the latter takes less than 6 seconds in inspecting an internal thread with diameter 15.3mm and length 20mm. The image registration time is the bottleneck of the OTPG approach. It is worth studying how to reduce the image registration time for further research.

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