Fig. 1. Grayscale distribution of interference fringe. (a) Tangential direction; (b) normal direction
Fig. 2. Interference fringe patterns. (a) Original image; (b) R-value image; (c) Gaussian filter image
Fig. 3. Grayscale along normal direction. (a) Original image; (b) after Gaussian filtering
Fig. 4. Schematic of interval fitting
Fig. 5. Results of curve fitting. (a) f1(x); (b) f2(x)
Fig. 6. Images of f1(x) and f2(x) and filtered image
Fig. 7. Image of f(x)=f2(x)-f1(x)
Fig. 8. Extraction results. (a) Interference fringe pattern; (b) centerline extraction result
Fig. 9. Interference fringe patterns. (a) Image 1; (b) image 2; (c) image 3; (d) image 4; (e) image 5
Fig. 10. Known centerline images. (a) Image 6; (b) image 7; (c) image 8; (d) image 9; (e) image 10
Fitting method | SSE | RMSE | Rsquare | RAdj-sq |
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Gaussian curve fitting | 218.7985 | 3.9533 | 0.9971 | 0.9965 | Polynomial curve fitting | 1187.9 | 9.2112 | 0.9835 | 0.9812 | Proposed method | 141.458 | 3.2970 | 0.9980 | 0.9976 |
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Table 1. Comparison of statistical parameters of three curve fitting methods
Algorithm | Average processing time /s |
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Image 1 | Image 2 | Image 3 | Image 4 | Image 5 |
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Gray threshold algorithm[8] | 0.8201 | 0.9554 | 0.9841 | 0.9344 | 0.8406 | Steger algorithm[12] | 6.8448 | 7.7812 | 8.2662 | 8.6523 | 7.0884 | Gray-gravity algorithm[22] | 0.3250 | 0.4390 | 0.4006 | 0.4305 | 0.2977 | Proposed algorithm | 0.6415 | 0.7981 | 0.7807 | 0.8347 | 0.6306 |
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Table 2. Comparison of average processing time of extracting results by four methods
Algorithm | RMSE /pixel |
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Image 6 | Image 7 | Image 8 | Image 9 | Image 10 |
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Gray threshold algorithm[8] | 0.9840 | 1.6773 | 2.5175 | 1.5126 | 1.4967 | Steger algorithm[12] | 0.0521 | 0.0642 | 0.0489 | 0.0562 | 0.0601 | Gray-gravity algorithm[22] | 0.3930 | 0.5581 | 0.2589 | 0.4374 | 0.4895 | Proposed algorithm | 0.0424 | 0.0441 | 0.0195 | 0.0463 | 0.0449 |
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Table 3. RMSE comparison between the extraction results of the four methods and the standard value