Table 1.
RMSE Comparisons for Different Methods in Simulated Fringe Pattern (1) with Carrier Frequency of
Method/Noise variance | Proposed method 1 | Proposed method 2 | DOG wavelet using our cost function | 1D Morlet with their cost function ridge | 2D Gabor with direct modulus maximum ridge | 2D Fan with direct modulus maximum ridge |
0.0 | 0.0273 | 0.0045 | 0.0041 | 0.0241 | 0.0213 | 0.0171 |
0.2 | 0.0366 | 0.0265 | 0.0410 | 0.0289 | 0.0221 | 0.0211 |
0.5 | 0.0602 | 0.0582 | 0.0401 | 0.0468 | 0.0267 | 0.0349 |
0.9 | 0.0974 | 0.0727 | 0.0714 | 0.0764 | 0.0363 | 0.0574 |
1.2 | 0.1213 | 0.0969 | 0.0952 | 0.1000 | 0.0448 | 0.0752 |
1.5 | 0.1397 | 0.1213 | 0.1191 | 0.1242 | 0.0538 | 0.0934 |
1.8 | 0.1580 | 0.1459 | 0.1433 | 0.1492 | 0.0632 | 0.1118 |
2.0 | 0.1713 | 0.1625 | 0.1596 | 0.1663 | 0.0696 | 0.1240 |
Table 2.
RMSE Comparisons for Different Methods in Simulated Fringe Pattern (1) with Carrier Frequency of
Method/Noise variance | Proposed method 1 | Proposed method 2 | DOG wavelet using our cost function | 1D Morlet with their cost function ridge | 2D Gabor with direct modulus maximum ridge | 2D Fan with direct modulus maximum ridge |
0.0 | 0.0120 | 0.0116 | 0.0134 | 0.0913 | 0.0453 | 0.0699 |
0.2 | 0.0155 | 0.0183 | 0.0164 | 0.0921 | 0.0455 | 0.0701 |
0.5 | 0.0250 | 0.0259 | 0.0272 | 0.0957 | 0.0462 | 0.0709 |
0.9 | 0.0389 | 0.0395 | 0.0405 | 0.1046 | 0.0480 | 0.0732 |
1.2 | 0.0494 | 0.0507 | 0.0516 | 0.1137 | 0.0499 | 0.0757 |
1.5 | 0.0598 | 0.0621 | 0.0630 | 0.1244 | 0.0523 | 0.0789 |
1.8 | 0.0710 | 0.0738 | 0.0747 | 0.1365 | 0.0550 | 0.0826 |
2.0 | 0.0770 | 0.0816 | 0.0826 | 0.1451 | 0.0570 | 0.0854 |
Table 3.
RMSE Comparisons for Different Methods in Simulated Fringe Pattern (1) with Carrier Frequency of
Method/Noise variance | Proposed method 1 | Proposed method 2 | DOG wavelet using our cost function | 1D Morlet with their cost function ridge | 2D Gabor with direct modulus maximum ridge | 2D Fan with direct modulus maximum ridge |
0.0 | 0.0349 | 0.0465 | 0.0439 | 0.2410 | 0.2544 | 0.1998 |
0.2 | 0.0361 | 0.0468 | 0.0442 | 0.2413 | 0.2567 | 0.1995 |
0.5 | 0.0452 | 0.0479 | 0.0547 | 0.2420 | 0.2602 | 0.1991 |
0.9 | 0.0514 | 0.0503 | 0.0573 | 0.2440 | 0.2644 | 0.1987 |
1.2 | 0.0566 | 0.0525 | 0.0600 | 0.2461 | 0.2670 | 0.1984 |
1.5 | 0.0620 | 0.0549 | 0.0634 | 0.2492 | 0.2688 | 0.1982 |
1.8 | 0.0674 | 0.0643 | 0.0672 | 0.2556 | 0.2705 | 0.1981 |
2.0 | 0.0711 | 0.0658 | 0.0700 | 0.2597 | 0.2719 | 0.1980 |
Table 4.
RMSE Comparisons for Different Methods in Simulated Fringe Pattern (2) with Carrier Frequency of
Method/Noise variance | Proposed method 1 | Proposed method 2 | DOG wavelet using our cost function | 1D Morlet with their cost function ridge | 2D Gabor with direct modulus maximum ridge | 2D Fan with direct modulus maximum ridge |
0.0 | 0.0899 | 0.0282 | 0.0138 | 0.0959 | 0.0519 | 0.0729 |
0.2 | 0.0934 | 0.0332 | 0.0348 | 0.0971 | 0.0525 | 0.0737 |
0.5 | 0.1062 | 0.0523 | 0.0536 | 0.1031 | 0.0553 | 0.0776 |
0.9 | 0.1210 | 0.0842 | 0.0857 | 0.1188 | 0.0622 | 0.0871 |
1.2 | 0.1356 | 0.1098 | 0.1116 | 0.1349 | 0.0691 | 0.0972 |
1.5 | 0.1541 | 0.1360 | 0.1382 | 0.1542 | 0.0771 | 0.1095 |
1.8 | 0.1760 | 0.1628 | 0.1655 | 0.1762 | 0.0859 | 0.1238 |
2.0 | 0.1912 | 0.1810 | 0.1841 | 0.1914 | 0.0921 | 0.1347 |
Table 5.
RMSE Comparisons for Different Methods in Simulated Fringe Pattern (2) with Carrier Frequency of
Method/Noise variance | Proposed method 1 | Proposed method 2 | DOG wavelet using our cost function | 1D Morlet with their cost function ridge | 2D Gabor with direct modulus maximum ridge | 2D Fan with direct modulus maximum ridge |
0.0 | 0.0630 | 0.0804 | 0.0655 | 0.1297 | 0.4034 | 0.1641 |
0.2 | 0.0643 | 0.0812 | 0.0966 | 0.1499 | 2.8211 | 0.1649 |
0.5 | 0.0687 | 0.0855 | 0.1016 | 0.2176 | 2.9587 | 0.1662 |
0.9 | 0.0772 | 0.0961 | 0.1137 | 0.1734 | 2.8102 | 0.1688 |
1.2 | 0.0846 | 0.1068 | 0.1260 | 0.1806 | 2.9319 | 0.1734 |
1.5 | 0.0931 | 0.1192 | 0.1405 | 0.1857 | 2.6358 | 0.1776 |
1.8 | 0.1017 | 0.1330 | 0.1565 | 0.1985 | 2.6364 | 0.1845 |
2.0 | 0.1077 | 0.1428 | 0.1680 | 0.2058 | 2.6390 | 0.1907 |
Table 6.
Time-Consuming Comparison Among Our Methods and the Others
Method | Proposed first method | Proposed second method | 1D Complex Morlet with cost function ridge | 2D fan WT | 2D Gabor WT |
Time-consuming (s) | 6.91 | 3.89 | 482.48 | 51.86 | 9.22 |
Table 7.
Comparison of Results between the Level (RMSE) Obtained Using the Proposed First Method and the Optimal Level ()
| Simulated fringe pattern (1) with carrier frequency of | Simulated fringe pattern (1) with carrier frequency of | Simulated fringe pattern (1) with carrier frequency of | Simulated fringe pattern (2) with carrier frequency of | Simulated fringe pattern (2) with carrier frequency of |
Noise variance 0 | 5 (0.0196) | 5 (0.0120) | 6 (0.0349) | 4 (0.0899) | 5 (0.0630) |
5 (0.0196) | 5 (0.0120) | 6 (0.0349) | 4 (0.0899) | 5 (0.0630) |
Noise variance 0.2 | 5 (0.0315) | 5 (0.0155) | 6 (0.0361) | 4 (0.0934) | 5 (0.0643) |
5 (0.0315) | 5 (0.0155) | 6 (0.0361) | 4 (0.0934) | 5 (0.0643) |
Noise variance 0.5 | 5 (0.0579) | 5 (0.0250) | 5 (0.0452) | 3 (0.1062) | 5 (0.0687) |
5 (0.0579) | 5 (0.0250) | 6 (0.0404) | 4 (0.1012) | 5 (0.0687) |
Noise variance 0.9 | 5 (0.0966) | 5 (0.0389) | 5 (0.0514) | 3 (0.1210) | 5 (0.0772) |
5 (0.0966) | 5 (0.0389) | 6 (0.0476) | 4 (0.1172) | 5 (0.0772) |
Noise variance 1.2 | 5 (0.1211) | 5 (0.0494) | 5 (0.0566) | 3 (0.1356) | 5 (0.0846) |
5 (0.1211) | 5 (0.0494) | 6 (0.0534) | 4 (0.1328) | 5 (0.0846) |
Noise variance 1.5 | 5 (0.1405) | 5 (0.0598) | 5 (0.0620) | 3 (0.1541) | 5 (0.0931) |
5 (0.1405) | 5 (0.0598) | 6 (0.0593) | 4 (0.1523) | 5 (0.0931) |
Noise variance 1.8 | 5 (0.1597) | 4 (0.0710) | 5 (0.0674) | 3 (0.1760) | 5 (0.1017) |
5 (0.1597) | 5 (0.0697) | 6 (0.0653) | 4 (0.1750) | 5 (0.1017) |
Noise variance 2.0 | 5 (0.1736) | 4 (0.0770) | 5 (0.0711) | 3 (0.1912) | 5 (0.1077) |
5 (0.1736) | 5 (0.0760) | 6 (0.0693) | 4 (0.1907) | 5 (0.1077) |
Table 8.
Comparison of Results between the Scale (RMSE) Obtained Using the Proposed Second Method and the Optimal Scale ()
| Simulated fringe pattern (1) with carrier frequency of | Simulated fringe pattern (1) with carrier frequency of | Simulated fringe pattern (1) with carrier frequency of | Simulated fringe pattern (2) with carrier frequency of | Simulated fringe pattern (2) with carrier frequency of |
Noise variance 0 | 2 (0.0069) | 3 (0.0116 | 4 (0.0804) | 2 (0.0282) | 4 (0.0804) |
1 (0.0045) | 2 (0.0093) | 2 (0.0412) | 1 (0.0129) | 2 (0.0412) |
Noise variance 0.2 | 2 (0.0174) | 4 (0.0183) | 4 (0.0812) | 2 (0.0332) | 4 (0.0812) |
2 (0.0174) | 3 (0.0160) | 2 (0.0551) | 2 (0.0332) | 2 (0.0551) |
Noise variance 0.5 | 2 (0.0406) | 4 (0.0259) | 4 (0.0855) | 2 (0.0523) | 4 (0.0855) |
2 (0.0406) | 4 (0.0259) | 3 (0.0676) | 2 (0.0523) | 3 (0.0676) |
Noise variance 0.9 | 2 (0.0724) | 4 (0.0395) | 4 (0.0961) | 2 (0.0842) | 4 (0.0961) |
2 (0.0724) | 4 (0.0395) | 3 (0.0868) | 2 (0.0842) | 3 (0.0868) |
Noise variance 1.2 | 2 (0.0965) | 4 (0.0507) | 4 (0.1068) | 2 (0.1098) | 4 (0.1068) |
2 (0.0965) | 4 (0.0507) | 4 (0.1068) | 2 (0.1098) | 3 (0.1045) |
Noise variance 1.5 | 2 (0.1208) | 4 (0.0621) | 4 (0.1192) | 2 (0.1360) | 4 (0.1192) |
2 (0.1208) | 4 (0.0621) | 4 (0.1192) | 2 (0.1360) | 4 (0.1192) |
Noise variance 1.8 | 2 (0.1454) | 4 (0.0738) | 4 (0.1330) | 2 (0.1628) | 4 (0.1330) |
2 (0.1454) | 4 (0.0738) | 4 (0.1330) | 2 (0.1628) | 4 (0.1330) |
Noise variance 2.0 | 2 (0.1619) | 4 (0.0816) | 4 (0.1428) | 2 (0.1810) | 4 (0.1428) |
2 (0.1619) | 4 (0.0816) | 4 (0.1428) | 2 (0.1810) | 4 (0.1428) |