Research Article
PRO: A Novel Approach to Precision and Reliability Optimization Based Dominant Point Detection
Table 2
Quantitative comparison of the results of Experiment 2 for standard digital curves [
14,
16]. (
: number of dominant points).
| | MPLS | MRLS | MPDC | MRDC | ADR | | ISE | FOM | Time (sec) | |
| Chromosome | Number of pixels = 61 | PRO0.2 | 0.1961 | 0.1538 | 0.0056 | 0.0074 | 0.5902 | 0.2774 | 0.1538 | 11.0139 | 0.1789 | 35 | PRO0.6 | 0.5606 | 0.5000 | 0.3559 | 0.2821 | 0.1967 | 0.8944 | 11.0088 | 0.4618 | 0.0454 | 11 | PRO1.0 | 0.9250 | 0.8200 | 0.4022 | 0.3222 | 0.1803 | 2.1213 | 16.3088 | 0.3400 | 0.0423 | 10 | RDP1 | 0.5606 | 0.5000 | 0.3559 | 0.2821 | 0.1967 | 0.8944 | 11.0088 | 0.4618 | 0.0479 | 11 | RDP2 | 1.2566 | 1.0032 | 0.7142 | 0.7065 | 0.1475 | 2.0000 | 59.9961 | 0.1130 | 0.0310 | 8 | RDP3 | 1.4320 | 1.5800 | 1.1293 | 0.9662 | 0.1148 | 2.3016 | 91.1803 | 0.0956 | 0.0235 | 6 | Masood [14] | 0.5298 | 0.3962 | 0.2607 | 0.2210 | 0.1967 | 1.2362 | 7.6233 | 0.6668 | 0.2368 | 11 | Carmona-Poyato et al. [16, 19] | 0.9798 | 1.1068 | 0.4103 | 0.3946 | 0.1803 | 1.5855 | 23.7435 | 0.2336 | 0.0293 | 10 | Marji and Siy [41] | 0.5298 | 0.3962 | 0.3252 | 0.2650 | 0.1803 | 1.2362 | 10.0067 | 0.5542 | — | 11 | Teh and Chin [9] | 3.0075 | 5.7931 | 0.5010 | 0.6940 | 0.2295 | 5.3852 | 124.8102 | 0.0349 | — | 14 | Ansari and Huang [10] | 0.9487 | 1.1000 | 0.3544 | 0.3226 | 0.2787 | 1.5811 | 16.1670 | 0.2219 | — | 17 | B. K. Ray and K. S. Ray [12] | 0.3835 | 0.2941 | 0.2087 | 0.1593 | 0.3115 | 0.6860 | 5.1227 | 0.6267 | — | 19 | B. K. Ray and K. S. Ray [42] | 0.3589 | 0.2459 | 0.2171 | 0.1601 | 0.3115 | 0.6402 | 4.8897 | 0.6566 | — | 19 | Arcelli and Ramella [43] | 1.4320 | 1.5405 | 0.6943 | 0.5715 | 0.1311 | 2.3016 | 44.2227 | 0.1724 | — | 8 | Sarkar [13] | 0.3101 | 0.2353 | 0.1341 | 0.1511 | 0.3279 | 0.5547 | 3.8567 | 0.7908 | — | 20 | Cronin [11] | 0.3162 | 0.2500 | 0.1400 | 0.1081 | 0.2951 | 0.6325 | 3.1812 | 1.0653 | — | 18 |
| Leaf | Number of pixels = 124 | PRO0.2 | 0.1961 | 0.1538 | 0.0036 | 0.0039 | 0.4516 | 0.2774 | 0.1538 | 14.3929 | 0.3427 | 55 | PRO0.6 | 0.5621 | 0.6000 | 0.3257 | 0.2935 | 0.1774 | 1.0525 | 21.6953 | 0.2598 | 0.0911 | 21 | PRO1.0 | 0.8165 | 0.7838 | 0.4123 | 0.3795 | 0.1532 | 1.3152 | 36.6993 | 0.1778 | 0.0712 | 18 | RDP1 | 0.5621 | 0.6000 | 0.3020 | 0.2679 | 0.1855 | 0.9939 | 19.1722 | 0.2812 | 0.1013 | 22 | RDP2 | 1.3651 | 1.1142 | 0.5172 | 0.4918 | 0.1371 | 2.0000 | 65.4687 | 0.1114 | 0.0598 | 16 | RDP3 | 1.3651 | 1.1142 | 0.5172 | 0.4918 | 0.1371 | 2.0000 | 65.4687 | 0.1114 | 0.0598 | 16 | Masood [14] | 0.4243 | 0.3909 | 0.2223 | 0.1983 | 0.1855 | 0.9487 | 12.7075 | 0.4243 | 0.6137 | 22 | Carmona-Poyato et al. [16, 19] | 0.5164 | 0.4698 | 0.2652 | 0.2431 | 0.1694 | 0.9899 | 16.8155 | 0.3512 | 0.0681 | 20 | Marji and Siy [41] | 0.7259 | 0.6034 | 0.4056 | 0.3605 | 0.1452 | 1.2957 | 31.3875 | 0.2195 | — | 18 | Teh and Chin [9] | 0.5621 | 0.5488 | 0.2062 | 0.2339 | 0.2419 | 1.0525 | 18.5508 | 0.2228 | — | 30 | Ansari and Huang [10] | 0.7906 | 1.5000 | 0.2665 | 0.2666 | 0.2419 | 1.4142 | 24.1675 | 0.1710 | — | 30 | B. K. Ray and K. S. Ray [12] | 0.5648 | 0.5410 | 0.2133 | 0.2069 | 0.2581 | 0.9959 | 15.3456 | 0.2525 | — | 32 | B. K. Ray and K. S. Ray [42] | 0.6112 | 0.5410 | 0.2027 | 0.1993 | 0.2661 | 1.1142 | 15.0609 | 0.2495 | — | 33 | Arcelli and Ramella [43] | 1.3651 | 1.1041 | 0.4999 | 0.4968 | 0.1371 | 1.9508 | 64.2461 | 0.1135 | — | 17 | Sarkar [13] | 0.6112 | 0.5172 | 0.2835 | 0.2614 | 0.1935 | 1.1142 | 18.0333 | 0.2865 | — | 24 | Cronin [11] | 0.4873 | 0.4500 | 0.1700 | 0.1397 | 0.2339 | 0.9487 | 8.9810 | 0.4761 | — | 29 |
| Semicircle | Number of pixels = 103 | PRO0.2 | 0.1961 | 0.1538 | 0.0178 | 0.0190 | 0.4369 | 0.2774 | 0.6154 | 3.7194 | 0.2545 | 44 | PRO0.6 | 0.5566 | 0.4148 | 0.3025 | 0.2732 | 0.1553 | 1.5860 | 18.1298 | 0.3551 | 0.0715 | 15 | PRO1.0 | 0.9539 | 0.8400 | 0.4547 | 0.3955 | 0.1262 | 1.5556 | 33.7812 | 0.2345 | 0.0494 | 12 | RDP1 | 0.4851 | 0.3448 | 0.2604 | 0.2159 | 0.1845 | 1.0000 | 13.6577 | 0.3969 | 0.0814 | 18 | RDP2 | 0.9539 | 0.8400 | 0.4547 | 0.3955 | 0.1262 | 1.5556 | 33.7812 | 0.2345 | 0.0495 | 12 | RDP3 | 1.6884 | 1.7692 | 0.7132 | 0.5987 | 0.1068 | 2.6047 | 77.7992 | 0.1204 | 0.0374 | 10 | Masood [14] | 0.5086 | 0.4054 | 0.1389 | 0.1021 | 0.2621 | 1.1508 | 5.3936 | 0.7073 | 0.4405 | 26 | Carmona-Poyato et al. [16, 19] | 0.4988 | 0.4390 | 0.2255 | 0.2061 | 0.2136 | 0.8835 | 11.9412 | 0.3921 | 0.0514 | 21 | Marji and Siy [41] | 0.7259 | 0.6034 | 0.4056 | 0.3605 | 0.1452 | 1.2957 | 31.3875 | 0.2195 | — | 16 | Teh and Chin [9] | 0.5621 | 0.5488 | 0.2062 | 0.2339 | 0.2419 | 1.0525 | 18.5508 | 0.2228 | — | 24 | Ansari and Huang [10] | 0.7906 | 1.5000 | 0.2665 | 0.2666 | 0.2419 | 1.4142 | 24.1675 | 0.1710 | — | 29 | B. K. Ray and K. S. Ray [12] | 0.5648 | 0.5410 | 0.2133 | 0.2069 | 0.2581 | 0.9959 | 15.3456 | 0.2525 | — | 30 | B. K. Ray and K. S. Ray [42] | 0.6112 | 0.5410 | 0.2027 | 0.1993 | 0.2661 | 1.1142 | 15.0609 | 0.2495 | — | 28 | Arcelli and Ramella [43] | 1.3651 | 1.1041 | 0.4999 | 0.4968 | 0.1371 | 1.9508 | 64.2461 | 0.1135 | — | 10 | Sarkar [13] | 0.6112 | 0.5172 | 0.2835 | 0.2614 | 0.1935 | 1.1142 | 18.0333 | 0.2865 | — | 20 | Cronin [11] | 0.4873 | 0.4500 | 0.1700 | 0.1397 | 0.2339 | 0.9487 | 8.9810 | 0.4761 | — | 31 |
| Infinity | Number of pixels = 46 | PRO0.2 | 0.1961 | 0.1538 | 0.0070 | 0.0101 | 0.6304 | 0.2774 | 0.1538 | 10.3103 | 0.1532 | 28 | PRO0.6 | 0.5684 | 0.5385 | 0.3128 | 0.2341 | 0.2174 | 1.1094 | 6.2977 | 0.7304 | 0.0329 | 9 | PRO1.0 | 0.8793 | 0.7123 | 0.4830 | 0.4264 | 0.1739 | 1.6386 | 19.9482 | 0.2882 | 0.0222 | 7 | RDP1 | 0.4758 | 0.3585 | 0.3042 | 0.2458 | 0.2174 | 0.9713 | 6.6735 | 0.6893 | 0.0363 | 9 | RDP2 | 0.8793 | 0.7123 | 0.4830 | 0.4264 | 0.1739 | 1.6386 | 19.9482 | 0.2882 | 0.0225 | 7 | RDP3 | 1.5479 | 1.5479 | 0.9760 | 0.8147 | 0.1304 | 2.3408 | 53.8220 | 0.1428 | 0.0195 | 5 | Masood [14] | 0.7268 | 0.5846 | 0.3556 | 0.3096 | 0.1957 | 1.4033 | 10.2482 | 0.4987 | 0.1503 | 8 | Carmona-Poyato et al. [16, 19] | 1.1243 | 0.9600 | 0.6911 | 0.5871 | 0.1522 | 1.8000 | 31.6866 | 0.2074 | 0.0266 | 6 |
| Dog | Number of pixels = 458 | PRO0.2 | 0.1961 | 0.1538 | 0.0055 | 0.0062 | 0.4672 | 0.2774 | 0.9231 | 2.3185 | 1.6761 | 213 | PRO0.6 | 0.5943 | 0.5098 | 0.2748 | 0.2467 | 0.1288 | 1.4486 | 73.6651 | 0.1054 | 0.3485 | 58 | PRO1.0 | 0.9841 | 0.8714 | 0.5626 | 0.4635 | 0.0873 | 2.1374 | 207.8683 | 0.0551 | 0.2178 | 39 | RDP1 | 0.8321 | 0.7500 | 0.2829 | 0.2397 | 0.1332 | 1.0000 | 71.7364 | 0.1047 | 0.3689 | 60 | RDP2 | 1.2774 | 1.1647 | 0.5298 | 0.4341 | 0.0917 | 1.9524 | 190.9351 | 0.0571 | 0.2283 | 41 | RDP3 | 1.8932 | 1.6500 | 0.8170 | 0.6867 | 0.0764 | 2.8460 | 454.1739 | 0.0288 | 0.2083 | 34 | Masood [14] | 0.3780 | 0.3000 | 0.1203 | 0.1155 | 0.2249 | 1.0000 | 21.3056 | 0.2087 | 26.4447 | 102 | Carmona-Poyato et al. [16, 19] | 0.9238 | 0.7844 | 0.3349 | 0.3152 | 0.1157 | 1.7171 | 115.3301 | 0.0749 | 0.6452 | 52 |
| Maple leaf | Number of pixels = 504 | PRO0.2 | 0.1961 | 0.1538 | 0.0094 | 0.0113 | 0.5000 | 0.2774 | 1.8462 | 1.0833 | 2.1433 | 251 | PRO0.6 | 0.5774 | 0.5000 | 0.2815 | 0.2379 | 0.1250 | 1.2308 | 69.1412 | 0.1157 | 0.4042 | 62 | PRO1.0 | 0.9623 | 0.7056 | 0.4776 | 0.4043 | 0.0853 | 2.0000 | 191.9178 | 0.0611 | 0.2627 | 42 | RDP1 | 0.5606 | 0.4667 | 0.2543 | 0.2176 | 0.1329 | 1.0000 | 58.8400 | 0.1278 | 0.4355 | 66 | RDP2 | 1.0871 | 0.9542 | 0.5028 | 0.4467 | 0.0813 | 2.0000 | 218.7481 | 0.0562 | 0.2436 | 40 | RDP3 | 1.6786 | 1.5244 | 1.0533 | 0.8735 | 0.0456 | 2.8943 | 724.6112 | 0.0302 | 0.1356 | 22 | Masood [14] | 0.7071 | 0.6667 | 0.2003 | 0.1742 | 0.1389 | 1.0000 | 36.7885 | 0.1957 | 52.6449 | 69 | Carmona-Poyato et al. [16, 19] | 1.9524 | 1.6100 | 1.1309 | 0.9602 | 0.0437 | 3.3661 | 871.9568 | 0.0263 | 0.7954 | 21 |
| Africa | Number of pixels = 431 | PRO0.2 | 0.1961 | 0.1538 | 0.0123 | 0.0132 | 0.4478 | 0.2774 | 1.8462 | 1.2096 | 1.4901 | 192 | PRO0.6 | 0.5572 | 0.4595 | 0.3255 | 0.2927 | 0.0905 | 1.3868 | 83.4013 | 0.1325 | 0.2132 | 38 | PRO1.0 | 0.9746 | 0.8985 | 0.5518 | 0.4355 | 0.0603 | 2.0000 | 175.1830 | 0.0946 | 0.1322 | 25 | RDP1 | 0.6417 | 0.5000 | 0.2755 | 0.2450 | 0.1114 | 1.0000 | 61.3082 | 0.1465 | 0.2818 | 47 | RDP2 | 1.0024 | 0.8985 | 0.5930 | 0.4758 | 0.0580 | 1.9723 | 203.4529 | 0.0847 | 0.1246 | 24 | RDP3 | 1.4404 | 1.2574 | 0.6865 | 0.5469 | 0.0534 | 2.4244 | 274.5463 | 0.0683 | 0.1185 | 22 | Masood [14] | 0.4880 | 0.3814 | 0.2147 | 0.1909 | 0.1206 | 1.0153 | 36.3878 | 0.2278 | 26.0222 | 51 | Carmona-Poyato et al. [16, 19] | 0.9354 | 0.7803 | 0.4861 | 0.4023 | 0.0603 | 2.0000 | 148.2542 | 0.1118 | 0.5915 | 25 |
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