Table 1
Values of c(m, N) for N ≤ 128
N | Values of c(m, N) |
---|
8 | 0.75 | 0.25 | | | | | | |
16 | 0.625 | 0.125 | 0.125 | 0.125 | | | | |
32 | 0.8125 | −0.1875 | 0.0625 | −0.1875 | −0.1875 | 0.3125 | 0.0625 | 0.3125 |
64 | 0.759191 | −0.181985 | 0.0900735 | −0.181985 | −0.093750 | 0.273897 |
| −0.0275735 | 0.0386029 | 0.0533088 | −0.055147 | −0.0275735 | −0 055147 |
| −0.093750 | 0.0386029 | 0.0900735 | 0.273897 | | |
128 | 0.763859 | −0.134031 | 0.0153034 | −0.047955 | −0.0905756 | 0.0186303 |
| −0.0594284 | −0.0456101 | 0.0266544 | −0.0174346 | −0.0594284 | −0.0174347 |
| −0.0317441 | −0.0456101 | 0.0153034 | 0.0186303 | −0.0466643 | −0.047955 |
| 0.0747702 | −0.134031 | −0.0031744 | 0.255267 | | 0.0318550 |
| 0.0266544 | 0.011920 | 0.0318550 | 0.011920 | −0.0905756 | 0.0842131 |
| 0.747702 | 0.255267 | | | | |
Table 2
Euclidean Distances between the Test Object and the Library Object for the DFT–FD Method
Test Object | Type of Normalization | Euclidean Distance from the Following Library Object |
---|
|
---|
a | b | c | d | e | f |
---|
a | I | 0 | 0.2500 | 0.3684 | 0.3216 | 0.2679 | 0.4985 |
| II | 0 | 0.293 | 0.4219 | 0.3814 | 0.355 | 0.422 |
| III | 0 | 0.293 | 0.4219 | 0.3814 | 0.355 | 0.422 |
b | I | 0 | 0.2500 | 0 | 0.4899 | 0.3067 | 0.5429 |
| II | 0.293 | 0 | 0.4105 | 0.3862 | 0.3428 | 0.3873 |
| III | 0.293 | 0 | 0.4105 | 0.3862 | 0.3428 | 0.3873 |
c | I | 0.3684 | 0.4864 | 0 | 0.1887 | 0.2824 | 0.4607 |
| II | 0.4219 | 0.4105 | 0 | 0.1231 | 0.4405 | 0.092 |
| III | 0.4219 | 0.4105 | 0 | 0.1231 | 0.4405 | 0.092 |
d | I | 0.3216 | 0.4899 | 0.1887 | 0 | 0.2906 | 0.4761 |
| II | 0.3814 | 0.3862 | 0.1231 | 0 | 0.4216 | 0.184 |
| III | 0.3814 | 0.3862 | 0.1231 | 0 | 0.4216 | 0.184 |
e | I | 0.2679 | 0.3067 | 0.2824 | 0.2906 | 0 | 0.4799 |
| II | 0.355 | 0.3428 | 0.4405 | 0.4216 | 0 | 0.415 |
| III | 0.355 | 0.3428 | 0.4405 | 0.4216 | 0 | 0.415 |
f | I | 0.4985 | 0.5429 | 0.4607 | 0.4761 | 0.4799 | 0 |
| II | 0.422 | 0.3873 | 0.092 | 0.184 | 0.415 | 0 |
| III | 0.422 | 0.3873 | 0.092 | 0.184 | 0.415 | 0 |
Table 3
Euclidean Distances between the Test Object and the Library Object for the DRWT–FD Method
Test Object | Type of Normalization | Euclidean Distance from the Following Library Object |
---|
|
---|
a | b | c | d | e | f |
---|
a | I | 0 | 0.2553 | 0.3762 | 0.3258 | 0.2767 | 0.5671 |
| II | 0 | 1.354 | 0.6161 | 0.6296 | 0.7224 | 0.5730 |
| III | 0 | 0.6816 | 0.3695 | 0.3241 | 0.2848 | 0.3328 |
b | I | 0.2553 | 0 | 0.5021 | 0.4979 | 0.3253 | 0.6251 |
| II | 1.354 | 0 | 1.402 | 1.366 | 1.352 | 1.356 |
| III | 0.6816 | 0 | 0.7352 | 0.7562 | 0.6119 | 0.6372 |
c | I | 0.3762 | 0.5021 | 0 | 0.1988 | 0.2984 | 0.5276 |
| II | 0;6161 | 1.402 | 0 | 0.1988 | 0.2986 | 0.1995 |
| III | 0.3695 | 0.7352 | 0 | 0.2201 | 0.2909 | 0.2105 |
d | I | 0.3258 | 0.4979 | 0.1988 | 0 | 0.2925 | 0.5399 |
| II | 0.6296 | 1.366 | 0.1988 | 0 | 0.2924 | 0.3124 |
| III | 0.3241 | 0.7562 | 0.2201 | 0 | 0.3213 | 0.3467 |
e | I | 0.2767 | 0.3253 | 0.2984 | 0.2925 | 0 | 0.5614 |
| II | 0.7224 | 1.352 | 0.2986 | 0.2924 | 0 | 0.2972 |
| III | 0.2848 | 0.6119 | 0.2909 | 0.3213 | 0 | 0.2821 |
f | I | 0.5671 | 0.6251 | 0.5276 | 0.5399 | 0.5614 | 0 |
| II | 0.5730 | 1.356 | 0.1995 | 0.3124 | 0.2972 | 0 |
| III | 0.3328 | 0.6372 | 0.2105 | 0.3467 | 0.2821 | 0 |
Table 4
Percentage of Correct Shape Recognition
SNR (dB) | Type of Normalization | % Correct Shape Recognition |
---|
|
---|
DFT Method | DRWT Method |
---|
3 | I | 16.7 | 33.3 |
II | 50 | 50 |
III | 50 | 83.3 |
10 | I | 50 | 66.7 |
II | 66.7 | 66.7 |
III | 66.7 | 100 |
20 | I | 83.3 | 83.3 |
II | 66.7 | 83.3 |
III | 66.7 | 100 |
30 | I | 83.3 | 83.3 |
II | 83.3 | 100 |
III | 83.3 | 100 |
∞ | I | 100 | 100 |
II | 100 | 100 |
III | 100 | 100 |
Table 5
Percentage of Correct Shape Recognition When the Test Object Is Rotated and the Starting Point Is Shifted
SNR (dB) | Type of Normalization | % Correct Shape Recognition |
---|
|
---|
DFT Method | DRWT Method |
---|
3 | I | 16.7 | 33.3 |
II | 50 | 66.7 |
III | 33.3 | 66.7 |
10 | I | 50 | 66.7 |
II | 66.7 | 66.7 |
III | 66.7 | 83.3 |
20 | I | 83.3 | 83.3 |
II | 66.7 | 83.3 |
III | 66.7 | 100 |
30 | I | 83.3 | 83.3 |
II | 83.3 | 83.3 |
III | 83.3 | 100 |
∞ | I | 100 | 100 |
II | 100 | 100 |
III | 100 | 100 |
Table 6
Percentage of Correct Signal Recognition When the Signals Are Similar
SNR (dB) | % Correct Signal Recognition |
---|
|
---|
DFT Method | DRWT Method |
---|
3 | 16.7 | 33.3 |
10 | 33.3 | 33.3 |
20 | 33.3 | 66.7 |
30 | 50.0 | 100 |
40 | 66.7 | 100 |
Table 7
Percentage of Correct Signal Recognition When the Signals Are Dissimilar
SNR (dB) | % Correct Signal 1 Recognition |
---|
|
---|
DFT Method | DRWT Method |
---|
3 | 100 | 66.7 |
10 | 100 | 100 |
20 | 100 | 100 |
30 | 100 | 100 |
40 | 100 | 100 |
Table 8
Percentage of Correct Image Recognition When the Images Are Dissimilar (Maximum-Amplitude Transform Coefficients As Features): Image Set 1
SD | % Correct Image Recognition |
---|
|
---|
DFT Method | DRWT Method |
---|
5 | 100 | 100 |
10 | 100 | 100 |
20 | 100 | 100 |
30 | 100 | 100 |
50 | 83.3 | 83.3 |
Table 9
Percentage of Correct Image Recognition When the Images Are Dissimilar (Low-Frequency Transform Coefficients As Features): Image Set 1
SD | % Correct Image Recognition |
---|
|
---|
DFT Method | DRWT Method |
---|
5 | 100 | 100 |
10 | 100 | 100 |
20 | 100 | 100 |
50 | 83.3 | 100 |
70 | 83.3 | 83.3 |
Table 10
Percentage of Correct Image Recognition When the Images Are Dissimilar (Maximum-Amplitude Transform Coefficients As Features): Image Set 2
SD | % Correct Image Recognition |
---|
|
---|
DFT Method | DRWT Method |
---|
5 | 100 | 100 |
10 | 100 | 100 |
20 | 100 | 100 |
50 | 100 | 100 |
70 | 83.3 | 83.3 |
Table 11
Percentage of Correct Image Recognition When the Images Are Dissimilar (Low-Frequency Transform Coefficients As Features): Image Set 2
SD | % Correct Image Recognition |
---|
|
---|
DFT Method | DRWT Method |
---|
5 | 100 | 100 |
10 | 100 | 100 |
20 | 100 | 100 |
50 | 100 | 100 |
70 | 83.3 | 100 |
Table 12
Percentage of Correct Image Recognition When the Images Are Similar (Maximum-Amplitude Transform Coefficients As Features): Gray-Level Image Set
SD | % Correct Image Recognition |
---|
|
---|
DFT Method | DRWT Method |
---|
5 | 100 | 100 |
10 | 100 | 100 |
20 | 100 | 100 |
30 | 66.7 | 88.3 |
50 | 50.0 | 66.7 |