4.4 Experimental Studies and Results
4.4.2 Experiments on hand posture classification
4.4.2.2 Verification of view invariance
poor user invariance.
3] The FDs and the Zernike moments fail in efficiently discriminating hand posture shapes with almost similar boundary profile. The FDs are derived from the frequency description of 1D boundary profile and hence, the information on spatial localization is lost. In the case of Zernike moments, the information about spatial local- ization in preserved in the polar domain representation. However, even small boundary deviations in the spatial domain may cause large shifts in the polar domain due to which misclassifications occur between samples with similar boundary profiles.
From the plot of the intraclass distance based on Pratt’s FOM as shown in Figure 4.15, it can be noted that the boundary distortion between the intraclass samples is comparatively more for posture classes 1, 6, 8 and 9. As a result, the misclassifications in FDs and Zernike moments are mainly due to postures 1, 6, 8 and 9.
Except for these postures, the FDs and the Zernike moments exhibit consistently high classification accuracies for other posture classes. Hence, the FDs and the Zernike moments are robust to user variations in classifying hand postures with distinct boundary profile.
4] The Gabor wavelets offer better classification accuracy when the number of users in the training is more.
As the number of users decreases to 7, the performance of the Gabor wavelets decreases by almost 4%. This implies that the Gabor wavelets based description requires large number of training samples for achieving user independence.
5] From the results obtained for the PCA, we infer that the performance efficiency of the PCA is similar to that of the Krawtchouk features and PCA offers high classification accuracy exhibiting more robustness to user variations. However, as the number of user is reduced to 1, the performance of PCA is significantly less than the DOMs.
4.4 Experimental Studies and Results
Table 4.9: Experimental validation of view invariance. Comparison of classification results obtained for Training set-I and II. The training set includes hand postures collected from 23 users. The number of testing samples in Dataset 1 and Dataset 2 is 2,030 and 1,570 respectively. (% CC- percentage of correct classification. )
Training set-I Training set-II
Methods % CC for
Dataset 1
% CC for Dataset 2
Overall
% CC
% CC for Dataset 1
% CC for Dataset 2
Overall
% CC
Krawtchouk moments 95.22 87.90 92.03 97.93 95.73 96.97
discrete Tchebichef moments 95.47 88.79 92.55 97.83 96.24 97.14
Geometric moments 82.07 71.4 77.42 87.39 80.57 84.42
Zernike moments 90.89 75.48 84.17 94.83 90.32 92.86
FDs 88.08 70.57 80.44 90.15 85.99 88.33
Gabor wavelets 92.81 73.12 84.22 95.52 88.47 92.44
PCA 95.37 88.79 91.38 97.93 96.24 97.19
Examples of posture ‘0’ Examples of posture ‘1’ Examples of posture ‘2’
Examples of posture ‘3’ Examples of posture ‘4’ Examples of posture ‘5’
Examples of posture ‘6’ Examples of posture ‘7’ Examples of posture ‘8’
Examples of posture ‘9’
Figure 4.24:Samples of the test postures from Dataset 2 that has less recognition accuracy with respect to all the methods.
From the results in Table 4.9, it is evident that among the considered methods, the Krawtchouk moments, the discrete Tchebichef moments and the PCA technique offer better classification accuracy. The performance efficiency of other methods that includes FDs, Zernike moments and Gabor wavelets mainly degrades for samples from Dataset 2. This implies that the DOMs and the PCA based descriptors exhibit more robustness to view angle variations. It should be noted that the discrete Tchebichef moments
By comparing the classification results given in the Tables 4.9, it is observed that the number of misclas- sifications is notably more for almost all the postures in Dataset 2. It is known that the perspective distortion affects the boundary profile and the geometric attributes of a shape. Hence, the FDs and the geometric mo- ments are insufficient for recognizing the postures under view angle variations. From the detailed scores in Tables 4.10(e), we infer that the number of classes misclassified in FD based technique is more than in the case of user independence and it is difficult to establish the perceptual correspondence between the mismatched samples.
From the comprehensive scores for the geometric moments based features given in Table 4.10(c), it is un- derstood that performance of the geometric moments becomes unstable for structural distortions due to view
Table 4.10: Confusion Matrix for the classification results given in Table 4.9 for Training set-I with 23 training samples\gesture sign and 360 testing samples\gesture sign. Detailed scores for
(a)Krawtchouk moments based features
@I/PO/P@ 0 1 2 3 4 5 6 7 8 9
0 355 3 0 0 0 0 0 0 2 0
1 0 323 1 0 0 0 0 34 0 2
2 6 17 334 0 0 0 0 3 0 0
3 18 1 10 317 1 1 0 0 2 10
4 12 0 0 7 331 3 0 3 3 1
5 1 0 0 0 0 337 4 0 3 15
6 0 0 0 0 4 0 304 39 9 4
7 0 1 2 0 0 0 2 346 9 0
8 13 5 0 0 6 0 1 5 329 1
9 6 0 0 0 0 0 8 9 0 337
(b) discrete Tchebichef moment based features
@I/PO/P@ 0 1 2 3 4 5 6 7 8 9
0 355 3 0 0 0 0 0 0 2 0
1 0 324 1 0 0 0 0 32 0 3
2 5 16 336 0 0 0 0 3 0 0
3 16 1 10 320 1 1 0 0 1 10
4 9 0 0 8 335 2 0 3 2 1
5 1 0 0 0 0 341 4 0 2 12
6 0 0 0 0 4 0 310 36 6 4
7 0 1 2 0 0 0 1 346 10 0
8 12 5 0 0 6 0 1 5 330 1
9 6 0 0 0 1 0 10 8 0 335
(c)Geometric moments based features
@I/PO/P@ 0 1 2 3 4 5 6 7 8 9
0 306 3 1 14 1 0 0 1 17 17
1 1 309 0 0 0 4 0 45 0 1
2 0 39 277 22 10 2 0 1 2 7 3 24 3 90 203 21 0 0 1 2 16 4 6 2 23 35 272 10 2 0 6 4 5 0 0 0 1 39 274 25 0 1 20 6 0 2 0 5 37 6 259 39 4 8 7 0 10 38 13 3 0 7 276 11 2 8 21 4 7 7 28 0 4 1 285 3
9 1 0 1 13 1 0 2 16 0 326
(d)Zernike moments based features
@I/PO/P@ 0 1 2 3 4 5 6 7 8 9
0 320 9 0 0 0 0 0 0 25 6
1 0 293 0 0 0 0 0 9 18 40 2 0 41 303 0 0 0 0 0 0 16 3 5 1 7 317 16 0 0 2 0 12
4 0 1 0 6 334 1 3 0 2 13
5 0 3 0 0 2 332 11 0 0 12 6 0 26 0 0 0 0 283 35 5 11
7 0 3 17 0 0 0 0 327 6 7
8 2 43 0 0 0 0 0 4 277 34
9 0 25 0 0 0 0 0 1 43 291
(e) FD based representation
@I/P@
O/P 0 1 2 3 4 5 6 7 8 9
0 350 2 0 0 0 0 0 0 8 0
1 0 265 0 0 0 0 0 0 83 12
2 0 11 341 0 0 0 0 1 6 1
3 4 2 13 297 17 0 2 4 1 20
4 1 5 0 9 338 0 0 0 0 7
5 1 3 1 0 34 320 0 0 0 1
6 0 36 0 0 0 0 286 20 6 12 7 0 4 27 0 0 0 6 285 12 26 8 0 58 0 0 0 0 0 1 277 24 9 3 103 0 0 0 0 1 1 115 137
(f) Gabor wavelets based descriptors
@I/P@
O/P 0 1 2 3 4 5 6 7 8 9
0 310 10 0 0 0 0 1 0 8 31 1 12 298 0 0 0 0 0 9 19 22 2 7 6 285 0 0 0 1 33 28 0 3 3 0 7 255 3 0 2 51 21 18 4 1 0 0 3 314 1 3 19 18 1
5 4 0 0 0 2 315 30 0 0 9
6 19 23 0 0 1 0 281 25 11 0
7 1 3 6 3 0 0 4 334 2 7
8 21 9 0 0 0 0 0 11 316 3
9 23 4 0 0 0 0 1 8 0 324
(g)PCA based description
@I/PO/P@ 0 1 2 3 4 5 6 7 8 9
0 352 4 0 0 0 0 0 1 3 0
1 1 319 1 0 0 0 0 35 0 4
2 7 16 337 0 0 0 0 0 0 0
3 26 1 8 310 2 0 0 0 7 6
4 16 0 0 9 334 1 0 0 0 0
5 2 0 0 0 0 319 19 0 0 20
6 0 0 0 0 1 0 303 48 5 3
7 1 11 3 0 0 0 0 334 10 1
8 8 4 0 0 3 0 1 3 341 0
9 7 3 1 4 0 0 0 4 0 341
4.4 Experimental Studies and Results
angle variation. Similarly, the Zernike moments are sensitive to boundary distortions and as a result the per- formance of the Zernike moments is low for the posture samples from Dataset 2. From the detailed scores in Table 4.10(d), it is observed that the maximum misclassification in Zernike moments based method is again due to the confusion among the postures 1, 8, and 9. Similarly, posture 7 is confused with posture 2 and posture 6 is misclassified as posture 7. Unlike FDs and the geometric moments, the Zernike moments exhibit some correspondence between the mismatched samples.
The detailed scores of the classification results of Gabor wavelet based description is given in Table 4.10(f).
From the table, it is evident that samples in most of the posture classes show misclassification. The perspective distortion caused by the view angle variations affects the orientation of contours and it can be observed that most of the mismatched samples are from the posture classes 0, 1, 7, 8 and 9.
The Krawtchouk and the discrete Tchebichef moments have higher recognition rates for the testing samples from Dataset 1 and 2. Particularly, in the case of Dataset 2, the improvement is almost by 11% for Training set-I and it indicates that the DOMs are robust to the view angle variations. The PCA based description method exhibits similar performance as the DOMs. From the detailed scores in Tables 4.10(a), 4.10(b) and 4.10(g), it is observed that the misclassifications in the case of DOMs and the PCA occur with respect to similar samples.
Accordingly, the maximum misclassification has occurred for posture classes 1 and 6. The samples in both of these posture classes are mismatched with posture 7.
From Table 4.9 it should be noted that the classification accuracy is better for the testing samples from Dataset 1. The samples of some of the postures from Dataset 2 with higher misclassification rates are shown in Figure 4.24. It can be understood that the recognition efficiency is reduced mainly due to the self-occlusion between the fingers and the boundary deviations. This is because the Training set-I is constructed using the samples taken from Dataset 1. This indicates that the performance for Dataset 2 can be improved if the training set also includes samples taken at varied view angles.