4.4 Experimental Studies and Results
4.4.1 Quantitative analysis of hand posture variations
The structural variations between the hand posture images of each class are verified from the intraclass and the interclass distances among the hand posture images. The intraclass and the interclass distances are computed using the Pratt’s FOM and the correlation coefficient. The samples required for this analysis are randomly chosen from Dataset 1 and Dataset 2. The reference set required for computing the distances are taken from Dataset 1 and there are 23 samples per hand posture class comprising of data collected from 23 users. Similarly, the query set is formed by collecting 69 samples per posture class from each of Dataset 1 and Dataset 2.
Figure 4.15 illustrates the intraclass distances computed in terms of the Pratt’s FOM. By comparing the plots in Figure 4.15(a) and Figure 4.15(b), we can infer that most of the samples in Dataset 1 exhibits comparatively higher values of FOM. Further, it is also evident that the range of variation in the FOM values corresponding to the samples from Dataset 2 is more than that of the samples from Dataset 1. The standard deviation plot of the intraclass FOMs shown in Figure 4.16 shows the variability in the values of Pratt’s FOM with respect to each class . By comparing the standard deviation values obtained for each class, it is observed that the intraclass distance is comparatively less only for the samples from posture classes 6, 7 and 9.
The plots illustrating the comparison between the intraclass and the interclass distances for hand posture
0 1 2 3 4 5 6 7 8 9 0.5
0.6 0.7 0.8 0.9
Index of the Posture Class
Pratt’s FOM
(a)
0 1 2 3 4 5 6 7 8 9
0.4 0.5 0.6 0.7 0.8 0.9
Index of the Posture Class
Pratt’s FOM
(b)
Figure 4.15: Intraclass distance measured in terms of Pratt’s FOM for samples in (a) Dataset 1 and (b) Dataset 2. The reference set is taken from Dataset 1. There are 690 testing samples with 69 samples\posture sign in each of the dataset and 230 samples in the reference set with 23 samples\posture sign.
0 1 2 3 4 5 6 7 8 9
0.02 0.04 0.06 0.08
Index of the Posture Class Standard deviation of intraclass Pratt’s FOM
Dataset 1 Dataset 2
(a)
Figure 4.16: Illustration of variability in the intraclass FOM values with respect to samples in each posture class.
images in Dataset 1 and Dataset 2 are shown in Figure 4.17. The plots are generated by computing the average of the correlation values obtained with respect to the samples in each posture class. From the distance values, it is evident that the intraclass samples exhibit higher similarity than the interclass samples. This implies that the posture signs comprising the database are structurally distinct shapes.
As we examine the correlation values in Figure 4.17 obtained for Dataset 1 and Dataset 2, it is observed that the correlation values with respect to the interclass samples are over 0.55. Further, the maximum difference between the intraclass and the interclass correlation values is approximately around 25%. Despite the structural distinctiveness, these values indicate that the samples corresponding to any class exhibit approximately 50%
structural similarity with respect to the samples in every other class. Therefore, it is clear that the hand posture shapes of different classes consist of overlapping regions.
It is known that the hand is composed of the palm and the finger regions. Of these, the fingers move at different degrees in order to constitute different hand postures. The palm region is a static region and the hand
4.4 Experimental Studies and Results
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 0
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 1
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 2
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 3
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 4
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 5
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 6
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 7
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 8
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 9
(a)
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 0
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 1
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 2
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 3
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 4
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 5
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 6
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 7
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 8
0 2 4 6 8
0.6 0.7 0.8 0.9
Index of the Posture Class
Correlation
Reference: Posture − 9
(b)
Figure 4.17: Illustration comparing the intraclass and the interclass variability of the samples in (a) Dataset 1 and (b) Dataset 2 based on the correlation measure. The correlation values exhibits the region based similarity between the samples.
postures considered in this work are such that the orientation of palm is uniform for all the hand postures.
Therefore, with respect to shape, the overlapping regions in different posture classes mainly comprise of the palm region. Along with the palm region, it is also observed that in some of the posture signs the finger regions also overlap such that some of the posture shapes in the database can be considered as the subsets of other posture shapes in the context of finger configuration.
The illustration of hand posture shapes that constitute the subset of other posture classes due to overlapping finger configurations is shown in Figure 4.18. Among the posture shapes, the shape of posture ‘5’ can be considered as a superset with respect to which the finger configurations of all the other posture classes for the subset. Since, the palm region is uniformly present over all the posture shapes, posture ‘0’ forms the subset of all the posture signs in the database.
Due to these associations between the hand postures, the interclass correlations between the hand posture
4 5
7 2
3
1 8
0 0
9 6 6
Figure 4.18: Illustration of the classes of the hand posture shapes that form the subsets of other posture class in the context of finger configuration.
shapes illustrated through Figure 4.17 are high. On comparing the correlation values obtained for Dataset 1 and Dataset 2, it is clear that the intraclass correlation and the difference between the intraclass and the interclass correlation values decreases for the samples in Dataset 2. Further, due to viewpoint changes the interclass correlation between the posture classes that form the set and the postures contained in the corresponding subsets is observed to increase.
The above analysis on the hand posture variations in terms of the intraclass and the interclass distances suggests that the database is composed of hand posture images with more structural deviations indicating the effects of user variations and the viewpoint changes. Therefore, the above analysis validates the applicability of the developed hand posture database for experiments on user and view invariant hand posture classification.