Image Processing Reference

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varies as well as the number of testing and training. We used two different sizes ([20 × 60] and

each time and, respectively, the remaining 8, 7, and 6 images to test. All implementations in

each part were repeated as many times as the number of total eigenvectors.

6.1 Experimental Setup-1

In this section, we explain the analysis with respect to the images with size of (20 × 60) for the

sake of understanding. To analyze the system in column direction and get the output, we irst

restate that the images are in dimension of (20 × 60) meaning that if we map them in column

direction, there will be 60 samples with the dimension of 20 to map. The output of such a map-

ping function will be a matrix with the dimension of (60 × 60). By applying 2DPCA on this

matrix, there will be 60 eigenvectors extracted with the dimension of 20. In this step, there

are 60 different dimensions which could be reduced using projection in 2DPCA meaning that

there are 60 different projections using different number of eigenvectors. We conducted the al-

gorithm 60 times in each of three different types (2, 3, and 4 samples to train and 8, 7, and 6

samples to test, respectively) of our implementation and calculated the accuracy rate in each

adding the number of samples for train, the accuracy goes up no matter which method to use.

Another expectation was that by using more eigenvectors, the accuracy rate goes higher up to

its optimized point, which here is almost near the dimension of 20. It is observed from
Figure

4
that using 2, 3, and 4 images to train leads to the accuracy rate of around 90%, 95%, and 97%,

respectively. Another prime issue is that the time consumed for this experiment is much more

than the next as there are 60 and 20 eigenvectors in column direction mapping. It is also ob-

served that by making the image size smaller the accuracy rate drops. It is because by making

the size of images smaller, some information are lost.

FIGURE 4
Accuracy rates obtained using K2DPCA in column direction on finger vein data-

base: (a) (10 × 20) sample size and (b) (20 × 60) sample size.

6.2 Experimental Setup-2

To analyze the system in row direction, the input images were used in a way that each image

consists of 20 samples with the dimension of 60 to map. The output of such a mapping func-

tion will be a (20 × 20) matrix. By applying 2DPCA on this matrix, there will be 20 eigenvectors

extracted with the dimension of 20. In this step, there are 20 different dimensions which could

be reduced using projection in 2DPCA meaning that there are 20 projection manners using

different number of eigenvectors.
Figure 5
demonstrates the accuracy rate of the experiments

along the row direction. Implementing this method using 2, 3, and 4 images to train results to

the accuracy rate of around 95%, 97%, and 99%, respectively, which is clearly higher than the

column direction. Mapping the input data along the row not only achieves higher accuracy

but also has less consumption of time as there are only 20 dimensions of data to be reduced.

Same as the previous experimental setup, the overall accuracy rate in (10 × 20) is not as high as

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