3.3.1. Calculation of Fractional Metrics Evaluation

In the proposed experimental project, a number of methods were used for calculating score-level fusion [57] (Figure 9).

**Figure 9.** Calculation of fractional metrics evaluation.


$$d = \sqrt{\sum\_{i=1}^{N} \left(x\_i - t\_i\right)^2} \tag{4}$$

where *N* is the number of dimensions, which is (in the case of a template and testing data) the number of measured biometric characteristics, *xi* is the *i*-th element of the tested data, and *ti* is the *i*-th element of the template.

The number of template dimensions is equal to one testing data. The resulting value is the addition of all differences between the template and testing data.


$$d(\mathbf{x}\_i, \overline{\mathbf{x}}\_i) = \# \{ i \in \{1..N\} / \left| \mathbf{x}\_i - \overline{\mathbf{x}}\_i \right| \succ \sigma\_i \} \tag{5}$$

where *xi* is a biometric characteristic of the testing data with a serial number *i*, *xi* is the average of the biometric characteristic (from the template) with the serial number *i*, *N* is the overall number of biometric characteristics for the given template, and σ*<sup>i</sup>* is the RMS error (from the template) with the serial number *i*


$$\overline{H}(A,B) = \max\_{\mathbf{x}\in A} \left\{ \min\_{y\in B} \{ \|\mathbf{x}\_{\prime}y\| \} \right\} \tag{6}$$

where , is a random evaluation function, which is mainly a Euclidean distance.

The oriented HV is asymmetric. Therefore, *H*(*A*, *B*) - *H*(*B*, *A*) applies. It also does not provide the distance between the sets *A* and *B*, but only provides the longest distance from the point *x* ∈ *A* to the closest point *y* ∈ *B*. On the other hand, the non-oriented HV, which is marked *H*, is the maximum from *H* in both directions, and indicates the difference of the two sets of points. The formula for the calculating non-oriented HV is shown below.

$$H(A,B) = \max\{\overline{H}(A,B), \overline{H}(B,A)\}\tag{7}$$


$$H(A,B) = \frac{1}{N\_A} \sum\_{x \in A} \min\_{y \in B} \{ \| \mathbf{x}, y \| \} \tag{8}$$

where *NA* is the number of elements in the set *A* and . is a random evaluation function, using mostly Euclidean distance.

## 3.3.2. Normalization of a Fractional Metric

Before merging the results of the individual metrics, it is necessary that the results undergo some form of normalization. Individual metrics provide results in different "dimensions." Normalization within this study is carried out using a 'min-max' method within the experimental software. It is calculated according to the formula below.

$$mo = \frac{o - \min\_{i=1}^{N} o\_t^i}{\max\_{i=1}^{N} o\_t^i - \min\_{i=1}^{N} o\_t^i} \tag{9}$$

where *o* is a coarse evaluation, *N* is the number of elements in the set of testing data, and *o<sup>i</sup> <sup>t</sup>* is an element of the testing data.

#### 3.3.3. Merging Fractions of Evaluation

The merging procedure in multiple biometric systems (blending of scans and results of different types of biometric characteristics) is carried out in different levels of processing. In the multi-biometric scanner proposed within this study, merging is done by recording fractional results from individual metrics. In this method, individual conformity assessments are combined after normalization. This method is most commonly used [59–61] while it provides clear and simple results processing.

In order to calculate the overall evaluation, it is first necessary to normalize the individual outputs from different metrics. Normalization ensures that all intermediate results have the same weight regardless of the method used.

The metrics merging itself is done using an arithmetic average. Furthermore, implementation is made possible. At the same time, the process provides the best results [62]. During the final verification phase, the template is tested with the best score-level feature. If the score level fulfills the requirement of the threshold (set to 50% in this case), then the process is tagged successful. If not, then it is tagged unsuccessful.

#### *3.4. Image Scanning*

#### 3.4.1. Proposal of the Scanning Device

Image scanning is the first step toward the experimental implementation of the multi-biometric scanner. Effective image scanning positively influences the results to a great extent, especially during the image evaluation. To arrive at an appropriate image that will be subjected to further processing, configurations such as background lighting, direct lighting, and side lighting can be used (Figures 10–12). The image selection process is based on the task requirements. For instance, background lighting is considered to be an ideal option to measure the shape of the object. This is because it highlights

the contour of the object (hand). In the context of the current work, direct lighting configuration was adopted.

For effective image processing, suppressing background noise (influence of the surrounding) is a very important requirement. Background noises negatively affect image processing and further assessment. Nevertheless, the use of additional lighting can resolve this problem. Additional lighting creates an improved scene and looks like an industrial light. The use of a filter that allows the passage of radiation only has the wavelength equivalent to that of the light in use, which also improves the process. A lighting requirement includes:


Due to these lighting requirements, experimental design and implementation of the multi-biometric scanner in this paper adopted an industrial type of lighting for the hardware component of the scanning device. This was needed to achieve the required homogeneity associated with further image processing. For the same reason, the proposed scanning device has been equipped with a special camera. This camera will, however, not function based on automatic corrections of the image as compared to commonly available cameras. Table 2 summarizes the approximated prices of some components of the proposed scanner.

