*2.3. Selection of Bit Plane*

In order to obtain more abundant gray information and overcome the interference of brightness and noise caused by the collection environment, we studied the bit planes generated by gray image that only retains the contour of dorsal hand vein. The concept of bit planes is now illustrated by a 256-level gray image. If per pixel value of the input gray image is within [0, 255], then each pixel can be denoted by a binary number of eight bits, i.e., *b*7, *b*6, *b*5, *b*4, *b*3, *b*2, *b*1, *b*0, as shown in Formula (2). From *b*<sup>7</sup> to *b*<sup>0</sup> are the highest to the lowest bit plane respectively as shown in Figure 7.

$$I = b\_7 \times 2^7 + b\_6 \times 2^6 + b\_5 \times 2^5 + b\_4 \times 2^4 + b\_3 \times 2^3 + b\_2 \times 2^2 + b\_1 \times 2^1 + b\_0 \times 2^0 \tag{2}$$

**Figure 7.** Bit plane stratification.

Each item in Formula (2) denotes a bit plane of a pixel, and eight bit planes are shown in Figure 8.

**Figure 8.** Eight-bit planes.

As we can see in Figure 8, the lower bit planes are close to binary images, which is easily interfered with by the noise from the collection environment and equipment, and the higher bit planes contain more gray information, which is close to the gray image that only retains the contour of the dorsal hand vein. It is susceptible to illumination and brightness during acquisition. Therefore, we chose the intermediate optimal bit plane to solve these problems effectively. In the following, the eight-bit planes are respectively divided into blocks to calculate mutual information, and the statistical recognition rate will be used to obtain the optimal bit plane to improve the accuracy and robustness of the hand vein recognition.
