# An Initial Dot Encoding Scheme with Significantly Improved Robustness and Numbers
## 2 Coded Mark Design and Detection
### Coded Mark Detection  
The process of image preprocessing is actually debugging the image information, highlighting the required parts, and eliminating the need for partial impact. Because the encoding points used in this paper are characterized by the circle, the central location of the circle is a critical step in decoding [23; 24]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Bit of Coded Points** & **4** & **6** & **8** & **10** & **12** & **18** \\ \hline Hattori scheme & 0 & 2 & 13 & 38 & 88 & 206 \\ Schneider scheme & 5 & 13 & 35 & 107 & 325 & 14,601 \\ [PERSON]’s scheme & 5 & 13 & 35 & 107 & 325 & 14,601 \\ Initial Dot scheme & 16 & 64 & 256 & 1024 & 4096 & 262,144 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the number of coded points. Figure 1: The coded mark points in this paper. First of all, in order to quickly detect the feature information of images, this paper used the method of local binaryzation. The idea of binaryzation is by setting a certain threshold \(T\), Data greater than \(T\) can be passed, its value changed to 1, less than \(T\) data cannot passed, and its value changed to 0. The threshold segmentation method can be divided into two kinds: global threshold method and local threshold method. Under the uneven illumination condition, the method of local threshold segmentation is better than the global threshold segmentation method. The basic idea of the algorithm is that the image is divided into two parts by threshold, one is the background, the other is the object graph. At the same time, the minimum variance within the class and the maximum variance between classes are needed to make the two sets of grey values. Specific algorithms are as follows: assuming that the gray range of the image is from 1 to \(L\), at this point the threshold \(k\) is used to divide it into two groups: \(C_{0}=\{1\sim k\}\) and \(C_{1}=\{k+1\sim L\}\)  
The probability distribution of the two groups is  
\[\omega_{0}=\sum_{i=1}^{k}P_{i}. \tag{1}\]  
\[\omega_{1}=\sum_{i=1+k}^{L}P_{i} \tag{2}\]  
Then the gray average of the two sets is  
\[\mu_{0}=\sum_{i=1}^{k}\frac{iP_{i}}{\omega_{0}} \tag{3}\]  
\[\mu_{1}=\sum_{i=1+k}^{L}\frac{iP_{i}}{\omega_{1}} \tag{4}\]  
The average gray value of the whole image is shown  
\[\mu=\mu_{0}\omega_{0}+\mu_{1}\omega_{1} \tag{5}\]  
The inter class variance between the two groups as follow  
\[\sigma^{2}(k)=\omega_{0}\omega_{1}(\mu_{1}-\mu_{0}) \tag{6}\]  
After the binaryzation of the image, in order to carry out the next step of feature extraction, segmentation needs to be carried out. Then the method used in this paper is the region growing method. Select a seed point to be detected the number of regions in the image, and then search in the eight neighborhood this seed point. If the gray value of a growth point value and seed point value is less than a threshold, it shows that the growth point and its seeds are in the same area. The most important part is the identification of the coded layer, the starting layer, and the marker layer. Since the coded schemes in this paper are composed of dots or circles, the information in the image can be judged by roundness, so that it can be used to distinguish whether it is the part of the coded mark. The criterion of roundness is as follows:  
\[C=\frac{P^{2}}{4\pi A} \tag{7}\]  
\(P\) stands for perimeter, and \(A\) stands for area, \(C\) is the roundness of an image, the more nearly 1, the closer to the circle. The difference between the starting point and the positioning point is mainly the size of the area. Then we can get a single coded mark point information by clustering the distance between the location of the encoding layer and the distance between the central points. First detectedis the starting point information, whose diameter is designed to be one-third of the center point. Then, the diameter of the surrounding code points is one-half of the center point, by which the number of code points can be determined.