## 3 Proposed Method
### Regressive Anchor Box Selection  
As detection accuracy is dependent on the correct localization of an object inside an image, optimal size and shape of anchor boxes are necessary. The designer of YOLOv3 proposed to use the K-means clustering for anchor box selection. This method takes into account the ground truth boxes dimension very well but fails to comprehend the ground truth distribution density. It could be noted that the distribution of ground truth bounding box dimensions are different in all datasets. Some may have a majority of bounding boxes dimensions lesser than 20 pixels or some greater than 60 pixels. A reasonable approach would be to assign majority anchor boxes in the higher concentration range of the bounding box dimension and vice versa to achieve better localization. To achieve this we analyzed the bounding box dimension distribution of the GTSDB training set as shown in Figure 2. The figure shows bounding box dimensions on the x-axis and the probability of the y-axis. The probability on the y-axis underlines the majority bounding box concentration areas. Furthermore, the figure also shows the fitted cost function on to the bounding box distribution. The cost function can be explained with the following Equations (1) and (2). \[W=S\times CF \tag{1}\]  
\[CF=e^{\frac{-d(p,q)}{\alpha n}} \tag{2}\]  
\[d(p,q)=\sqrt{\sum_{i=1}^{m}(q_{i}-p_{i})^{2}} \tag{3}\]  
where \(W\) be the probability-weighted number of clusters, \(S\) represents a peak value for a maximum number of clusters, \(CF\) represents the cost function, \(n\) is the number of histogram probabilities, \(\alpha\) is a hyper-parameter, and \(d(p,q)\) represents the Euclidean distance between the current histogram probability and lowest histogram probability of the bounding boxes dimensions as shown in the Equation (3). Figure 1: Proposed block diagram for small objects (traffic signs) in an image. The dotted rectangle is the proposed technique and the shaded blue blocks are proposed modifications. Figure 2: Distribution of traffic sign Bounding Boxes dimension with fitted cost function on the training set of GTSDB (a) Distribution of X Bounding Box dimension with fitted cost function (b) Distribution of Y Bounding Box dimension with fitted cost function. The fitted cost function on to the bounding box distribution represents the amount of focus our proposed algorithm would have for finding the anchor boxes. It should be noted that higher concentration areas have a higher focus than the lower concentration areas of the bounding box distribution. In the proposed method, we translated the focus as the amount of probability-weighted clusters \(W\) to exist and \(S\) define a maximum number of clusters that may form. Hence, the nearer we are towards the high concentration area, the more clusters are to be formed and vice versa. Once probability-weighted clusters from Equation (1) are formed, the Median is calculated. In the higher concentration regions, large numbers of clusters are formed to accommodate more anchors than the lower concentration regions. We then fitted a linear regression model using least-squares in the acquired Median values from the clusters as shown in Figure 3.  
By conducting experiments, we found that changing the number of elements per cluster also influences the subsequent anchor boxes. We denote this term as Omega and empirically found that when Omega is four, the algorithm yields the highest traffic sign detection accuracy. Finally, we predict the anchors from the linear model by taking random samples in the range from the lowest bounding box dimension to the highest bounding box dimension. Seventy percent of random samples were taken from the higher concentration regions and the remaining thirty percent from the lower concentration region. The split 70-30% was acquired by adding up the probabilities of higher concentration region (from pixel 18 to 50) and lower concentration region (from pixel 51 onwards). In Figure 3, it is  
Figure 3: Regression models for finding the anchor boxes.