## 2 Materials and Methods
### Seed Sampling Strategy  
Any natural image contains a lot of uneven image information. The change in the local color intensity of the image reflects the change in the amount of local information. Therefore, it is but natural to place more seeds in content-dense regions of the image and to place fewer seeds in content-sparse regions of the image. However, the uniformity of seeds is also strongly important for the compactness of superpixels. Then, the proposed seeds distribution strategy based on image local entropy achieved a balance between the content sensitivity and uniformity of seeds. The heterogeneity of each pixel was captured using Normalized Shannon Entropy. The entropy operator calculates the entropy of the pixel value in the neighbor center. Let the pixel gray values in the center and the \(N\) neighbor pixels be \(a_{0}\), \(a_{1}\), \(a_{2}\),..., \(a_{N}\), respectively. The entropy operator is given in Table 1.  
The entropy \(H\) was normalized so that \(H\in[0,1]\). For color images in the CIELAB color space \(\mathsf{c}=\left[ \begin{array}{cc}l&a&b\end{array} \right]^{T}\), the image local entropy is defined as  
\[H=q_{l}H_{l}+q_{a}H_{a}+q_{b}H_{b} \tag{1}\]  
where  
\[\left\{ \begin{array}{l}q_{l}=l/\left(l+a+b\right)\\ q_{a}=a/\left(l+a+b\right)\\ q_{b}=b/\left(l+a+b\right)\end{array} \right. \tag{2}\]  
Both brightness information and tone information were used to measure the local entropy carried by natural color images. Therefore, when the brightness or the color tone of the region changed greatly, the entropy value of the color image was small. The part of the image should contain more information \begin{table}
\begin{tabular}{|c|c|c|} \hline \hline \(a_{1}\) & \(a_{2}\) & \(a_{3}\) \\ \hline \(a_{4}\) & \(a_{0}\) & \(a_{5}\) \\ \hline \(a_{6}\) & \(a_{7}\) & \(a_{8}\) \\ \hline \hline \end{tabular}
\begin{tabular}{|c|c|c|} \hline \hline \(H\)=\(-\sum\limits_{i=0}^{N}P_{i}\log P_{i}/\log(N+1)\) \\ \hline \(P_{i}=a_{i}/\sum\limits_{j=0}^{N}a_{j}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Entropy operator. when the color intensity of the part of the image changes drastically, and vice versa. For neighborhood center \(i\), the local information of each pixel \(I(i)\) is defined as  
\[I(i)=\omega\log(1+(1-H)\times 10^{\
u}) \tag{3}\]  
where \(\omega\) and \(\gamma\) are scaling parameters. We outline seed sampling strategy in Algorithm 1. Different from the placement method of simple regular grids seeds [26] and two-level quad-tree split-up seeds [25], the proposed approach considered the local information of the image in the process of placing seeds. In order to make each superpixel contain an approximate amount of image information, the information interval was \(s=\sum_{i=1}^{n}I(i)/k\), where \(n\) is the number of pixels in the image and \(k\) is the desired number of superpixels. The images were scanned from left to right and from top to bottom, and the pixels were added that were four- or eight-connected to the currently growing region. When the scanned pixels reached the information interval, the seed was placed. For an initial superpixel \(S_{i}\), its position center \(\mathbf{x}_{i}=\left[ \begin{array}{cc}x_{i}&y_{i}\end{array}