4.2.1. Setting of the Weighting Coefficient *cTS*

The most important step in achieving flexible partitioning is to the minimum of the weighted MIE, where the design of the weighting coefficient function is the most critical point. Therefore, this section focuses on the specific design of the function which ensures optimal partitioning of the image:

$$\begin{split} \mathbf{c}\_{TS} = f(\mathbf{g}\_{TS}) &= \left\{ (f(\mathbf{g}\_{TS}))\_{j'}, 1, \dots, {}^{\prime}, T\_2 \right\} = \left\{ (f(\lfloor \mathbf{g}\_{TS}^H, \mathbf{g}\_{TS}^V \rfloor))\_{j'}, 1, \dots, {}^{\prime}, T\_2 \right\} \\ \mathbf{g}\_{TS} &= \left\{ \begin{array}{l} \text{ones}(1, T\_2) & \mathbf{g}\_{TS}^H \le G\_{TS} \& \mathbf{g}\_{TS}^V \le G\_{TS} \\ \left[0, 1, \dots, {}^{\prime}, b\right] / \left(b/2\right) & \mathbf{g}\_{TS}^H \le G\_{TS} \& \mathbf{g}\_{TS}^V > G\_{TS} \\ \left[b, \dots, 1, 0\right] / \left(b/2\right) & \mathbf{g}\_{TS}^H > G\_{TS} \& \mathbf{g}\_{TS}^V \le G\_{TS} \\ \left[\frac{b\log\_2^{(n/2+2)}, \log\_2^{(n/4+4)}, -\log\_2^{(4+n/4)}, \log\_2^{(2+n/2)}, b\right]}{b/2 + 1} & \mathbf{g}\_{TS}^H > G\_{TS} \& \mathbf{g}\_{TS}^V > G\_{TS} \end{array} \right. \end{split} \tag{48}$$

where, *gH TS* and *<sup>g</sup><sup>V</sup> TS* represent the value of horizontal and vertical TS by using ASM, and *GTS* represents the threshold at which the TS feature value reaches a significant degree.
