Algorithm 2. FCM quantification process.

[Step 1] Initialize c (2 ≤ c < n) for n pixels of the area as the result of (3) by DBSCAN quantization, and exponential weight m (1 ≤ m < ∞). Also initialize the error threshold (ε) for terminating condition and the membership degree U(0). [Step 2] Compute the centroid of a cluster as the mean of all points, weighted by their degree of belonging to the cluster as following, where i denotes the cluster number, j denotes the node number on input x of total n data. $$v_{ij}={\displaystyle {\displaystyle \sum }_{k=1}^n}{\left(u_{ik}\right)}^m{x}_{kj}/{\displaystyle {\displaystyle \sum }_{k=1}^n}{\left(u_{ik}\right)}^m$$ [Step 3] Then, compute the distance between the data point and each centroid point of the cluster as following where i denotes the number of nodes. $$d_{ik}={\left[{\displaystyle {\displaystyle \sum }_{j=1}^l}{\left(x_{kj}-v_{ij}\right)}^2\right]}^{1/2}$$ [Step 4] Then, update the membership function U of its (r + 1)th repetition as following. $$u_{ik}^{\left(r+1\right)}=\frac{1}{{\sum }_{j=1}^c{\left[\frac{d_{jk}^r}{d_{ik}^r}\right]}^2} for I_k=\varnothing$$ [Step 5] Repeat above steps until the difference between Ur+1 and Ur becomes less than predetermined threshold value.