Algorithm 2 Two-dimensional Monte Carlo sample entropy (MCSampEn2D)

Require: Sequence $\mathbf{U}:=\{u_{i,j}:1\le i\le w,1\le j\le h\}$, template length m, threshold r,   Sample numbers $N_0$ and experimental rounds $N_1$. 1:procedure MCSampEn2D($\mathbf{U},m,r,N_0,N_1$) 2:    Set ${\overline{\varphi }}_{N_1}^{\mathbf{m}}=0$ and ${\overline{\varphi }}_{N_1}^{\mathbf{m}+1}=0$, 3:    for $k=1$ to $N_1$ do 4:        Set $\mathrm{Cor}=\{(h_s,w_s):1\le s\le N_0\}$ where $h_s$ and $w_s$ are selected on $\mathbf{U}$ pixel coordinates with uniform distribution, 5:        Compute ${\tilde{\varphi }}_k^{\mathbf{m}}$ by calling SampEn2D($\mathbf{U},\mathrm{Cor},m,r$), 6:        Compute ${\tilde{\varphi }}_k^{\mathbf{m}+1}$ by calling SampEn2D($\mathbf{U},\mathrm{Cor},m+1,r$), 7:        ${\overline{\varphi }}_{N_1}^{\mathbf{m}}={\overline{\varphi }}_{N_1}^{\mathbf{m}}+\frac{1}{N_1}{\sum }_{k=1}^{N_1}{\tilde{\varphi }}_k^{\mathbf{m}}$, 8:        ${\overline{\varphi }}_{N_1}^{\mathbf{m}+1}={\overline{\varphi }}_{N_1}^{\mathbf{m}+1}+\frac{1}{N_1}{\sum }_{k=1}^{N_1}{\tilde{\varphi }}_k^{\mathbf{m}+1}$ 9:    $entropy=-log\frac{{\overline{\varphi }}_{N_1}^{\mathbf{m}+1}}{{\overline{\varphi }}_{N_1}^{\mathbf{m}}}$, 10:    return $entropy$