Algorithm 2 The 3D moments computation [83]

Input:$\mathbf{F}$ = 3D image, ${\mathbf{Q}}_d$ = Charlier polynomials.

Output:$FV$ = Charlier moments.

1: Generate extended 3D image ($\mathbf{G}$) from the 3D image $\mathbf{F}$ {Equation (22).}

2: Get stored Charlier polynomials ${\mathbf{Q}}_x$, ${\mathbf{Q}}_y$, and ${\mathbf{Q}}_z$ {Using Equation (26).}

3: for z = 1 to $Or{d}_z$ do

4:     $\mathbf{M}\leftarrow \mathbf{M}+{\mathbf{R}}_z\otimes \left[{\mathbf{Q}}_x\mathbf{G}{\mathbf{Q}}_y\right]$

5: end for

6: $FV\leftarrow reshape\left(\mathbf{M}\right)$ {Reshape the computed moments as a feature vector.}

7: return $FV$ {Note: in the training and testing phases, the feature vector is normalized.}