An Algorithm for Fast Computation of 3D Zernike Moments for Volumetric Images

Table 1

3D symmetry points and their coordinates.

Points	Coordinates
𝑃1	𝑥𝑖,𝑦𝑗,𝑧𝑘
𝑃2	𝑥𝑁−𝑖+1,𝑦𝑗,𝑧𝑘
𝑃3	𝑥𝑁−𝑖+1,𝑦𝑁−𝑗+1,𝑧𝑘
𝑃4	𝑥𝑖,𝑦𝑁−𝑗+1,𝑧𝑘
𝑃5	𝑥𝑖,𝑦𝑗,𝑧𝑁−𝑘+1
𝑃6	𝑥𝑁−𝑖+1,𝑦𝑗,𝑧𝑁−𝑘+1
𝑃7	𝑥𝑁−𝑖+1,𝑦𝑁−𝑗+1,𝑧𝑁−𝑘+1
𝑃8	𝑥𝑖,𝑦𝑁−𝑗+1,𝑧𝑁−𝑘+1