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

Table 2

Numerical values of 𝑥^𝑟𝑦^𝑠𝑧^𝑡 are dependent on whatever 𝑟, 𝑠, and 𝑡 are even or odd.

𝑟	𝑠	𝑡	𝑥^𝑟𝑦^𝑠𝑧^𝑡
			𝑃1	𝑃2	𝑃3	𝑃4	𝑃5	𝑃6	𝑃7	𝑃8
𝐸=2	𝐸=0	𝐸=2	+; 0.00156	+0.00156	+0.00156	+0.00156	+0.00156	+0.00156	+0.00156	+0.00156
𝐸=0	𝐸=2	𝑂=1	−0.03107	−0.03107	−0.03107	−0.03107	+0.03107	+0.03107	+0.03107	+0.03107
𝐸=2	𝑂=1	𝐸=0	−0.002071	−0.002071	+0.002071	+0.002071	−0.002071	−0.002071	+0.002071	+0.002071
𝐸=2	𝑂=1	𝑂=1	+0.00092	+0.00092	−0.00092	−0.00092	−0.00092	−0.00092	+0.00092	+0.00092
𝑂=1	𝐸=2	𝐸=0	−0.00621	+0.00621	+0.00621	−0.00621	−0.00621	+0.00621	+0.00621	−0.00621
𝑂=1	𝐸=0	𝑂=3	+0.007629	−0.007629	−0.007629	+0.007629	−0.007629	+0.007629	+0.007629	−0.007629
𝑂=1	𝑂=1	𝐸=2	+0.004577	−0.004577	+0.004577	−0.004577	+0.004577	−0.004577	+0.004577	−0.004577
𝑂=1	𝑂=1	𝑂=3	−0.002023	+0.002023	−0.002023	+0.002023	+0.002023	−0.002023	+0.002023	−0.002023