Table 2: Comparison of the gradients, i.e., ∂ I ^ i / ∂ α i in four scenes (BOX, C-BOX, TORUS, and WATER) calculated using the finite difference method (FD) and analytic gradient (ours) to verify the correctness of our analytic gradient computation.

	FD	Ours	Absolute error
BOX	−1.9237 × 10−4	−1.9248 × 10−4	3.1773 × 10−5
C-BOX	−3.6945 × 10−5	−3.6950 × 10−5	1.2040 × 10−7
TORUS	−3.5058 × 10−6	3.5050 × 10−6	1.9545 × 10−5
WATER	−9.7976 × 10−5	−9.7084 × 10−5	1.6310 × 10−3