What is the main point of shape-radiance ambiguity

[yjhong89]

Dear author,

While I read your nerf++ paper, I coudn't fully understand shape-radiance ambiguity (Section 3 of nerf++ paper).

1. Is the purpose of Figure 2 experiment illustrating the ambiguity to show that NERF model can fit to arbitrary 3d shape setting of training data ?
   And if it were correct (verified by Figure 2 experiment), how this fact is related to the Factor 1 ("c" must become a high-frequency function as "sigma" deviates from the correct shape) ?

2. Why the Factor 2 (NERF MLP structure implicitly regularize to make "c" have smooth BRDF prior w.r.d. "d") helps NERF to avoid the shape-radiance ambiguity ?

3. How the Factor 1 and 2 is logically related ? It seems unrelated since the Factor 1 argues NERF MLP has a limited capacity to model high complexity given incorrect shape, and the Factor 2 argues NERF MLP model implictly regularize to make "c" smooth w.r.d "d" at any given "x"

Thanks you.

Best regards,
YJHong.