TensoRF에서 Spehrical Harmonics 코드 자체는 Hard coded되어 있다. → viewing dependent color를 찾을 때, MLP 대신에 사용함.
:param deg: int SH max degree. Currently, 0-4 supported
import torch
################## sh function ##################
C0 = 0.28209479177387814
C1 = 0.4886025119029199
C2 = [
1.0925484305920792,
-1.0925484305920792,
0.31539156525252005,
-1.0925484305920792,
0.5462742152960396
]
C3 = [
-0.5900435899266435,
2.890611442640554,
-0.4570457994644658,
0.3731763325901154,
-0.4570457994644658,
1.445305721320277,
-0.5900435899266435
]
C4 = [
2.5033429417967046,
-1.7701307697799304,
0.9461746957575601,
-0.6690465435572892,
0.10578554691520431,
-0.6690465435572892,
0.47308734787878004,
-1.7701307697799304,
0.6258357354491761,
]
def eval_sh(deg, sh, dirs):
"""
Evaluate spherical harmonics at unit directions
using hardcoded SH polynomials.
Works with torch/np/jnp.
... Can be 0 or more batch dimensions.
**:param deg: int SH max degree. Currently, 0-4 supported**
:param sh: torch.Tensor SH coeffs (..., C, (max degree + 1) ** 2)
:param dirs: torch.Tensor unit directions (..., 3)
:return: (..., C)
"""
assert deg <= 4 and deg >= 0
assert (deg + 1) ** 2 == sh.shape[-1]
C = sh.shape[-2]
result = C0 * sh[..., 0]
if deg > 0:
x, y, z = dirs[..., 0:1], dirs[..., 1:2], dirs[..., 2:3]
result = (result -
C1 * y * sh[..., 1] +
C1 * z * sh[..., 2] -
C1 * x * sh[..., 3])
if deg > 1:
xx, yy, zz = x * x, y * y, z * z
xy, yz, xz = x * y, y * z, x * z
result = (result +
C2[0] * xy * sh[..., 4] +
C2[1] * yz * sh[..., 5] +
C2[2] * (2.0 * zz - xx - yy) * sh[..., 6] +
C2[3] * xz * sh[..., 7] +
C2[4] * (xx - yy) * sh[..., 8])
if deg > 2:
result = (result +
C3[0] * y * (3 * xx - yy) * sh[..., 9] +
C3[1] * xy * z * sh[..., 10] +
C3[2] * y * (4 * zz - xx - yy)* sh[..., 11] +
C3[3] * z * (2 * zz - 3 * xx - 3 * yy) * sh[..., 12] +
C3[4] * x * (4 * zz - xx - yy) * sh[..., 13] +
C3[5] * z * (xx - yy) * sh[..., 14] +
C3[6] * x * (xx - 3 * yy) * sh[..., 15])
if deg > 3:
result = (result + C4[0] * xy * (xx - yy) * sh[..., 16] +
C4[1] * yz * (3 * xx - yy) * sh[..., 17] +
C4[2] * xy * (7 * zz - 1) * sh[..., 18] +
C4[3] * yz * (7 * zz - 3) * sh[..., 19] +
C4[4] * (zz * (35 * zz - 30) + 3) * sh[..., 20] +
C4[5] * xz * (7 * zz - 3) * sh[..., 21] +
C4[6] * (xx - yy) * (7 * zz - 1) * sh[..., 22] +
C4[7] * xz * (xx - 3 * yy) * sh[..., 23] +
C4[8] * (xx * (xx - 3 * yy) - yy * (3 * xx - yy)) * sh[..., 24])
return result
def eval_sh_bases(deg, dirs):
"""
Evaluate spherical harmonics bases at unit directions,
without taking linear combination.
At each point, the final result may the be
obtained through simple multiplication.
:param deg: int SH max degree. Currently, 0-4 supported
:param dirs: torch.Tensor (..., 3) unit directions
:return: torch.Tensor (..., (deg+1) ** 2)
"""
assert deg <= 4 and deg >= 0
result = torch.empty((*dirs.shape[:-1], (deg + 1) ** 2), dtype=dirs.dtype, device=dirs.device)
result[..., 0] = C0
if deg > 0:
x, y, z = dirs.unbind(-1)
result[..., 1] = -C1 * y;
result[..., 2] = C1 * z;
result[..., 3] = -C1 * x;
if deg > 1:
xx, yy, zz = x * x, y * y, z * z
xy, yz, xz = x * y, y * z, x * z
result[..., 4] = C2[0] * xy;
result[..., 5] = C2[1] * yz;
result[..., 6] = C2[2] * (2.0 * zz - xx - yy);
result[..., 7] = C2[3] * xz;
result[..., 8] = C2[4] * (xx - yy);
if deg > 2:
result[..., 9] = C3[0] * y * (3 * xx - yy);
result[..., 10] = C3[1] * xy * z;
result[..., 11] = C3[2] * y * (4 * zz - xx - yy);
result[..., 12] = C3[3] * z * (2 * zz - 3 * xx - 3 * yy);
result[..., 13] = C3[4] * x * (4 * zz - xx - yy);
result[..., 14] = C3[5] * z * (xx - yy);
result[..., 15] = C3[6] * x * (xx - 3 * yy);
if deg > 3:
result[..., 16] = C4[0] * xy * (xx - yy);
result[..., 17] = C4[1] * yz * (3 * xx - yy);
result[..., 18] = C4[2] * xy * (7 * zz - 1);
result[..., 19] = C4[3] * yz * (7 * zz - 3);
result[..., 20] = C4[4] * (zz * (35 * zz - 30) + 3);
result[..., 21] = C4[5] * xz * (7 * zz - 3);
result[..., 22] = C4[6] * (xx - yy) * (7 * zz - 1);
result[..., 23] = C4[7] * xz * (xx - 3 * yy);
result[..., 24] = C4[8] * (xx * (xx - 3 * yy) - yy * (3 * xx - yy));
return result
Resource [https://github.com/apchenstu/TensoRF/blob/main/models/sh.py]
Resource [https://www.youtube.com/watch?v=knkoEeiFQfk&list=PLpdM-9cH8WoeosvDJNsutvIJgG96cPMDj&ab_channel=AndrewMcKinley]