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Fix SH #3010

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Fix SH #3010

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200 changes: 158 additions & 42 deletions nerfstudio/utils/math.py
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Original file line number Diff line number Diff line change
Expand Up @@ -36,60 +36,176 @@ def components_from_spherical_harmonics(
levels: Number of spherical harmonic levels to compute.
directions: Spherical harmonic coefficients
"""
num_components = levels**2
components = torch.zeros((*directions.shape[:-1], num_components), device=directions.device)

assert 1 <= levels <= 5, f"SH levels must be in [1,4], got {levels}"
assert directions.shape[-1] == 3, f"Direction input should have three dimensions. Got {directions.shape[-1]}"

x = directions[..., 0]
y = directions[..., 1]
z = directions[..., 2]

xx = x**2
yy = y**2
zz = z**2

# l0
components[..., 0] = 0.28209479177387814
ones = torch.ones_like(x)
xy, xz, yz = x * y, x * z, y * z
x2, y2, z2 = x * x, y * y, z * z
x4, y4, z4 = x2 * x2, y2 * y2, z2 * z2
x6, y6, z6 = x4 * x2, y4 * y2, z4 * z2

# l1
# SH polynomials generated using scripts/gen_sh.py based on the recurrence relations in appendix A1 of https://www.ppsloan.org/publications/StupidSH36.pdf
data_out = []
data_out.append(0.28209479177387814 * ones) # 1/(2*sqrt(pi))
if levels > 1:
components[..., 1] = 0.4886025119029199 * y
components[..., 2] = 0.4886025119029199 * z
components[..., 3] = 0.4886025119029199 * x

# l2
data_out.append(-0.48860251190291987 * y) # -sqrt(3)*y/(2*sqrt(pi))
data_out.append(0.48860251190291987 * z) # sqrt(3)*z/(2*sqrt(pi))
data_out.append(-0.48860251190291987 * x) # -sqrt(3)*x/(2*sqrt(pi))
if levels > 2:
components[..., 4] = 1.0925484305920792 * x * y
components[..., 5] = 1.0925484305920792 * y * z
components[..., 6] = 0.9461746957575601 * zz - 0.31539156525251999
components[..., 7] = 1.0925484305920792 * x * z
components[..., 8] = 0.5462742152960396 * (xx - yy)

# l3
data_out.append(1.0925484305920792 * xy) # sqrt(15)*xy/(2*sqrt(pi))
data_out.append(-1.0925484305920792 * yz) # -sqrt(15)*yz/(2*sqrt(pi))
data_out.append(0.94617469575755997 * z2 - 0.31539156525251999) # sqrt(5)*(3*z2 - 1)/(4*sqrt(pi))
data_out.append(-1.0925484305920792 * xz) # -sqrt(15)*xz/(2*sqrt(pi))
data_out.append(0.54627421529603959 * x2 - 0.54627421529603959 * y2) # sqrt(15)*(x2 - y2)/(4*sqrt(pi))
if levels > 3:
components[..., 9] = 0.5900435899266435 * y * (3 * xx - yy)
components[..., 10] = 2.890611442640554 * x * y * z
components[..., 11] = 0.4570457994644658 * y * (5 * zz - 1)
components[..., 12] = 0.3731763325901154 * z * (5 * zz - 3)
components[..., 13] = 0.4570457994644658 * x * (5 * zz - 1)
components[..., 14] = 1.445305721320277 * z * (xx - yy)
components[..., 15] = 0.5900435899266435 * x * (xx - 3 * yy)

# l4
data_out.append(0.59004358992664352 * y * (-3.0 * x2 + y2)) # sqrt(70)*y*(-3*x2 + y2)/(8*sqrt(pi))
data_out.append(2.8906114426405538 * xy * z) # sqrt(105)*xy*z/(2*sqrt(pi))
data_out.append(0.45704579946446572 * y * (1.0 - 5.0 * z2)) # sqrt(42)*y*(1 - 5*z2)/(8*sqrt(pi))
data_out.append(0.3731763325901154 * z * (5.0 * z2 - 3.0)) # sqrt(7)*z*(5*z2 - 3)/(4*sqrt(pi))
data_out.append(0.45704579946446572 * x * (1.0 - 5.0 * z2)) # sqrt(42)*x*(1 - 5*z2)/(8*sqrt(pi))
data_out.append(1.4453057213202769 * z * (x2 - y2)) # sqrt(105)*z*(x2 - y2)/(4*sqrt(pi))
data_out.append(0.59004358992664352 * x * (-x2 + 3.0 * y2)) # sqrt(70)*x*(-x2 + 3*y2)/(8*sqrt(pi))
if levels > 4:
components[..., 16] = 2.5033429417967046 * x * y * (xx - yy)
components[..., 17] = 1.7701307697799304 * y * z * (3 * xx - yy)
components[..., 18] = 0.9461746957575601 * x * y * (7 * zz - 1)
components[..., 19] = 0.6690465435572892 * y * z * (7 * zz - 3)
components[..., 20] = 0.10578554691520431 * (35 * zz * zz - 30 * zz + 3)
components[..., 21] = 0.6690465435572892 * x * z * (7 * zz - 3)
components[..., 22] = 0.47308734787878004 * (xx - yy) * (7 * zz - 1)
components[..., 23] = 1.7701307697799304 * x * z * (xx - 3 * yy)
components[..., 24] = 0.6258357354491761 * (xx * (xx - 3 * yy) - yy * (3 * xx - yy))

return components
data_out.append(2.5033429417967046 * xy * (x2 - y2)) # 3*sqrt(35)*xy*(x2 - y2)/(4*sqrt(pi))
data_out.append(1.7701307697799304 * yz * (-3.0 * x2 + y2)) # 3*sqrt(70)*yz*(-3*x2 + y2)/(8*sqrt(pi))
data_out.append(0.94617469575756008 * xy * (7.0 * z2 - 1.0)) # 3*sqrt(5)*xy*(7*z2 - 1)/(4*sqrt(pi))
data_out.append(0.66904654355728921 * yz * (3.0 - 7.0 * z2)) # 3*sqrt(10)*yz*(3 - 7*z2)/(8*sqrt(pi))
data_out.append(
-3.1735664074561294 * z2 + 3.7024941420321507 * z4 + 0.31735664074561293
) # 3*(-30*z2 + 35*z4 + 3)/(16*sqrt(pi))
data_out.append(0.66904654355728921 * xz * (3.0 - 7.0 * z2)) # 3*sqrt(10)*xz*(3 - 7*z2)/(8*sqrt(pi))
data_out.append(
0.47308734787878004 * (x2 - y2) * (7.0 * z2 - 1.0)
) # 3*sqrt(5)*(x2 - y2)*(7*z2 - 1)/(8*sqrt(pi))
data_out.append(1.7701307697799304 * xz * (-x2 + 3.0 * y2)) # 3*sqrt(70)*xz*(-x2 + 3*y2)/(8*sqrt(pi))
data_out.append(
-3.7550144126950569 * x2 * y2 + 0.62583573544917614 * x4 + 0.62583573544917614 * y4
) # 3*sqrt(35)*(-6*x2*y2 + x4 + y4)/(16*sqrt(pi))
if levels > 5:
data_out.append(
0.65638205684017015 * y * (10.0 * x2 * y2 - 5.0 * x4 - y4)
) # 3*sqrt(154)*y*(10*x2*y2 - 5*x4 - y4)/(32*sqrt(pi))
data_out.append(8.3026492595241645 * xy * z * (x2 - y2)) # 3*sqrt(385)*xy*z*(x2 - y2)/(4*sqrt(pi))
data_out.append(
-0.48923829943525038 * y * (3.0 * x2 - y2) * (9.0 * z2 - 1.0)
) # -sqrt(770)*y*(3*x2 - y2)*(9*z2 - 1)/(32*sqrt(pi))
data_out.append(4.7935367849733241 * xy * z * (3.0 * z2 - 1.0)) # sqrt(1155)*xy*z*(3*z2 - 1)/(4*sqrt(pi))
data_out.append(
0.45294665119569694 * y * (14.0 * z2 - 21.0 * z4 - 1.0)
) # sqrt(165)*y*(14*z2 - 21*z4 - 1)/(16*sqrt(pi))
data_out.append(
0.1169503224534236 * z * (-70.0 * z2 + 63.0 * z4 + 15.0)
) # sqrt(11)*z*(-70*z2 + 63*z4 + 15)/(16*sqrt(pi))
data_out.append(
0.45294665119569694 * x * (14.0 * z2 - 21.0 * z4 - 1.0)
) # sqrt(165)*x*(14*z2 - 21*z4 - 1)/(16*sqrt(pi))
data_out.append(
2.3967683924866621 * z * (x2 - y2) * (3.0 * z2 - 1.0)
) # sqrt(1155)*z*(x2 - y2)*(3*z2 - 1)/(8*sqrt(pi))
data_out.append(
-0.48923829943525038 * x * (x2 - 3.0 * y2) * (9.0 * z2 - 1.0)
) # -sqrt(770)*x*(x2 - 3*y2)*(9*z2 - 1)/(32*sqrt(pi))
data_out.append(
2.0756623148810411 * z * (-6.0 * x2 * y2 + x4 + y4)
) # 3*sqrt(385)*z*(-6*x2*y2 + x4 + y4)/(16*sqrt(pi))
data_out.append(
0.65638205684017015 * x * (10.0 * x2 * y2 - x4 - 5.0 * y4)
) # 3*sqrt(154)*x*(10*x2*y2 - x4 - 5*y4)/(32*sqrt(pi))
if levels > 6:
data_out.append(
1.3663682103838286 * xy * (-10.0 * x2 * y2 + 3.0 * x4 + 3.0 * y4)
) # sqrt(6006)*xy*(-10*x2*y2 + 3*x4 + 3*y4)/(32*sqrt(pi))
data_out.append(
2.3666191622317521 * yz * (10.0 * x2 * y2 - 5.0 * x4 - y4)
) # 3*sqrt(2002)*yz*(10*x2*y2 - 5*x4 - y4)/(32*sqrt(pi))
data_out.append(
2.0182596029148963 * xy * (x2 - y2) * (11.0 * z2 - 1.0)
) # 3*sqrt(91)*xy*(x2 - y2)*(11*z2 - 1)/(8*sqrt(pi))
data_out.append(
-0.92120525951492349 * yz * (3.0 * x2 - y2) * (11.0 * z2 - 3.0)
) # -sqrt(2730)*yz*(3*x2 - y2)*(11*z2 - 3)/(32*sqrt(pi))
data_out.append(
0.92120525951492349 * xy * (-18.0 * z2 + 33.0 * z4 + 1.0)
) # sqrt(2730)*xy*(-18*z2 + 33*z4 + 1)/(32*sqrt(pi))
data_out.append(
0.58262136251873131 * yz * (30.0 * z2 - 33.0 * z4 - 5.0)
) # sqrt(273)*yz*(30*z2 - 33*z4 - 5)/(16*sqrt(pi))
data_out.append(
6.6747662381009842 * z2 - 20.024298714302954 * z4 + 14.684485723822165 * z6 - 0.31784601133814211
) # sqrt(13)*(105*z2 - 315*z4 + 231*z6 - 5)/(32*sqrt(pi))
data_out.append(
0.58262136251873131 * xz * (30.0 * z2 - 33.0 * z4 - 5.0)
) # sqrt(273)*xz*(30*z2 - 33*z4 - 5)/(16*sqrt(pi))
data_out.append(
0.46060262975746175 * (x2 - y2) * (11.0 * z2 * (3.0 * z2 - 1.0) - 7.0 * z2 + 1.0)
) # sqrt(2730)*(x2 - y2)*(11*z2*(3*z2 - 1) - 7*z2 + 1)/(64*sqrt(pi))
data_out.append(
-0.92120525951492349 * xz * (x2 - 3.0 * y2) * (11.0 * z2 - 3.0)
) # -sqrt(2730)*xz*(x2 - 3*y2)*(11*z2 - 3)/(32*sqrt(pi))
data_out.append(
0.50456490072872406 * (11.0 * z2 - 1.0) * (-6.0 * x2 * y2 + x4 + y4)
) # 3*sqrt(91)*(11*z2 - 1)*(-6*x2*y2 + x4 + y4)/(32*sqrt(pi))
data_out.append(
2.3666191622317521 * xz * (10.0 * x2 * y2 - x4 - 5.0 * y4)
) # 3*sqrt(2002)*xz*(10*x2*y2 - x4 - 5*y4)/(32*sqrt(pi))
data_out.append(
10.247761577878714 * x2 * y4
- 10.247761577878714 * x4 * y2
+ 0.6831841051919143 * x6
- 0.6831841051919143 * y6
) # sqrt(6006)*(15*x2*y4 - 15*x4*y2 + x6 - y6)/(64*sqrt(pi))
if levels > 7:
data_out.append(
0.70716273252459627 * y * (-21.0 * x2 * y4 + 35.0 * x4 * y2 - 7.0 * x6 + y6)
) # 3*sqrt(715)*y*(-21*x2*y4 + 35*x4*y2 - 7*x6 + y6)/(64*sqrt(pi))
data_out.append(
5.2919213236038001 * xy * z * (-10.0 * x2 * y2 + 3.0 * x4 + 3.0 * y4)
) # 3*sqrt(10010)*xy*z*(-10*x2*y2 + 3*x4 + 3*y4)/(32*sqrt(pi))
data_out.append(
-0.51891557872026028 * y * (13.0 * z2 - 1.0) * (-10.0 * x2 * y2 + 5.0 * x4 + y4)
) # -3*sqrt(385)*y*(13*z2 - 1)*(-10*x2*y2 + 5*x4 + y4)/(64*sqrt(pi))
data_out.append(
4.1513246297620823 * xy * z * (x2 - y2) * (13.0 * z2 - 3.0)
) # 3*sqrt(385)*xy*z*(x2 - y2)*(13*z2 - 3)/(8*sqrt(pi))
data_out.append(
-0.15645893386229404 * y * (3.0 * x2 - y2) * (13.0 * z2 * (11.0 * z2 - 3.0) - 27.0 * z2 + 3.0)
) # -3*sqrt(35)*y*(3*x2 - y2)*(13*z2*(11*z2 - 3) - 27*z2 + 3)/(64*sqrt(pi))
data_out.append(
0.44253269244498261 * xy * z * (-110.0 * z2 + 143.0 * z4 + 15.0)
) # 3*sqrt(70)*xy*z*(-110*z2 + 143*z4 + 15)/(32*sqrt(pi))
data_out.append(
0.090331607582517306 * y * (-135.0 * z2 + 495.0 * z4 - 429.0 * z6 + 5.0)
) # sqrt(105)*y*(-135*z2 + 495*z4 - 429*z6 + 5)/(64*sqrt(pi))
data_out.append(
0.068284276912004949 * z * (315.0 * z2 - 693.0 * z4 + 429.0 * z6 - 35.0)
) # sqrt(15)*z*(315*z2 - 693*z4 + 429*z6 - 35)/(32*sqrt(pi))
data_out.append(
0.090331607582517306 * x * (-135.0 * z2 + 495.0 * z4 - 429.0 * z6 + 5.0)
) # sqrt(105)*x*(-135*z2 + 495*z4 - 429*z6 + 5)/(64*sqrt(pi))
data_out.append(
0.07375544874083044 * z * (x2 - y2) * (143.0 * z2 * (3.0 * z2 - 1.0) - 187.0 * z2 + 45.0)
) # sqrt(70)*z*(x2 - y2)*(143*z2*(3*z2 - 1) - 187*z2 + 45)/(64*sqrt(pi))
data_out.append(
-0.15645893386229404 * x * (x2 - 3.0 * y2) * (13.0 * z2 * (11.0 * z2 - 3.0) - 27.0 * z2 + 3.0)
) # -3*sqrt(35)*x*(x2 - 3*y2)*(13*z2*(11*z2 - 3) - 27*z2 + 3)/(64*sqrt(pi))
data_out.append(
1.0378311574405206 * z * (13.0 * z2 - 3.0) * (-6.0 * x2 * y2 + x4 + y4)
) # 3*sqrt(385)*z*(13*z2 - 3)*(-6*x2*y2 + x4 + y4)/(32*sqrt(pi))
data_out.append(
-0.51891557872026028 * x * (13.0 * z2 - 1.0) * (-10.0 * x2 * y2 + x4 + 5.0 * y4)
) # -3*sqrt(385)*x*(13*z2 - 1)*(-10*x2*y2 + x4 + 5*y4)/(64*sqrt(pi))
data_out.append(
2.6459606618019 * z * (15.0 * x2 * y4 - 15.0 * x4 * y2 + x6 - y6)
) # 3*sqrt(10010)*z*(15*x2*y4 - 15*x4*y2 + x6 - y6)/(64*sqrt(pi))
data_out.append(
0.70716273252459627 * x * (-35.0 * x2 * y4 + 21.0 * x4 * y2 - x6 + 7.0 * y6)
) # 3*sqrt(715)*x*(-35*x2*y4 + 21*x4*y2 - x6 + 7*y6)/(64*sqrt(pi))
return torch.stack(data_out, dim=-1)


@dataclass
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3 changes: 2 additions & 1 deletion tests/model_components/test_renderers.py
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Original file line number Diff line number Diff line change
Expand Up @@ -31,7 +31,8 @@ def test_sh_renderer():
levels = 4
num_samples = 10

sh = torch.ones((3, num_samples, 3 * levels**2))
sh = torch.zeros((3, num_samples, 3 * levels**2))
sh[..., 0] = 3.6
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what is this for? maybe add a comment

weights = torch.ones((3, num_samples, 1))
weights /= torch.sum(weights, dim=-2, keepdim=True)
directions = torch.zeros((3, num_samples, 3))
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