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Backward formula #89

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Backward formula #89

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06ca6db
support initial with color
wanmeihuali Jul 10, 2023
0a2b8a3
fix bug.
wanmeihuali Jul 10, 2023
968cef4
try the same formula with the original implementation
wanmeihuali Jul 10, 2023
c0c9afb
Merge branch 'main' into backward-formula
wanmeihuali Jul 12, 2023
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18 changes: 12 additions & 6 deletions taichi_3d_gaussian_splatting/GaussianPointCloudRasterisation.py
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Original file line number Diff line number Diff line change
Expand Up @@ -668,7 +668,9 @@ def gaussian_point_rasterisation_backward(
# let w_i = \sum_{j=i+1}^{n} c_j a_j T(j)
# we have w_n = 0, w_{i-1} = w_i + c_i a_i T(i)
# \frac{dC}{da_i} = c_i T(i) - \frac{1}{1 - a_i} w_i
w_i = ti.math.vec3(0.0, 0.0, 0.0)
accum_res = ti.math.vec3(0.0, 0.0, 0.0)
prev_color = ti.math.vec3(0.0, 0.0, 0.0)
prev_alpha:ti.f32 = 0.0

pixel_rgb_grad = ti.math.vec3(
rasterized_image_grad[pixel_v, pixel_u, 0], rasterized_image_grad[pixel_v, pixel_u, 1], rasterized_image_grad[pixel_v, pixel_u, 2])
Expand Down Expand Up @@ -769,12 +771,16 @@ def gaussian_point_rasterisation_backward(
point_grad_color = d_pixel_rgb_d_color * pixel_rgb_grad

# \frac{dC}{da_i} = c_i T(i) - \frac{1}{1 - a_i} w_i
alpha_grad_from_rgb = (color * T_i - w_i / (1. - alpha)) \
* pixel_rgb_grad
# alpha_grad_from_rgb = (color * T_i - w_i / (1. - alpha)) \
# * pixel_rgb_grad
accum_res = prev_alpha * prev_color + (1. - prev_alpha) * accum_res
prev_color = color
alpha_grad = ((color - accum_res) * pixel_rgb_grad).sum() * T_i
prev_alpha = alpha
# w_{i-1} = w_i + c_i a_i T(i)
w_i += color * alpha * T_i
alpha_grad: ti.f32 = alpha_grad_from_rgb[0] + \
alpha_grad_from_rgb[1] + alpha_grad_from_rgb[2]
# w_i += color * alpha * T_i
# alpha_grad: ti.f32 = alpha_grad_from_rgb[0] + \
# alpha_grad_from_rgb[1] + alpha_grad_from_rgb[2]
point_alpha_after_activation_grad = alpha_grad * gaussian_alpha
gaussian_point_3d_alpha_grad = point_alpha_after_activation_grad * \
(1. - point_alpha_after_activation_value) * \
Expand Down
1 change: 1 addition & 0 deletions taichi_3d_gaussian_splatting/GaussianPointCloudScene.py
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Original file line number Diff line number Diff line change
Expand Up @@ -164,6 +164,7 @@ def from_parquet(path: str, config=PointCloudSceneConfig()):
scene = GaussianPointCloudScene(
point_cloud, config)


point_cloud_rgb = scene_df[["r", "g", "b"]
].to_numpy() if df_has_color else None
scene.initialize(point_cloud_rgb=point_cloud_rgb)
Expand Down