Comments (4)
Hi, Thanks for your interest in our work!
The Silhouette is basically the cumulative opacity along a ray. This is naturally obtained by the alpha-compositing in the rasterization of 3D Gaussians.
Instead of implementing the gradient for the alpha-compositing in CUDA. Here, we render the Silhouette by considering it one channel of dummy color, where the other two channels are depth and depth squared. We essentially assign a color of 1 to each Gaussian. Let's say there are 3 Gaussians along a ray; the cumulative opacity will be given by (Opacity_Gaussian_1 * 1 + Opacity_Gaussian_2 * 1 + Opacity_Gaussian_3 * 1)
. On the other hand, in the original 3D Gaussian Splatting color rendering, the following would happen: (Opacity_Gaussian_1 * (r, g, b) + Opacity_Gaussian_2 * (r, g, b) + Opacity_Gaussian_3 * (r, g, b))
.
In this fashion, for each pixel, you will directly get a cumulative opacity along the ray, which is the Silhouette. For empty space, the value will be 0 because no Gaussians exist along the ray.
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Thank u for your explanation. I have understood the principle by thinking in terms of the α-compositing.
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Hi, thanks for your question and the author`s explanation.
I want to get the detailed formula of Silhouette as equation(5) furthermore in the SplaTAM paper.
Firstly, equation(1) in the paper tells us each Gaussian in the 3D space
, and the Silhouette for each pixel
, where
Above all are the descriptions in the SplaTAM paper. However, I don`t know the exact
However, I found it a little weird to directly exchange the $\mathbf{x} \in \mathbb{R}^{3} $ to
Since the
On the contrary,
, the function
The views expressed above are my preliminary thoughts on the matter, and I would be grateful for any critiques or corrections from yours. Thanks very much!!
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Hi @lvmingzhe, Thanks for sharing your views!
Yes, you are correct. The detailed equation would be similar to what you outlined. One small addition is that the contribution coefficient of the Gaussian is the opacity (alpha) of the Gaussian. Hence, the Silhouette is the output of the alpha-compositing process in the rasterization of 3D Gaussians.
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Related Issues (20)
- How to create a new dataset HOT 1
- Query regarding constant camera intrinsics HOT 8
- Type of Loss Function HOT 2
- GPU memory during training HOT 1
- Query regarding first camera pose HOT 2
- Query regarding Scannet dataset config HOT 2
- Query regarding data loading for custom dataset HOT 2
- Question about the evaluation metrics
- Query regarding Replica Dataset Version & Performance HOT 3
- Question regarding number of frames tracked during SLAM HOT 1
- Inquiry Regarding Runtime Discrepancies in Splatam HOT 4
- Why is the projmatrix in cam the same to first frame? HOT 3
- diff-gaussian-rasterization error HOT 2
- PSNR are not good.
- Video was taken for map reconstruction
- Clarification Needed on Code Questions
- Confusing about Trajectory Evaluation Function evaluate_ate
- CUDA OUT OF MEMORY
- D435i real-time or offline slam?
- Question regarding the shape of the mask created from the `depth`.
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