Hello, and thank you for your inspiring work.
I have been following the line of research from Objects as Volumes [1] to Geometry Fields Splatting [2], and your work. It seems to consistently emphasize Gaussian splatting as a radiance field representation rather than a collection of independent particles, which I find to be a particularly elegant and principled direction.
However, I would like to raise a conceptual question regarding the treatment of overlapping splats.
As discussed in GFS [2], when two splats are non-interacting, their footprint functions can be denoted as ρ₁ and ρ₂. When two 3D splats partially overlap (but are not fully coincident), the resulting radiance field in the overlapping region cannot be accurately represented by a simple additive combination of their alpha values (i.e., ρ₁ + ρ₂). This suggests that the standard Riemann-sum-style approximation of the rendering equation may introduce bias in such cases. In contrast, formulations like 2DGS appear to mitigate this issue by construction.
In your work, this aspect does not seem to be explicitly discussed. Instead, a decay-based formulation (e.g., Equation 12) is used to model transmittance variation along the ray, yielding a continuous transmittance curve for each individual splat.
My question is: what is your perspective on ignoring inter-splat overlap when reconstructing the radiance field? Do you believe this approximation introduces non-negligible bias, or is it effectively handled by the current formulation?
Additionally, another potential source of discontinuity in transmittance arises from depth ordering based on centroids, which may not reflect the true intersection order along each pixel ray. I am wondering whether incorporating a reordering strategy (e.g., similar to StopThePop [3]) before computing vacancy/transmittance could further improve the results.
This is intended as an open and exploratory question. I may not have expressed it perfectly clearly, so please feel free to point out any misunderstandings. I would greatly appreciate your thoughts and would be very interested in further discussion.
Thank you again for your excellent work.
[1] Miller, Bailey, et al. "Objects as volumes: A stochastic geometry view of opaque solids." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.
[2] Jiang, Kaiwen, et al. "Geometry field splatting with gaussian surfels." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2025.
[3] Radl, Lukas, et al. "Stopthepop: Sorted gaussian splatting for view-consistent real-time rendering." ACM Transactions on Graphics (TOG) 43.4 (2024): 1-17.
Hello, and thank you for your inspiring work.
I have been following the line of research from Objects as Volumes [1] to Geometry Fields Splatting [2], and your work. It seems to consistently emphasize Gaussian splatting as a radiance field representation rather than a collection of independent particles, which I find to be a particularly elegant and principled direction.
However, I would like to raise a conceptual question regarding the treatment of overlapping splats.
As discussed in GFS [2], when two splats are non-interacting, their footprint functions can be denoted as ρ₁ and ρ₂. When two 3D splats partially overlap (but are not fully coincident), the resulting radiance field in the overlapping region cannot be accurately represented by a simple additive combination of their alpha values (i.e., ρ₁ + ρ₂). This suggests that the standard Riemann-sum-style approximation of the rendering equation may introduce bias in such cases. In contrast, formulations like 2DGS appear to mitigate this issue by construction.
In your work, this aspect does not seem to be explicitly discussed. Instead, a decay-based formulation (e.g., Equation 12) is used to model transmittance variation along the ray, yielding a continuous transmittance curve for each individual splat.
My question is: what is your perspective on ignoring inter-splat overlap when reconstructing the radiance field? Do you believe this approximation introduces non-negligible bias, or is it effectively handled by the current formulation?
Additionally, another potential source of discontinuity in transmittance arises from depth ordering based on centroids, which may not reflect the true intersection order along each pixel ray. I am wondering whether incorporating a reordering strategy (e.g., similar to StopThePop [3]) before computing vacancy/transmittance could further improve the results.
This is intended as an open and exploratory question. I may not have expressed it perfectly clearly, so please feel free to point out any misunderstandings. I would greatly appreciate your thoughts and would be very interested in further discussion.
Thank you again for your excellent work.
[1] Miller, Bailey, et al. "Objects as volumes: A stochastic geometry view of opaque solids." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.
[2] Jiang, Kaiwen, et al. "Geometry field splatting with gaussian surfels." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2025.
[3] Radl, Lukas, et al. "Stopthepop: Sorted gaussian splatting for view-consistent real-time rendering." ACM Transactions on Graphics (TOG) 43.4 (2024): 1-17.