A potential mistake when calculating the opacity gradient.

[XiaoXinyyx]

I believe there is an error in the opacity calculation within the 3dgs_accel branch.

In backward.cu, the gradient of alpha is calculated at line 608 as follows:

dL_dalpha += ((c[ch] * T) - (1.0f / (1.0f - alpha)) * (-ar[ch])) * dL_dchannel;

Subsequently, at line 619, the influence of the background color is added:

// Account for the last sample for color
dL_dalpha += (-T_final / (1.0f - alpha)) * bg_dot_dpixel;

However, I believe this addition is unnecessary. This is because ar[] is initialized earlier at line 576:

ar[ch] = -pixel_colors[ch * H * W + pix_id] + sampled_ar[global_bucket_idx * BLOCK_SIZE * C + ch * BLOCK_SIZE + idx];

Here, pixel_colors represents the output color of the forward render pass, which already includes the background color. As such, the influence of the background color is already accounted for. Therefore, I suggest removing line 619.

[tobias-kirschstein]

I believe you could be right.
I encountered some optimization issues with the 3dgs_accel branch specifically on studio captures with empty background where correct alpha blending with the background really matters.
After removing line 619 in backward.cu the issues were gone:

https://github.com/user-attachments/assets/aa8733fd-e17e-4bf0-be63-8de82b90d8ec (Original code, artifacts in background)
https://github.com/user-attachments/assets/81a87576-bce5-4fd0-abd7-a588beced34a (l. 619 removed, artifacts fixed)

Thanks for posting your fix here, it helped me!