Alpha Compositing
What the parent explanation assumed you knew:
You understand that Gaussians are blended together front-to-back to create the final image, and that each has an opacity (alpha) value.
What this page explains:
The exact math of how multiple semi-transparent layers combine, why order matters, and how this enables differentiable rendering.
The Explanation
When you stack semi-transparent objects, the final color isn't a simple average - it follows specific blending rules.
The Formula: For each pixel, we process Gaussians in depth order (front to back):
C_final = Σ (c_i × α_i × T_i)Where:
- •`c_i` is the color of Gaussian i
- •`α_i` is the opacity of Gaussian i
- •`T_i` is the transmittance (how much light got through all previous Gaussians)
Transmittance:
`
T_i = Π (1 - α_j) for all j < i
`
This means: each Gaussian in front 'blocks' some light. If the first Gaussian has α=0.5, only 50% of light reaches the second one.
Why Order Matters: Swap two Gaussians with different alphas and colors, and you get a different result. This is why depth sorting is critical before rendering.
Why It's Differentiable: Every operation here (multiplication, addition) has well-defined gradients. This means we can backpropagate through the entire rendering process to optimize Gaussian parameters.
Visual Aid
Drag to reorder layers. Watch how the final color changes. Try setting different alpha values to see the transmittance effect.
Open interactive demo →The "Aha" Moment
Alpha compositing is what makes Gaussian Splatting both visually correct (proper transparency) and trainable (differentiable end-to-end).
Go Even Deeper
This explanation assumes you understand these fundamentals. Click to learn more:
rgba color
Level 1 fundamental
basic calculus
Level 1 fundamental