3D Gaussian Split Conditions

Overview

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3D Gaussian Splatting uses adaptive density control to refine scene representation. Gaussians are split or cloned based on specific conditions during optimization.

Split Conditions

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Two Primary Criteria

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1. Gradient Magnitude Threshold

When positional gradient exceeds threshold:

Indicates the Gaussian needs refinement to better represent the scene.

2. Size Threshold

When Gaussian scale exceeds limit:

Large Gaussians should be split into smaller ones.

Adaptive Control Operations

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Split (Over-reconstruction)

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When Gaussian is too large with high gradient:

Parent Gaussian → 2 Child Gaussians
- Positions: Along principal axes
- Scale: 1/2 to 2/3 of original
- Opacity: Inherited, then adjusted
- Color: NOT inherited (re-learned)

Clone (Under-reconstruction)

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When Gaussian is too small with high gradient:

Parent Gaussian → Parent + 1 Clone
- Clone positioned along gradient direction
- Same scale as parent

Prune

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Remove Gaussians with:

• Very low opacity: \(\alpha < \tau_{opacity}\)
• Very large scale in world space

Algorithm

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for gaussian in gaussians:
    grad = compute_gradient(gaussian)

    if norm(grad) > tau_grad:
        if gaussian.scale > tau_size:
            # Split: Too large
            split_gaussian(gaussian)
        else:
            # Clone: Too small
            clone_gaussian(gaussian)

    if gaussian.opacity < tau_opacity:
        prune_gaussian(gaussian)

Axis-Aligned Benefits

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Trade-offs

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Training Schedule

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Typical adaptive control:

Opacity reset at iteration ~3000 to remove floaters.

Parameters

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