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    "headline": "Math Framework Proves 3D Gaussian Splatting Surface Recovery Limits",
    "dek": "Researchers prove 3D Gaussian Splatting recovers true surfaces only when angular capacity is bounded.",
    "prose": "Researchers developed a mathematical framework based on a first-hit rendering abstraction to isolate geometry from appearance in 3D Gaussian Splatting. [^1]\n\nThe authors propose DualDiff3D, a novel 3D reconstruction framework designed to enhance the reliability of 3D Gaussian Splatting (3DGS) in scenarios with limited input views. [^2]\n\nResearchers proposed a new framework named X-SG²S to enable simultaneous injection of 1D to 3D watermarks for copyright protection while maintaining high fidelity. [^3]\n\nA strict identifiability window is established where surface-consistent solutions are mathematically preferred if angular capacity is bounded. [^4]\n\nIf angular capacity is unrestricted, the same images can be perfectly explained by an incorrect, opaque billboard geometry. [^5]\n\nExisting diffusion-based methods for 3D reconstruction often fail to separate structural information from appearance consistency, leading to blur and artifacts in rendered novel views. [^6]\n\nExtensive experiments demonstrate that the DualDiff3D approach outperforms state-of-the-art methods even in the inference-only setting. [^7]\n\nThe proposed DualDiff pipeline leverages dual diffusion priors with a Structure-Appearance Attention (SAA) module to refine low-quality novel views. [^8]",
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