提出水下色彩恢复的理论边界，证明高分辨率相机可实现无不确定性的还原。
Underwater Color Restoration with Vanishing Uncertainty
- 从理论上分析水下色彩恢复的不确定性，推导出有限误差的条件。
- 证明当相机分辨率提高时，色彩恢复误差趋近于零。
- 为真实水下成像提供可信赖的数学基础，适合计算机视觉与海洋科学研究者。
水下色彩恢复有望使颜色成为水生科学中可靠的信号，但要以科学信心实现这一目标仍遥不可及。当前方法几乎仅通过经验验证，其可信度取决于是否在已知真实值的情况下，覆盖了可能的能见度条件多样性。这被色彩恢复在数学上完全病态的本质所加剧——需额外约束才能将解缩小到有限的不确定性区间。理论上的约束与现实数据满足的约束之间的差距尚不明确，因此不清楚现有方法是否在解决一个真正可解的问题。本文探讨这一差距的理论方面，识别出理想条件下可保证不确定性有界，并随着相机空间分辨率增加而收敛至零。
原文摘要 · Abstract (English)
Underwater color restoration promises to unlock color as a reliable signal for aquatic sciences, but achieving this with scientific confidence remains out of reach. Current methods are validated almost exclusively on an empirical basis, which provides confidence only to the extent that the vast diversity of possible visibility conditions is covered with end-to-end testing using a known ground truth. This is exacerbated by color restoration being a fatally ill-posed problem when considered in full mathematical generality, requiring additional constraints to narrow the solution to a finite uncertainty interval. The gap between which constraints suffice in theory and which constraints are satisfied by real-world data is poorly understood, making it unclear whether existing methods are solving a problem that is actually solvable. In this article, we investigate the theoretical side of this gap, identifying idealized conditions which guarantee bounded uncertainty that converges to zero as the spatial resolution of the camera increases.
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