散焦像差理论证实了大多数成像设备中的高斯模型
Defocus Aberration Theory Confirms Gaussian Model in Most Imaging Devices
AI总结：
本文通过散焦像差理论验证了高斯模型在大多数成像设备中的适用性，证明其在实时应用中的准确性与可靠性。
摘要：
在过去三十年中，散焦一直为场景图像提供了突破性的深度信息。然而，从2D图像准确估计深度仍然是3D恢复领域持续且根本性的挑战。启发式方法涉及对空间变散焦模糊的 ill-posed 问题进行推断，因为所需的模糊无法与固有的模糊区分开来。给定对散焦模型的先验知识，问题变为具有解析解的问题，用于推断在同一视角下不同相机设置下的两幅图像之间的相对模糊。高斯模型因其数学简洁性和计算效率而成为实时应用的最佳选择。从理论上讲，它是唯一可以同时应用于单幅图像中由深度引起的绝对模糊和两幅图像之间由深度差异引起的相对模糊的模型。本文介绍了传统成像设备的设置，以确保散焦操作符遵循高斯模型。散焦分析始于几何光学框架，并通过衍射受限光学中的散焦像差理论进行，以获得将实际模型拟合到其高斯近似值的准确性。对于典型的一组聚焦深度在1到100米之间，最大深度变化为10%在聚焦深度的情况下，结果确认了高斯模型在大多数成像设备中的散焦操作符的适用性。研究结果表明，最大平均绝对误差（MAE）低于1%，突显了模型的准确性和可靠性。
英文摘要：
Over the past three decades, defocus has consistently provided groundbreaking depth information in scene images. However, accurately estimating depth from 2D images continues to be a persistent and fundamental challenge in the field of 3D recovery. Heuristic approaches involve with the ill-posed problem for inferring the spatial variant defocusing blur, as the desired blur cannot be distinguished from the inherent blur. Given a prior knowledge of the defocus model, the problem become well-posed with an analytic solution for the relative blur between two images, taken at the same viewpoint with different camera settings for the focus. The Gaussian model stands out as an optimal choice for real-time applications, due to its mathematical simplicity and computational efficiency. And theoretically, it is the only model can be applied at the same time to both the absolute blur caused by depth in a single image and the relative blur resulting from depth differences between two images. This paper introduces the settings, for conventional imaging devices, to ensure that the defocusing operator adheres to the Gaussian model. Defocus analysis begins within the framework of geometric optics and is conducted by defocus aberration theory in diffraction-limited optics to obtain the accuracy of fitting the actual model to its Gaussian approximation. The results for a typical set of focused depths between $1$ and $100$ meters, with a maximum depth variation of $10\%$ at the focused depth, confirm the Gaussian model's applicability for defocus operators in most imaging devices. The findings demonstrate a maximum Mean Absolute Error $(\!M\!A\!E)$ of less than $1\%$, underscoring the model's accuracy and reliability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
