Optical imaging systems are found everywhere in modern society. They are integral to computer vision, where the goal is often to infer geometric and radiometric information about a 3D environment given limited sensing resources. It is helpful to develop relationships between these real-world properties and the actual measurements that are taken, such as 2D images. To this end, we propose a new relationship between object radiance and image irradiance based on power conservation and a thin lens imaging model. The relationship has a closed-form solution for in-focus points and can be solved via numerical integration for points that are not focused. It can be thought of as a generalization of Horn's commonly accepted irradiance equation. Through both ray tracing simulations and comparison to the intensity values of actual images, we believe our equation provides better accuracy than Horn's equation. An improvement is most notable for large lenses and near-focused images where the pinhole imaging model implicit in Horn's derivation breaks down. Outside of this regime, our model validates the use of Horn's approximation through a more thorough theoretical foundation.

中文翻译：

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任意立体角下薄透镜图像辐照度的封闭形式解决方案。

光学成像系统在现代社会中随处可见。它们是计算机视觉不可或缺的组成部分，计算机视觉的目标通常是在感知资源有限的情况下推断有关3D环境的几何和辐射信息。在这些现实世界的属性和所进行的实际测量（例如2D图像）之间建立关系非常有帮助。为此，我们提出了基于功率守恒和薄透镜成像模型的物体辐射与图像辐射之间的新关系。该关系具有对焦点的封闭形式的解决方案，并且可以通过对未聚焦的点进行数值积分来解决。可以将其视为Horn普遍接受的辐照度方程的推广。通过光线跟踪模拟以及与实际图像强度值的比较，我们相信我们的方程比霍恩方程具有更好的精度。对于大型镜头和近聚焦图像而言，最显着的改进是，霍恩推导中隐含的针孔成像模型崩溃了。在此范围之外，我们的模型通过更详尽的理论基础验证了Horn近似的使用。