Abstract Photon recollision probability p is a spectrally invariant structural parameter and a powerful tool to link canopy optical properties at any wavelengths to model reflectance, transmittance, or absorption of vegetation canopies. The concepts of the p-theory have been reported and examined at the shoot and canopy scales, but not yet for the crown level. Currently, the p-value is estimated indirectly, such as converted from the spherically averaged silhouette to total area ratio ( STAR ¯ ) or canopy transmittance measurements. In this work, we first validate the theoretical considerations of the p concept at the crown level (e.g., its relationship with STAR ¯ ), and then provide the first method to directly estimate photon recollision probability using Terrestrial Laser Scanning (TLS) data. The proposed geometric method is data-driven and avoids explicit reconstructions of tree structures. The p-value estimated here is the average recollision probability over spatial locations. We showed that the average recollision probability can be interpreted as the local spherical openness on phytoelement (leaf or needle) surfaces, which enabled a simple visibility calculation by avoiding explicit ray tracing. The developed method was tested on synthetic crowns of needle-leaved tree species, for which the reference p-values were known. Results confirmed the validity of the p- STAR ¯ relationship at the crown level, and showed that p-values can be accurately estimated from TLS point clouds with a relative root measure square error of less than 10%. This study displays the distinct advantage of TLS in delineating detailed tree crown structures and highlights its potential in studies of forest reflectance modeling.

中文翻译：

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使用地面激光扫描直接估计光子再碰撞概率

摘要 光子重新碰撞概率 p 是一个光谱不变的结构参数，是将任何波长的冠层光学特性联系起来以模拟植被​​冠层的反射率、透射率或吸收率的强大工具。p 理论的概念已经在枝条和冠层尺度上进行了报道和检验，但还没有在树冠水平上进行过研究。目前，p 值是间接估计的，例如从球面平均轮廓转换为总面积比 (STAR¯) 或冠层透射率测量值。在这项工作中，我们首先在冠级验证了 p 概念的理论考虑（例如，它与 STAR ¯ 的关系），然后提供了第一种使用地面激光扫描 (TLS) 数据直接估计光子再碰撞概率的方法。所提出的几何方法是数据驱动的，避免了树结构的显式重建。此处估计的 p 值是空间位置上的平均重新碰撞概率。我们表明，平均再碰撞概率可以解释为植物元素（叶或针）表面上的局部球形开放度，这通过避免显式光线追踪实现了简单的可见性计算。开发的方法在针叶树种的合成树冠上进行了测试，其参考 p 值是已知的。结果证实了 p-STAR 关系在冠层水平的有效性，并表明可以从 TLS 点云准确估计 p 值，相对根测量平方误差小于 10%。