发表机构
Northwestern Polytechnical University（西北工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出能量加权球谐矩的最大熵编码方法，针对不同参数子族提供相关解析与重建方案，在981个HDRI场景实验中较QZH取得显著性能提升，且保持零负辐照度。
AI 中文摘要
我们研究如何利用有限矩对由非负蒙特卡洛路径采样构成的角能量信号进行压缩与重建，以用于辐照度计算。将每个采样表示为能量加权方向特征 $x = r u$，我们采用总能量、一阶方向矩和无迹二阶矩作为 $1+3+5$ 个线性可加、旋转协变的统计量。在固定勒贝格参考测度下，最大熵闭合解给出 $p(r,u) \propto \exp(-\beta r g(u))$，其中 $g(u) = 1 - b \cdot u + u^T Q u$，其方向概率和角能量密度分别与 $g^{-3}$ 和 $g^{-4}$ 成正比。当 $g_{\min} > 0$ 时，该闭合解可归一化，且重建结果严格为正。我们进一步针对纯偶极子四参数子族提供解析矩匹配、方差、逆采样和闭式漫反射响应，以及偶极子-二阶矩共轴五参数子族的可实现域、配分函数、方位角代数积分和面向查找表（LUT）的重建形式。实验覆盖981个Poly Haven HDRI 2K场景和3个Debevec探测图。五参数MaxEnt相较于存储的QZH，实现了78.7%的单场景胜率，平均亮度均方根误差（RMSE）降低15.8%；在强方向性场景中，该优势更为显著。两种MaxEnt变体在所有场景中均保持零负辐照度。完整二阶球谐函数（SH-2）的整体误差最低，五参数MaxEnt排名第二，且在高方向性分组中优于SH-2；共轴子族在非共轴多源场景中存在系统性闭合误差。
英文摘要
We study how angular energy signals composed of non-negative Monte Carlo path samples can be compressed and reconstructed for irradiance using finite moments. Writing each sample as an energy-weighted directional feature $x = r u$, we adopt total energy, the first directional moment, and the traceless second moment as $1+3+5$ linearly additive, rotationally covariant statistics. Under a fixed Lebesgue reference measure, the maximum-entropy closure yields $p(r,u) \propto \exp(-βr g(u))$, where $g(u) = 1 - b \cdot u + u^T Q u$, whose directional probability and angular energy density are proportional to $g^{-3}$ and $g^{-4}$, respectively. When $g_{\min} > 0$ the closure is normalizable and the reconstruction is strictly positive. We further provide analytic moment matching, variance, inverse sampling, and closed-form diffuse response for the pure-dipole four-parameter subfamily, as well as the realizability domain, partition function, azimuthal algebraic integral, and LUT-oriented reconstruction form for the dipole-second-moment coaxial five-parameter subfamily. Experiments cover 981 Poly Haven HDRI 2K scenes and three Debevec probes. Five-parameter MaxEnt achieves a 78.7% per-scene win rate against stored QZH, with mean luminance RMSE reduced by 15.8%; the advantage is more pronounced in scenes with strong directionality. Both MaxEnt variants maintain zero negative irradiance across all scenes. Full second-order SH-2 yields the lowest overall error, while five-parameter MaxEnt ranks second and outperforms SH-2 in the high-directionality bucket; the coaxial subfamily shows systematic closure error on non-coaxial multi-source scenes.
Comments23 pages, 12 figures, 5 tables
