Title: Hypothesis Testing for Progressive Kernel Estimation and VCM Framework Show Chinese title

Title: 渐进核估计和VCM框架的假设检验

Abstract: Identifying an appropriate radius for unbiased kernel estimation is crucial for the efficiency of radiance estimation. However, determining both the radius and unbiasedness still faces big challenges. In this paper, we first propose a statistical model of photon samples and associated contributions for progressive kernel estimation, under which the kernel estimation is unbiased if the null hypothesis of this statistical model stands. Then, we present a method to decide whether to reject the null hypothesis about the statistical population (i.e., photon samples) by the F-test in the Analysis of Variance. Hereby, we implement a progressive photon mapping (PPM) algorithm, wherein the kernel radius is determined by this hypothesis test for unbiased radiance estimation. Secondly, we propose VCM+, a reinforcement of Vertex Connection and Merging (VCM), and derive its theoretically unbiased formulation. VCM+ combines hypothesis testing-based PPM with bidirectional path tracing (BDPT) via multiple importance sampling (MIS), wherein our kernel radius can leverage the contributions from PPM and BDPT. We test our new algorithms, improved PPM and VCM+, on diverse scenarios with different lighting settings. The experimental results demonstrate that our method can alleviate light leaks and visual blur artifacts of prior radiance estimate algorithms. We also evaluate the asymptotic performance of our approach and observe an overall improvement over the baseline in all testing scenarios. Show Chinese abstract

Abstract: 确定一个合适的半径用于无偏核估计对于辐射估计的效率至关重要。 然而，确定半径和无偏性仍然面临巨大的挑战。 本文首先提出了一个基于渐进核估计的光子样本及其相关贡献的统计模型，在此模型下，如果该统计模型的零假设成立，则核估计是无偏的。 然后，我们提出了一种通过方差分析中的F检验来决定是否拒绝关于统计总体（即光子样本）的零假设的方法。 由此，我们实现了一个渐进光子映射(PPM)算法，其中核半径由这个假设检验来确定以实现无偏辐射估计。 其次，我们提出了VCM+，这是顶点连接与合并(VCM)的一种增强，并推导出了它的理论无偏公式。 VCM+通过多重重要性采样(MIS)结合了基于假设检验的PPM和双向路径追踪(BDPT)，其中我们的核半径可以利用PPM和BDPT的贡献。 我们在具有不同照明设置的各种场景中测试了我们的新算法——改进的PPM和VCM+。 实验结果表明，我们的方法能够减轻先前辐射估计算法的漏光和视觉模糊伪影。 我们还评估了我们方法的渐近性能，并观察到在所有测试场景中都优于基线的整体改进。