焦散、聚光的繪製一直是長期存在於光線傳輸模擬領域中的問題。這些複雜的照明效果是因為光線與具有接近Dirac Delta分布的雙向反射分佈函數(BRDF)之specular材料相互作用而產生。儘管光子映射類型的演算法可以有效地採樣這些困難的路徑，但代價是偏差。另一方面，許多無偏方法則是採用局部探索方法（如流形採樣）來解決此問題，這些方法利用specular表面的形成的流形性質來搜索其中可能的路徑，但需要時間讓其牛頓求解器進行迭代計算。
在這篇論文中，我們提出了一種無偏的焦散採樣方法，稱為光子驅動的流形採樣 (Photon-driven Manifold Sampling)。與Specular Manifold Sampling類似，這種方法提供了一個從primary hit point通過流形採樣採樣焦散路徑的方法。但是與其使用隨機採樣specular interaction，我們使用鄰近區域中的光子路徑作為我們局部探索的初始猜測。這使我們能夠結合光子映射和流形採樣的優點，在相同時間內實現噪點減少和改善焦散採樣品質。

Caustic rendering is a long-lasting challenge within the realm of light transport simulation, as light interacts with specular materials with near Dirac delta distribution as their Bidirectional Reflectance Distribution Function (BRDF), causing these complex lighting effects to manifest. Photon mapping is an efficient technique for sampling these challenging light paths, but introduces bias. Conversely, several unbiased methods address this problem by employing local exploration techniques such as Manifold sampling, which exploit the properties of specular surfaces to find admissible paths, but require time for their Newton solver to iterate.
In this thesis, we introduce an unbiased method for sampling caustics called Photon-driven Manifold Sampling. Similar to Specular Manifold Sampling, this approach provides a means of sampling caustic paths from the primary hit point using manifold sampling. However, instead of stochastically sampling specular interactions, we use photon paths in the neighboring area as an initial guess for our local exploration. This enables us to combine the benefits of both photon mapping and manifold sampling, reducing noise and improving the quality of caustic sampling in the same amount of time.

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