以密度估計技術實現強韌光傳輸模擬

Abstract

本研究提出了一套基於密度估計技術的全局光照演算法。此方法奠基於現有之漸進式光子映射法，在疊代的過程中逐步加入更高頻率的光影細節。我們的方法藉由移除所有在場景模型內的奇異點，以強韌地捕捉所有可能的光傳輸路徑，且不必像一般光子映射法需在能量估計階段時進行材質相關參數的計算。我們所提出的光子錐收縮形式能確保在使用有限記憶體的前提下達成一致的估計，並有正式之數學證明與漸進誤差分析實驗以佐證其收斂性。最後，我們將含有複雜光傳輸路徑之場景其渲染結果與現今一致及無偏方法進行了質與量的分析和比較。

We propose a robust light transport algorithm that is able to capture all possible transport paths where the vast majority of the techniques involved are based on density estimation. It builds on top of existing progressive photon mapping methods where higher frequency lighting effects are added in subsequent iterations. Our approach is capable of eliminating all singularities encountered in a scene representation, and does not require evaluating material properties during the energy estimation process unlike the rest of photon mapping methods. The proposed photon cone focusing scheme is a consistent method that requires only finite memory to converge. A formal proof of convergence is given along with asymptotic analysis of estimation variance and bias. We compare our results to recent consistent and unbiased methods with scenes that contain difficult light paths in both qualitative and quantitative ways.