以光源對物體可見度為導向之重要性取樣法

Abstract

本論文在產生取樣點時考量光源與物體之間的可見度，提出一個新的重要性取樣方法。本演算法將之前使用球面輻射基底函數(SRBF)考量BRDF與環境光源的重要性取樣法做了延伸，藉由使用先前可見度測試的結果來調整每個球面輻射基底的權重而將可見度的影響結合於重要性取樣函式(Importance Sampling Function)中。與先前許多在二維空間考量可見度關連性的重要性取樣法不同，本演算法在三維空間中考量可見度的影響，避免重複地在先前可見度測試失敗的方向上放置取樣點。因此較多的取樣點能通過可見度的測試而對最後繪製的結果產生貢獻。在三維空間中考量可見度關連性將使我們的演算法更適用於一些大部分光源為不可視的特殊場景。由結果可以看出來，本演算法大量的減少了整張畫面的誤差與雜訊，而並不只是針對陰影邊緣而已。在花費相同時間下，本演算法所產生的結果也遠優於先前未考慮可見度的方法。雖然我們的演算法是架構在以球面輻射基底函數(SRBF)上，但是本論文的想法亦可被延伸至其它基底，像是小波函數(Wavelet)或是球面調和函數(Spherical harmonics)。

We propose a novel sampling algorithm by considering the importance of visibility in the sampling process. This algorithm extends the bidirectional importance sampling techniques based on SRBF representation by adjusting the weight of each SRBF basis according to the previous history in visibility tests, thus combing the visibility term into importance function. Unlike previous visibility-related researches in importance sampling exploit image-space visibility coherence, we consider visibility in object space by avoiding redrawing samples in invisible directions. Consequently more samples pass the visibility test and contribute to the final rendered result. Considering visibility in object space would make our algorithm more flexible, even for scenes which have heavy occlusion. Our approach successfully reduces the variance over the entire image, not only along the shadow boundaries. Under the same computing performance, we can obtain higher quality than previous bidirectional importance approaches. Although our proposed algorithm is based on the SRBF representation, it can also be applied to other basis such as wavelet or spherical harmonics.