整體照明中熱輻射法與其誤差估計之研究

Abstract

在逼真的影像合成中，整體照明是一項基本的要素，而熱輻射法能提供一 個解決整體照明問題的方法。然而，一般而言，熱輻射法只能得到近似解 ，於是會產生誤差。若沒有誤差估計，熱輻射法將會花更多的計算時間以 達到更高精確度的結果。因此，誤差估計對熱輻射法是很重要的。在本論 文裡，我們研究整體照明中的熱輻射法與其誤差估計。我們做精確的誤差 估計以及提出可靠的誤差界以改進階層式熱輻射演算法。首先，我們對型 式因子提出一個較緊密的誤差界用來當作階層式熱輻射演算法的分割準則 。這樣的誤差界能對階層式熱輻射演算法減少很多不必要的連結和改進其 效能。在型式因子的計算裡，我們也提出一個加權誤差測度使得更多的計 算自動地花在陰影的邊界。在陰影邊界用高精確度的型式因子計算可增強 人類知覺的品質。使用加權誤差測度的較緊密誤差界，我們不僅能改進階 層式熱輻射演算法的效能而且可增加其精確度。其次，我們也對階層式熱 輻射演算法提出一個增強精確度的方法。在上層的表面，其核心函數有較 多精確的估計進而得到精確的誤差界和型式因子。這些精確的誤差界和型 式因子能加強階層式熱輻射演算法的精確度。最後，我們應用模糊推理的 技巧對階層式熱輻射演算法提出一個有效估計可見度的方法。在階層式熱 輻射演算法裡，可見度計算在所有的計算中是最花費時間的一部份。藉由 降低可見度計算的時間，階層式熱輻射演算的效能即可改善。我們利用模 糊的觀念對熱輻射法有效地估計可見度。我們的方法可明顯地改進階層式 熱輻射演算法的效能。 Global illumination plays an essential role in realistic image synthesis. Radiosity provides a solution in solving the global illumination problem. However, in general, the radiosity approach can only produce approximate results and, thus, errors are introduced. Without error estimation, it takes much computation time to achieve higher accurate results. Therefore, the error estimation is very important for radiosity. In this dissertation, we study the radiosity algorithm and its error estimation in global illumination. We make accurate error estimations and propose reliable error bounds to improve the hierarchical radiosity algorithm. First, we derive a tighter error bound of form factors as a subdivision criteria for the hierarchical radiosity algorithm. Such an error bound can reduce unnecessary links and improve the performance of the hierarchical radiosity algorithm. We also propose a weighted error metric in form-factor computation such that more efforts are applied toward shadow boundaries automatically. Evaluating form factors along shadow boundaries with a higher degree of precision would enhance the quality of human perception. Using the proposed tighter error bound on the weighted error metric, we not only improve the performance but also increase the accuracy of the hierarchical radiosity algorithm. Besides, we propose an accuracy enhancement approach for the hierarchical radiosity algorithm. The upper-level patches have more accurate estimates on the kernel. More accurate error bounds and form factors can be obtained for the upper-level patches. These accurate error bounds and form factors can enhance the accuracy of hierarchical radiosity. Finally, we present a way to estimate the visibility among patches efficiently for the hierarchical radiosity algorithm by using fuzzy reasoning techniques. The visibility computation of the hierarchical radiosity algorithm is the most signficiant part of the whole computation. The performance of the hierarchical radiosity algorithm can be improved by reducing the computation cost of visibility. We apply the fuzzy concept to the estimation of visibility for radiosity. Our approach can improve the performance of the hierarchical radiosity algorithm significiantly.