計算機圖學在幾個重要的演算法推進下，產生出了幾種針對不同物理效果的算圖方法，包含比較早的雙向路徑追蹤（Bidirectional Path Tracing），以及對於焦散（Caustic）效果卓越的光子映射（Photon Mapping），這兩種方法在基礎上有所不同，擅長的物理效果也不一樣，而後來則有人結合兩種方法，並稱之為Vertex Connection and Merging，結合兩種演算法不同的優點，對某些難以計算的路徑產生較好的效果，是VCM成功的地方。

雙向路徑追蹤能讓蒙地卡羅路徑追蹤快速收斂，進而在短時間達到相當好的圖像品質，然而對於某些材質與路徑卻難以達到理想的效果，例如Specular鏡面以及焦散效果。而光子映射演算法則能對於這兩種物理現象產生理想的圖像品質，但該方法若是光子數量不足，則會在Diffuse表面產生斑紋等效果不佳的情況。

本篇論文主要探討VCM與雙向路徑追蹤在某些固定場景下的效果與優劣，並藉由調整雙向路徑追蹤與光子映射使用的比例權重，改善VCM對於Diffuse表面帶來的缺點。

Computer Graphics in advances of several important algorithms has been result some rendering solutions aim for different physical effects. They included Bidirectional Path Tracing, Photon Mapping for specializing Caustic effect. Both algorithms were built on distinctive basis so they are special at different physical effects. Later, theorist combined two algorithms into one as Vertex Connection and Merging. This algorithm integrate their strengths to solve some complex rendering path in better result as the main part of why VCM success.
Bidirectional Path Tracing is able to create faster convergence of Monte Carlo Path Tracing. This will reach high picture quality in a short time cost. However, it is hard to reach ideal result while facing specified materials and paths for example such as Specular Reflection and Caustic. On the other hand, Photon Mapping is able to create ideal results for both the cases mentioned above in enough amount of photon. Otherwise this will make Diffuse surface generate unwanted noise on the surface.
The purpose of this thesis was to investigate and compare VCM and Bidirectional Path Tracing in several scenes. The intention is to changing the usage weight of Photon Mapping and Bidirectional Path Tracing to improve VCM’s behavior on Diffuse surfaces.

[GKDS 12] Iliyan Georgiev, Jaroslav Křivánek, Tomáš Davidovič and Philipp Slusallek, “Light Transport Simulation with Vertex Connection and Merging,” ACM Trans. Graph. (SIGGRAPH Asia 2012), 2012.
[HOJ08] Toshiya Hachisuka, Shinji Ogaki, Henrik Wann Jensen, “Progressive photon mapping,” ACM SIGGRAPH Asia 2008.
[Jen 96] Henrik Wann Jensen, “Global Illumination using Photon Maps,” In Proceedings of the eurographics workshop on Rendering techniques '96. 1996.
[LW 93] Eric P. Lafortune and Yves D. Willems, “Bi-Directional Path Tracing,” Proceedings of Third International Conference on Computational Graphics and Visualization Techniques (Compugraphics '93), 1993.
[Vea 97] Eric Veach, “Robust Monte Carlo Methods for Light Transport Simulation,” Ph.D. dissertation, Stanford University, 1997.

[1] SmallVCM, http://www.smallvcm.com.
[2] GitHub, https://github.com/SmallVCM/SmallVCM.
[3] Technical report, Iliyan Georgiev, Implementing vertex connection and merging, https://www.iliyan.com/publications/ImplementingVCM.