蒙地卡羅路徑追蹤演算法透過模擬真實環境中光的反射和折射來產生逼真的畫面，此技術在影視、遊戲、物理模擬、建築設計中皆有著舉足輕重的地位。近幾年隨著電腦硬體的進步，以及更多有效的路徑採樣和去雜訊方法被提出，已經可以在電腦上即時地產生低雜訊的路徑追蹤影像。

我們發現，雖然低頻的直接照明和間接照明有明顯的改善，但高頻的鏡面成像和焦散依舊無法保持銳利甚至消失，主要是因為能產生高頻效果的「含有鏡面鏈的光傳輸路徑」難以被找到，因此即使再透過後處理的方法去雜訊，也無法在動態場景中即時產生清晰且正確的高頻效果。

低頻效果可以提升整體影像的層次感，但高頻效果往往是最能吸引眼球的部分，因此我們致力於研究針對高頻效果即時路徑追蹤的演算法。在本論文中，我們發明了新的尋找鏡面鏈的技術SMBS和PMS來降低路徑追蹤在高頻效果的雜訊，SMBS透過大擾動改善鏡面鏈路徑的搜索，PMS透過光子重用優化起始鏡面鏈路徑的選擇。對於後續的去噪，我們提出了針對高頻效果的去雜訊演算法IGD，透過再利用路徑追蹤的資訊來提升去雜訊的品質。對於整體的算圖流程，我們設計了一個利於手機的低計算量方法RMNEE，將鏡面鏈演算法透過延遲著色和重採樣來機率性地不計算較低顏色貢獻的鏡面鏈路徑。

與過去的方法相比，我們的方法在相同的採樣數下，大大提高了尋找鏡面鏈的成功率；等時比較下的高頻效果，路徑追蹤的雜訊更少、去雜訊後的誤差值更低；對於低算力的手機平台，更可以在畫面品質和執行速度上達到不錯的平衡。

The Monte Carlo path tracing algorithm produces realistic images by simulating the reflection and refraction of light in the real world. This technique plays a crucial role in film production, gaming, physical simulations, and architectural design. With the advancement of hardware and the development of more effective path sampling and denoising methods, low-noise path-traced images can be generated in real time on computers now.

However, while low-frequency effects such as direct and indirect illumination have seen significant improvements, high-frequency effects like mirror reflections, glass refractions and caustics often blur or miss. This limitation arises from the difficulty in finding light transport paths containing "specular chains", which are essential for producing high-frequency effects. As a result, even with post-processing denoising techniques, it remains challenging to achieve sharp and accurate high-frequency effects in real-time for dynamic scenes.

Although low-frequency effects make images more stereoscopic, high-frequency effects are often the most visually striking elements. Therefore, this paper focuses on developing algorithms for real-time path tracing of high-frequency effects. We introduce two novel techniques, Specular Manifold Bisection Sampling (SMBS) and Photon-Driven Manifold Sampling (PMS), to reduce noise in high-frequency effects. SMBS improves the search for specular chains through large perturbations, while PMS optimizes the selection of initial paths by reusing photon information. For subsequent denoising, we propose the Improved G-Buffer Denoising (IGD), which enhances denoising quality by leveraging additional path tracing information. For the overall rendering pipeline, we design a computationally efficient method, Resampled Manifold Next Event Estimation (RMNEE), optimized for mobile devices. RMNEE reduces the computation of low-contribution specular chains by integrating deferred shading and resampled importance sampling techniques.

Compared to previous methods, our approach significantly increases the success rate of finding specular chains with the same number of samples. In equal-time comparisons, we reduce noise in high-frequency effects and achieve lower error rates after denoising. On low-power mobile platforms, our method strikes a favorable balance between image quality and execution speed.

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