基于低秩矩阵补全的光场空间重建

发布时间：2018-06-28 08:53

本文选题：真实感绘制 + 稀疏性　；参考：《浙江大学》2016年硕士论文

【摘要】：蒙特卡罗路径追踪(path tracing)是目前最重要的真实感绘制方法,是照片级真实感绘制的基础,然而这种方法面临着收敛速度慢的问题,在采样不足时图像会出现明显噪点,如何减少采样加快收敛是一个很重要的研究问题。“光场具有局部稀疏性”是绘制中早已存在的共识,这是因为场景空间相邻点接收的光辐射度也倾向相似。压缩感知相关知识表明,以极少采样量恢复原始稀疏信号是可能的。如果将场景空间临近的着色点排列成行,上半球面域入射光采样方向细分铺开成列,组成一个光传输矩阵,则该矩阵是低秩的,可以利用压缩感知中广泛应用的低秩矩阵补全方法稀疏采样重建出光场。我们关心的是,这种方法补全一个矩阵最低需要多少采样数?这方面已有成熟的研究成果,其中与矩阵的元素分布结构有较大关系,数学上用Coherence这一变量来表示。基于此,本文首先研究了传输光场的矩阵Coherence相关性质,推导论证出一些定性和定量的数学结论;然后以此为指导,设计出一种似K-means聚类算法,用于将场景空间分割成局部光场具有较好稀疏性和低列空间Coherence的局部块(local patch),并通过实验证实该聚类算法优于传统的K-means算法;最后本文引入一种基于自适应采样的低秩矩阵补全算法对聚类后的局部光场进行重建,该算法运行速度快,补全需要的采样数比其他算法低,且非常适用于本文的绘制问题,本文也通过若干实验结果证实了这些优越性;另外,本文在不改变原算法逻辑的前提下,还对该算法作了进一步的优化,矩阵补全结果未受影响,但是运行速度却显著地提升了 2～4倍。重建出来的光场可以作为重要度函数,用于后续蒙特卡罗光线追踪的重采样过程。如果重建光场与真实光场足够接近,也可以被直接用于最终图像的绘制。
[Abstract]:Monte Carlo path tracing (path tracing) is the most important method of realistic rendering at present, which is the basis of photo-level realistic rendering. However, this method is faced with the problem of slow convergence. "the local sparsity of light field" is a consensus in rendering, which is because the intensity of light radiance received by adjacent points in scene space also tends to be similar. The knowledge of compressed sensing shows that it is possible to recover the original sparse signal with a small sample amount. If the coloring points near the scene space are arranged in rows and the sampling direction of the incident light in the upper hemispherical domain is subdivided into columns to form an optical transmission matrix, the matrix is of low rank. The low rank matrix complement method widely used in compressed sensing can be used to reconstruct the light field by sparse sampling. Our concern is, what is the minimum number of samples needed by this method to complement a matrix? There have been mature research results in this field, in which there is a great relationship with the element distribution structure of the matrix, which is expressed mathematically by coherence as a variable. Based on this, this paper first studies the matrix coherence correlation properties of the transmission light field, deduces some qualitative and quantitative mathematical conclusions, and then designs a K-means like clustering algorithm under the guidance of this method. The local block (local patch), is used to divide the scene space into local light fields with good sparsity and coherence in low column space. The experimental results show that the clustering algorithm is superior to the traditional K-means algorithm. Finally, this paper introduces a low rank matrix complement algorithm based on adaptive sampling to reconstruct the local light field after clustering. The algorithm runs faster and needs less samples than other algorithms, and it is very suitable for the rendering problem in this paper. In addition, without changing the logic of the original algorithm, the algorithm is further optimized, and the results of matrix complement are not affected. However, the speed of the operation was significantly increased by 2 times. The reconstructed light field can be used as an importance function for the subsequent Monte Carlo ray tracing resampling process.
【学位授予单位】：浙江大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP391.41

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