Application Of Tensor Completion In Monte Carlo Path Tracing Method

Offline rendering usually needs a lot of samples to get converge results. If not enough samples are given, the pictures rendered always have sensible noise. How to reduce samples is an important issue in offline rendering.The key properties of light filed are coherence and low rank. Light field can be considered as a matrix with redundant. Nearby pixels in the scene usually have similar light field. Consider pixels as rows, and directions as columns, then light field can be viewed as a matrix. The matrix is always low rank. Matrix completion, which is a powerful tool in machine learning, can be used here to sample radiance sparsely to recovery the whole light filed, and then calculate contribution in each direction to the sample point. What’s more, spectrum has three channels, RGB, then the matrix can be extended to a 3-dimension tensor. Tensor completion can be used to recovery the light field.Based on previous description and background, the thesis studies about how to apply tensor completion to monte carlo path tracing framework, try to use very few samples to approximately recovery the whole light field and calculate the results. Each element in tensor store the product of radiance and cos. Besides, without knowing the information of scene previously, we cannot know which cluster should use more samples to do the completion, the completion process may fail. Based on previous information from tensor completion, we can judge which clusters may fail in completion process and do the filtering process use information that are already known, in order to get better rendering results.The article analyses the rationality of applying tensor completion in ray tracing, fulfill the algorithm, and give some examples. The results show that our algorithm can converge very fast.