Ray-space Reconstruction By Low-Rank Matrix Completion

Monte Carlo path tracing is currently the most important photorealistic rendering methods.However,this method faces the problem of slow convergence.under-sampling leads to noisy result.How to reduce samples is a very important research issues.Local sparsity of the light field has been a consensus,because the incident light of space-adjacent vertexs tends to be the same.Compressed sensing knowledge shows that recovering sparse signals with very few samples is possible.Consider pixels as rows,and directions as columns,then light field can be viewed as a matrix.The matrix is low rank.Matrix completion,which is a powerful tool in Compressed sensing,can be used here to sparsely sample radiance to recover it.We are concerned about at least how many samples do this method need to successfully accomplish recovery.Mature research results show that it has a lot to do with the matrix Coherence.Based on this,this thesis studies the Coherence of the light transport field,and demonstrate some important mathematical results;Then a guided-K-means clustering algorithm is proposed to segment scene space into local patchs with good sparsity and low column space Coherence;Finally we introduce an excellent adaptive-sampling-based low rank matrix completion algorithm to recover the light field.this algorithm runs fast,needs few samples and fits well for our rendering problem.We prove its superiority through several experimental results;what's more,we make further optimization by simplifing calculation and gain a speed-up of 2?4 times.The reconstructed light field can be used as importance function for subsequent resampling..If the reconstructed light field and real light field is close enough,which can also be directly used to render the final image.