Theoretical Analysis of Multi-View Camera Arrangement and Light-Field Super-Resolution

We analyzed a light-field super-resolution problem in which, with a given set of multi-view images with a low resolution, the 3-D scene is reconstructed with a higher resolution using super-resolution (SR) reconstruction. The arrangement of the multi-view cameras is important because it determines the quality of the reconstruction. To simplify the analysis, we considered a situation in which a plane is located at a certain depth and a texture on that plane is super-resolved. We formulated the SR reconstruction process in the frequency domain, where the camera arrangement can be independently expressed as a matrix in the image formation model. We then evaluated the condition number of the matrix to quantify the quality of the SR reconstruction. We clarified that when the cameras are arranged in a regular grid, there exist singular depths in which the SR reconstruction becomes ill-posed. We also determined that this singularity can be avoided if the arrangement is randomly perturbed.