Sampling and interpolation of the plenoptic function

In this paper, we present reconstruction schemes for the plenoptic function. Using new sampling methods, we show that, for some particular scenes, it is possible to perfectly reconstruct the plenoptic function from a finite number of cameras with finite resolution (Theorem 1 and Corollary 1). In more general cases, we demonstrate new ways of interpolating exactly the plenoptic function (Theorem 2). Finally, we show that it is possible to infer camera locations from a finite set of images. In all cases, we have perfect solutions due to the super-resolution property of the sampling. First numerical experiments on noisy observations show the potentiality of this new theoretical developments.