On the Spectrum of the Plenoptic Function

The plenoptic function is a powerful tool to analyze the properties of multi-view image data sets. In particular, the understanding of the spectral properties of the plenoptic function is essential in many computer vision applications, including image-based rendering. In this paper, we derive for the first time an exact closed-form expression of the plenoptic spectrum of a slanted plane with finite width and use this expression as the elementary building block to derive the plenoptic spectrum of more sophisticated scenes. This is achieved by approximating the geometry of the scene with a set of slanted planes and evaluating the closed-form expression for each plane in the set. We then use this closed-form expression to revisit uniform plenoptic sampling. In this context, we derive a new Nyquist rate for the plenoptic sampling of a slanted plane and a new reconstruction filter. Through numerical simulations, on both real and synthetic scenes, we show that the new filter outperforms alternative existing filters.