Lightfield Recovery from Its Focal Stack

The Focal Stack Transform integrates a 4D lightfield over a set of appropriately chosen 2D planes. The result of such integration is an image focused on a determined depth in 3D space. The set of such images is the Focal Stack of the lightfield. This paper studies the existence of an inverse for this transform. Such inverse could be used to obtain a 4D lightfield from a set of images focused on several depths of the scene. In this paper, we show that this inversion cannot be obtained for a general lightfield and introduce a subset of lightfields where this inversion can be computed exactly. We examine the numerical properties of such inversion process for general lightfields and examine several regularization approaches to stabilize the transform. Experimental results are provided for focal stacks obtained from several plenoptic cameras. From a practical point of view, results show how this inversion procedure can be used to recover, compress, and denoise the original 4D lightfield.