Publication
Digital photography exists since 1975, when Steven Sasson attempted to build the first digital camera. Since then the concept of digital camera did not evolve much: an optical lens concentrates light rays onto a focal plane where a planar photosensitive array transforms the light intensity into an electric signal. During the last decade a new way of conceiving digital photography emerged: a photography is the acquisition of the entire light ray field in a confined region of space. The main implication of this new concept is that a digital camera does not acquire a 2-D signal anymore, but a 5-D signal in general. Acquiring an image becomes more demanding in terms of memory and processing power; at the same time, it offers the users a new set of possibilities, like choosing dynamically the focal plane and the depth of field of the final digital photo. In this thesis we develop a complete mathematical framework to acquire and then reconstruct the omnidirectional light field around an observer. We also propose the design of a digital light field camera system, which is composed by several pinhole cameras distributed around a sphere. The choice is not casual, as we take inspiration from something already seen in nature: the compound eyes of common terrestrial and flying insects like the house fly. In the first part of the thesis we analyze the optimal sampling conditions that permit an efficient discrete representation of the continuous light field. In other words, we will give an answer to the question: how many cameras and what resolution are needed to have a good representation of the 4-D light field? Since we are dealing with an omnidirectional light field we use a spherical parametrization. The results of our analysis is that we need an irregular (i.e., not rectangular) sampling scheme to represent efficiently the light field. Then, to store the samples we use a graph structure, where each node represents a light ray and the edges encode the topology of the light field. When compared to other existing approaches our scheme has the favorable property of having a number of samples that scales smoothly for a given output resolution. The next step after the acquisition of the light field is to reconstruct a digital picture, which can be seen as a 2-D slice of the 4-D acquired light field. We interpret the reconstruction as a regularized inverse problem defined on the light field graph and obtain a solution based on a diffusion process. The proposed scheme has three main advantages when compared to the classic linear interpolation: it is robust to noise, it is computationally efficient and can be implemented in a distributed fashion. In the second part of the thesis we investigate the problem of extracting geometric information about the scene in the form of a depth map. We show that the depth information is encoded inside the light field derivatives and set up a TV-regularized inverse problem, which efficiently calculates a dense depth map of the sce