Super-Resolved Fourier-Slice Refocusing in Plenoptic Cameras

A fast and memory-efficient Discrete Focal Stack Transform for plenoptic sensors

“…To describe the Fast Discrete Focal Stack Transform we use the following decomposition of (1): (14) and the δ representation in the Fourier domain:…”

“…Based on this 3D information it is possible to obtain all-in-focus images in which all the elements in the image are in focus. In order to test the suitability of the Fast Discrete Fourier Transform for these tasks we will use Depth-from-focus (DFF) technique [14] to recover depth. DFF is a 3D reconstruction method based on applying a focus measure to a set of differently focused photos.…”

“…We use a Laplacian based focus measure FM [21]: [14]. The convolutions in (22) can either be implemented in the spatial domain or in the frequency domain modifying…”

“…Note that although a plenoptic camera captures O(n 2 m 2 ) pixels they are decomposed into O(n 2 ) pixels providing spatial information and O(m 2 ) providing directional information, so the resolution of the refocused image is O(n 2 ) and several algorithms have been developed to increase the spatial resolution of the photographs in the Focal Stack using super-resolution methods. In [14] the Discrete Focal Stack transform is used to increase the resolution of the refocused photographs, so refocusing methods in the frequency domain can be used to generate super-resolution in refocused photographs. In this paper we present a fast and memory-efficient Discrete Focal Stack Transform based on the frequency decomposition of the 3D Focal Stack.…”

“…In Section 2 we introduce the algorithms to compute the Focal Stack in the frequency domain that are based on the Fourier Slice technique in [11,15]. In Section 3 we present our new Focal Stack frequency decomposition technique and discuss its properties.…”