Synthetic Aperture Focusing using a Shear-Warp Factorization of the Viewing Transform

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Abstract
Synthetic aperture focusing consists of warping and adding together the images in a 4D light field so that objects lying on a specified surface are aligned and thus in focus, while objects lying of this surface are misaligned and hence blurred. This provides the ability to see through partial occluders such as foliage and crowds, making it a potentially powerful tool for surveillance. If the cameras lie on a plane, it has been previously shown that after an initial homography, one can move the focus through a family of planes that are parallel to the camera plane by merely shifting and adding the images. In this paper, we analyze the warps required for tilted focal planes and arbitrary camera configurations. We characterize the warps using a new rank- 1 constraint that lets us focus on any plane, without having to perform a metric calibration of the cameras. We also show that there are camera configurations and families of tilted focal planes for which the warps can be factorized into an initial homography followed by shifts. This shear-warp factorization permits these tilted focal planes to be synthesized as efficiently as frontoparallel planes. Being able to vary the focus by simply shifting and adding images is relatively simple to implement in hardware and facilitates a real-time implementation. We demonstrate this using an array of 30 videoresolution cameras; initial homographies and shifts are performed on per-camera FPGAs, and additions and a final warp are performed on 3 PCs.

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