A 4D frequency-planar IIR filter and its application to light field processing

Abstract

A 4D frequency-planar filter is described, having a steady-state frequency response with a pass band that approximates that of a 4D plane. It is shown that a light field containing Lambertian surfaces with no occlusions may be selectively filtered for depth using such a filter.Examples are given showing the effectiveness of the filter in scenes with and without occlusions. A technique for effectively reducing the length of the transient response of the filter is also proposed and the effectiveness of this technique demonstrated.

Linear Volumetric Focus for Light Field Cameras

“…We further test a 4D Gaussian filter as well as a 4D planar Gaussian filter that is the basis for synthetic refocusing of light fields [Dansereau and Bruton 2003;Ng 2005]. Dictionary-based image denoising approaches do not exploit the structure of the light field; nevertheless, by collapsing the light field into a tiling of images, we test the overcomplete discrete cosine transform (DCT) [Guleryuz 2007] and K-SVD methods ].…”

“…The frequency content of light fields has been the subject of extensive research [Chai et al 2000;Durand et al 2005;], with the frequency plane being a commonly identified feature. To the authors' knowledge, the first frequency-planar light field filter was proposed by Isaksen et al [2000], and the same idea has since reappeared with minor variations, including efficient recursive and frequency-slicing approaches for carrying out light field focus [Dansereau and Bruton 2003;Ng 2005].…”

“…As depicted in Figure 3(a), if one begins with a ray that intersects P (highlighted), then translates that ray's point of intersection along s, its point of intersection along u must follow at a proportional rate in order for the ray to maintain its intersection with P. In other words, the rays emanating from P follow a linear relationship in s and u. This is the light field manifestation of parallax motion [Bolles et al 1987;Dansereau and Bruton 2003].…”

Light field image denoising using a linear 4D frequency-hyperfan all-in-focus filter

“…17,18 The linear relationship in (x, u) describes a hyperplane in 4D space, and by extension a similar hyperplane exists in (y, v). Taken simultaneously these hyperplanes intersect to describe the plane λ, a slice of which is depicted in (x, u) in Fig.…”

“…18 A scene consisting of surface elements at a single depth will therefore yield a light field of parallel, constant-valued planes with orientation determined by the surface's depth, following (1). The Fourier transform of such a set of parallel planes is a single plane through the origin 18 -this arises because the light field is constant-valued in two directions parallel to the constant-valued spatial planes. The frequency plane can be described as…”