A unifying resolution-independent formulation for early vision

Abstract

We present a model for early vision tasks such as denoising, super-resolution, deblurring, and demosaicing. The model provides a resolution-independent representation of discrete images which admits a truly rotationally invariant prior. The model generalizes several existing approaches: variational methods, finite element methods, and discrete random fields. The primary contribution is a novel energy functional which has not previously been written down, which combines the discrete measurements from pixels with a continuous-domain world viewed through continousdomain point-spread functions. The value of the functional is that simple priors (such as total variation and generalizations) on the continous-domain world become realistic priors on the sampled images. We show that despite its apparent complexity, optimization of this model depends on just a few computational primitives, which although tedious to derive, can now be reused in many domains. We define a set of optimization algorithms which greatly overcome the apparent complexity of this model, and make possible its practical application. New experimental results include infinite-resolution upsampling, and a method for obtaining "subpixel superpixels".

OpenDR: An Approximate Differentiable Renderer

“…Instead he uses MCMC sampling and suggests that sampling could be used in conjunction with a differentiable renderer to avoid problems due to occlusion. See also [34], which addresses similar issues in image modeling with a continuous image representation.…”

8. Bilevel approaches for learning of variational imaging models

“…Hence, it makes sense to seek images which have certain properties in an infinite dimensional function space. That is, we aim for a processing method that accentuates and preserves qualitative properties in images independent of the resolution of the image itself [83]. Moreover, optimisation methods conceived in function space potentially Figure 1: Camera technology tending towards continuum images?…”

Super-resolution via Transform-Invariant Group-Sparse Regularization

“…The most common choice in the literature is to penalize the 1 norm of the gradient [11], also known as the total variation (TV) of the image, or related non-convex penalties [10] in order to obtain an estimate with a sparse gradient (see also [15] for a recent approach that takes discretization into account). Unfortunately, minimizing the total variation often fails to superresolve two-dimensional edges, even in the case of very simple piecewise-constant images such as the checkerboard shown in Figure 3.…”