Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shapes From Pixels   Continuous-domain visual signals are usually captured as discrete (digital)
images. This operation is not invertible in general, in the sense that the
continuous-domain signal cannot be exactly reconstructed based on the discrete
image, unless it satisfies certain constraints (\emph{e.g.}, bandlimitedness).
In this paper, we study the problem of recovering shape images with smooth
boundaries from a set of samples. Thus, the reconstructed image is constrained
to regenerate the same samples (consistency), as well as forming a shape
(bilevel) image. We initially formulate the reconstruction technique by
minimizing the shape perimeter over the set of consistent binary shapes. Next,
we relax the non-convex shape constraint to transform the problem into
minimizing the total variation over consistent non-negative-valued images. We
also introduce a requirement (called reducibility) that guarantees equivalence
between the two problems. We illustrate that the reducibility property
effectively sets a requirement on the minimum sampling density. One can draw
analogy between the reducibility property and the so-called restricted isometry
property (RIP) in compressed sensing which establishes the equivalence of the
$\ell_0$ minimization with the relaxed $\ell_1$ minimization. We also evaluate
the performance of the relaxed alternative in various numerical experiments.

21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph