Digital geometry is about deriving geometric information from digital pictures. The field
emerged from its mathematical roots some forty-years ago through work in computer-based …

Advances in Discrete Tomography and Its Applications is a unified presentation of new
methods, algorithms, and select applications that are the foundations of multidimensional …

We study the computational complexity of various inverse problems in discrete tomography.
These questions are motivated by demands from the material sciences for the reconstruction …

We present a novel approach to the tomographic reconstruction of binary objects from few
projection directions within a limited range of angles. A quadratic objective functional over …

A close discrete analog of the classical Brunn-Minkowksi inequality that holds for finite
subsets of the integer lattice is obtained. This is applied to obtain strong new lower bounds …

Let A be a® nite subset of Zl. We consider the problem of reconstructing a function f: A 3 f0Y
1g if all the line sums in® nitely many directions are given. In Theorem 1 we give a complete …

A transportation polytope consists of all multidimensional arrays or tables of non-negative
real numbers that satisfy certain sum conditions on subsets of the entries. They arise …

Computed Tomography (CT) is an essential non-destructive three dimensional imaging
modality used in medicine, security screening, and inspection of manufactured components …

In this paper, we study the problem of reconstructing special lattice sets from X-rays in a
finite set of prescribed directions. We present the class of “Q-convex” sets which is a new …

In this paper we examine the problem of reconstructing a discrete two-dimensional set from
its two orthogonal projection (H, V) when the set satisfies some convexity conditions. We …