9 research outputs found
Boundary length of reconstructions in discrete tomography
We consider possible reconstructions of a binary image of which the row and
column sums are given. For any reconstruction we can define the length of the
boundary of the image. In this paper we prove a new lower bound on the length
of this boundary. In contrast to simple bounds that have been derived
previously, in this new lower bound the information of both row and column sums
is combined
Stability results for uniquely determined sets from two directions in discrete tomography
In this paper we prove several new stability results for the reconstruction
of binary images from two projections. We consider an original image that is
uniquely determined by its projections and possible reconstructions from
slightly different projections. We show that for a given difference in the
projections, the reconstruction can only be disjoint from the original image if
the size of the image is not too large. We also prove an upper bound for the
size of the image given the error in the projections and the size of the
intersection between the image and the reconstruction.Comment: Title changed, minor revision
Bounds for discrete tomography solutions
We consider the reconstruction of a function on a finite subset of
if the line sums in certain directions are prescribed. The real
solutions form a linear manifold, its integer solutions a grid. First we
provide an explicit expression for the projection vector from the origin onto
the linear solution manifold in the case of only row and column sums of a
finite subset of . Next we present a method to estimate the
maximal distance between two binary solutions. Subsequently we deduce an upper
bound for the distance from any given real solution to the nearest integer
solution. This enables us to estimate the stability of solutions. Finally we
generalize the first mentioned result to the torus case and to the continuous
case