2011/04/29 by Birgit van Dalen, Lajos Hajdu, van Dalen, Birgit +3
Computer Science · Medicine · #94A08 (Primary) 15A06 (Secondary) #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1104.5589
openalex publication_date 2011/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the reconstruction of a function on a finite subset of ℤ2 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 Z2. 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.