In 1978, Osserman [124] wrote a rather comprehensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can be proved in a page, yet quickly yields the classical isoperimetricâ€¦ (More)

We study the determination of finite subsets of the integer lattice Zn, n â‰¥ 2, by X-rays. In this context, an X-ray of a set in a direction u gives the number of points in the set on each lineâ€¦ (More)

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 for theâ€¦ (More)

We investigate algorithms for reconstructing a convex body K in R from noisy measurements of its support function or its brightness function in k directions u1, . . . , uk. The key idea of theseâ€¦ (More)

IEEE Transactions on Pattern Analysis and Machineâ€¦

2009

We introduce a new algorithm for reconstructing an unknown shape from a finite number of noisy measurements of its support function. The algorithm, based on a least squares procedure, is very easy toâ€¦ (More)

Basic properties of finite subsets of the integer lattice Z are investigated from the point of view of geometric tomography. Results obtained concern the Minkowski addition of convex lattice sets andâ€¦ (More)