✦ LIBER ✦
Detecting and reconstructing centrally symmetric sets from the autocorrelation: Two discrete cases
✍ Scribed by Gennadiy Averkov
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 435 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
Let A be a finite, centrally symmetric set in R d , d ≥ 1, and let B be a set homometric to A, that is, for all x ∈ R d the sets A ∩ (A + x) and B ∩ (B + x) have equal cardinalities. We show that B is a translate of A. As a consequence, an analogous statement is obtained for bodies which are unions of lattice cubes. We notice that homometric sets are relevant in several research areas including image analysis, geometric probability, and X-ray crystallography.