Total Curvature and Intersection Tomography

✍ Scribed by T.J. Richardson

• Book ID: 102966911
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 512 KB
• Volume: 130
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1996.1640

✦ Synopsis

We show how to reconstruct certain one-dimensional generalized sets in the plane, which we call K-sets, from their projections. A projection onto a line G at the point p counts (with multiplicities) the number of points in the set which lie on the line which is perpendicular to G and passes through p. We also prove a formula, analogous to Crofton's formula, relating the total absolute curvature'' of such a set to the average total variation of its projections. The formulation of the class of K-sets captures a notion of finite total absolute curvature that is independent of parametrizations. We define the total absolute curvature of a K-set to be the minimal total absolute curvature of a collection of curves which represent'' the set.