Description
We combine the Isoperimetric Inequality (Dido's Problem) and the Cauchy-Crofton formula to approximate the area enclosed by Jordan curves in the 2D plane. The Cauchy-Crofton formula provides a consistent estimate of a curve's length, which the Isoperimetric Inequality then uses to approximate the enclosed area. We additionally present software that automates the Cauchy-Crofton length computation, making the method practical for real-world use. Empirical testing validates the accuracy of this combined approach, with potential applications in tumor segmentation from MRI scans.
Date of Event
Thursday, April 23, 2026
Location
Parker Building 338
Included in
Area Approximation of Jordan Curves via the Isoperimetric Inequality and Cauchy-Crofton Formula
Parker Building 338
We combine the Isoperimetric Inequality (Dido's Problem) and the Cauchy-Crofton formula to approximate the area enclosed by Jordan curves in the 2D plane. The Cauchy-Crofton formula provides a consistent estimate of a curve's length, which the Isoperimetric Inequality then uses to approximate the enclosed area. We additionally present software that automates the Cauchy-Crofton length computation, making the method practical for real-world use. Empirical testing validates the accuracy of this combined approach, with potential applications in tumor segmentation from MRI scans.
Presenter Bio
Nikita Veselkin is a senior at the NSU University school whose academic interests include programming and engineering. He has competed in programming competitions and Mathematics Olympiads while living in Russia and is looking for new and innovative ways to improve in his areas of interest.
Rashad Kaiyal is a senior at the NSU University School whose primary academic interests are theoretical physics and mathematics. He plans to major in physics and minor in math in his future undergraduate studies.