Applications of Signatures in Diagnosing Breast Cancer

  • Anna M Grim University of St. Thomas
  • Cheri Shakiban University of St. Thomas


Noninvasive diagnosis of breast tumors persists as a challenge in oncology because the structural differences between benign and malignant tumors are indistinguishable to the human eye. However, the application of signature curve symmetry can diagnose tumors by mathematically analyzing curvature. Our methodology quantifies a two-dimensional (2D) tumor contour by the rigidly invariant signature curve parametrization taken with respect to arc length. The differing shape of benign and malignant tumors results in contrasting global and local symmetry patterns in the signature curve. Benign tumors are distinctive by a high degree of global symmetry in the 2D tumor contour, whereas, malignant tumors exhibit multiple types of local symmetry embedded within their signature curve. The methodology has been implemented on over 150 tumors, demonstrating a statistically significant correlation between curvature complexity and malignancy.

How to Cite
GRIM, Anna M; SHAKIBAN, Cheri. Applications of Signatures in Diagnosing Breast Cancer. Minnesota Journal of Undergraduate Mathematics, [S.l.], v. 1, n. 1, dec. 2015. ISSN 2378-5810. Available at: <>. Date accessed: 25 sep. 2020.