Fast radial symmetry detection under affine transformations

Jie Ni, Maneesh Kumar Singh, Claus Bahlmann

Abstract: The fast radial symmetry (FRS) transform has been very popular for detecting interest points based on local radial symmetry <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> . Although FRS delivers good performance at a relatively low computational cost and is very well suited for a variety of real-time computer vision applications, it is not invariant to perspective distortions. Moreover, even perfectly (radially) symmetric visual patterns in the real world are perceived by us after a perspective projection. In this paper, we propose a systematic extension to the FRS transform to make it invariant to (bounded) cases of perspective projection - we call this transform the generalized FRS or GFRS transform. We show that GFRS inherits the basic characteristics of FRS and retains its computational efficiency. We demonstrate the wide applicability of GFRS by applying it to a variety of natural images to detect radially symmetric patterns that have undergone significant perspective distortions. Subsequently, we build a nucleus detector based on the GFRS transform and apply it to the important problem of digital histopathology. We demonstrate superior performance over state-of-the-art nuclei detection algorithms, validated using ROC curves.