State of the Art of Compactness and Circularity Measures 1

Abstract

Compactness is an intrinsic property of objects. This feature is often associated with the old and classical ratio perimeter2/area. This ra-tio is used in many scientific fields as shape descriptor in shape analysis tasks. However, when we use this ratio for measuring shape compactness in the digital domain some problems arise. Several approaches have been proposed for measuring shape compactness of discrete regions. This pa-per presents a review of several methods for measuring shape circularity and compactness and surveys some of them when scaling transforma-tion is applied to discrete regions. Also, we present a comparison of the studied methods using the same set of examples of binary shapes under different conditions: shapes with holes and with noisy perimeters.