Compactness measure of digital shapes

This paper presents a method for measuring the compactness of digital shapes, namely, the digital compactness. Unlike analog shapes, boundary of a digital shape (especially for low-resolution image) has measurable width and thus both its perimeter and area may have different measurements using different methods. Furthermore, rotating a digital shape results in changes in its perimeter and area, and thus its digital compactness. The purpose of this paper is to search for a method for measuring the perimeter, area, and compactness of a digital shape so that, for a given analog geometric shape, the difference between its analog compactness and digital compactness is minimized.