A new area-based convexity measure with distance weighted area integration for planar shapes

Abstract

A new area-based convexity measure with distance weighted area integration for planar shapes http://researchonline.ljmu.ac.uk/id/eprint/10645/ Article LJMU has developed LJMU Research Online for users to access the research output of the University more effectively. AbstractIn this paper we propose a new area-based convexity measure. We assume that convexity evaluation of an arbitrary planar shape is related to the total influence of dents of the shape, and discover that those attributes of the dents, such as the position, area, and depth with respect to the Geometric Center of Convex Hull (GCCH) of the shape, determine the dent influence. We consider that the convex hull of the shape consists of infinitely small patches, to each of which we assign a weight showing the patch influence. We can simply integrate all the patch weights in any regions within the convex hull to calculate their total influence. We define this operation as the Distance Weighted Area Integration, if the weight is associated with the Euclidean distance from the patch to the GCCH. Our new measure is a distance weighted generalization of the most commonly used convexity measure, making this conventional measure fully replaceable for the first time. Experiments demonstrate advantages of the new convexity measure against the existing ones.

Fuzzy circularity: A new fuzzy shape-based descriptor of the object

“…Some of them have a clear geometric or topological interpretation, which allows them to be relatively easily contextually and numerically described as such. To mention only some of them: convexity [18,19], elongation [20,21], hexagonality [21], Euler number [22,23], circularity [24,25] , disconnectedness [26], etc. In addition, there are shape measures that are not initially designed to assess the degree to which a considered shape exhibits certain properties, but are able to provide a feature vector of sufficient dimensionality to describe the observed shape.…”