Measures of Q-convexity

by Sara Brunetti (Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche, Universita di Siena, Italy)
and Péter Balázs (Institute of Informatics, University of Szeged, Hungary)

For details see the paper „P. Balázs, S. Brunetti: A measure of Q-convexity for shape analysis, Journal of Mathematical Imaging and Vision 62, pages 1121–1135 (2020)”.

Consider a binary image and define four quadrants around each point as

,
,
,
.

A binary image is Q-convex if and only if for all implies

The Q-convex hull of is the set of points such that for all .

For a given binary image , its Q-convexity measure is defined to be

A point is a salient point of if We denote the set of salient points of by . The set of the generalized salient points of is defined by , where and is the smallest integer for which .

For a given binary image , its Q-convexity measure is defined to be

For a given binary image , its Q-convexity measure is defined to be

For a given binary image , its Q-convexity measure is defined to be

For a given binary image , its Q-convexity measure is defined to be

You can download the file for calculating the above measures here.

The .zip file contains an executable (tested for Windows), a readme, and an example image with its output. When using this program, please refer to the paper „P. Balázs, S. Brunetti: A measure of Q-convexity for shape analysis, Journal of Mathematical Imaging and Vision 62, pages 1121–1135 (2020)”.