A Convexity Measure for Gray-Scale Images Based on hv-Convexity

There are several measures for the convexity of digital images that extend the basic binary decision of the classic geometrical convexity. Some algorithms measure the convexity of a binary image using intensity profiles from horizontal and vertical directions. In this paper, we generalize the idea of binary, directional convexity and evaluate the proposed algorithm on gray-scale images. Furthermore, instead of a single convexity value, a vector can be formed using our approach, which provides a more prominent feature for various applications, such as computer vision, classification, retrieval, or medical image processing. The proposed feature can also be used locally on image parts, which makes that applicable as a shape descriptor.