Analyzing a Curvature Scale Space Approach to Dent Counting in Blobs

Shapes arise in image analysis in many domains, and having a shape in hand is often not the end of the story. How do we measure properties of the shape, especially those related to features like indentations? In this article we review existing methods for analyzing simple closed curves, such as the Curvature Scale Space image concept, mean curvature flow, and smoothing filters. We then present a novel application of the Curvature Scale Space method in which we seek to answer two rather subtle questions: what is a dent, and how do we count them? In order to answer these questions, we first demonstrate that indentations are tied to the local curvature along the boundary, so to properly identify them, we need to analyze the sign and magnitude of this local curvature. In this process, the Curvature Scale Space image is very useful because it depicts theses changes in curvature at different scales using Gaussian smoothing functions of increasing widths. To count the dents, we wish to identify the width of the smoothing function below which indicates noise on the boundary and the radius of curvature above which designates larger structural features in the boundary. Removing all of these will leave us with only those areas of curvature that we identify as dents. We then discuss one possible value for each of the above parameters, examine pathological cases, and note areas for further research.