Identifying Curve Characteristics by Extracting Convex and Concave Points

In various graphical data representations, identifying curve characteristics by extracting convex and concave points serves as a fundamental technique. This code implementation employs curvature relationships to specifically extract concave point counts and evaluate curve bending patterns. Such curvature-based analysis is widely applied in computer vision and machine learning systems. By extracting curve features through mathematical curvature calculations (typically using derivatives or discrete curvature estimation algorithms), the method enables object recognition in images including faces, vehicles, and buildings, playing a crucial role in pattern recognition applications. Furthermore, this approach finds practical implementations in manufacturing and medical fields - for instance, detecting surface defects in industrial products during quality control or analyzing tumor shape variations in medical diagnostics. The curvature relationship thus represents a powerful and versatile computational tool that leverages mathematical geometry principles to deliver significant value across multiple domains.