Automated shape recognition is a common problem which have been faced in computer vision applications. The feature(s) used to classify shapes should be chosen well for an accurate and fast way. Centroid distance function curve is a widely used feature in this field because of its quick and easy calculation properties. This study which is aimed to classify 2D convex geometric shapes based on the analysis of extreme points of the curve is proposed. The proposed method is robust to translation, rotation and scale of the objects.