Foundation of a new technique for geometric and non-geometric multi-shapes similarities degrees using boundary unfolding transformation with applications

Abstract

This paper presents a novel approach for measuring multi-shapes degrees of similarities. A new shape transformation concept is suggested through mapping the closed boundary of the shape using unfolded process into one-to-one equivalent graph (or signal) where ample number of approaches for similarity testing can be applied. The degree of similarity is then measured by calculating the discrepancies between each of the two transformed unfolded-graphs autocorrelation functions. The proposed method is also effective in applying clustering technique for clustering groups of shapes into three hierarchical similarity levels depending on their mutual degree of similarity. The suggested similarity method handles two categories of shapes: geometric and non-geometric. Unlike other well-known techniques in the subject of machine learning and deep learning, the presented method represents a powerful analytical-based technique for similarity analysis of both regular and irregular shapes regardless of size or orientation, and in effectively handling compound or multi-shapes degrees of similarities. The results of testing the approach on selected datasets have successfully demonstrated the great effectiveness of the developed technique in yielding output multi-shape degrees of similarities in new graphical and comprehensive forms. Finally, it is pointed out that the new approach will have many potential real-life applications such as in industry, medicine, biology, security, and authentications.