Morphological evaluation of closed planar curves and its application to aesthetic evaluation

In this study, we defined the order of closed planar curves as a characteristic to reduce the human effort for recognizing the shape. We propose an order index counting mirror and rotational symmetries, along with a calculation method using the autocorrelation function of curvature functions. To confirm the effectiveness of the proposed index, we conducted the experiments using two sample groups of closed curved shapes: the shapes used in Birkhoff's study and silhouettes of humidifiers. The coefficient of determination between the proposed index and sensory evaluation values of these samples were greater than 0.70, supporting the applicability of the proposed index. Additionally, this study calculated the Eysenck's beauty index as the product of the proposed order index and conventional complexity index, and confirmed the correlation between the index and sensory evaluation values of beauty against same closed shape samples. This suggests the possibility to evaluate an industrial design requirement quantitatively, and contributes to develop the automatic shape generation in product design.