Quantitative Analysis of the Shapes of Liquid Soap Bottles Using Elliptic Fourier Descriptors

Abstract

This study aims at establishing a quantitative method to evaluate bottle shapes by using a combination of elliptic Fourier descriptors (EFDs) and principal component analysis (PCA). EFDs are used for analytically parsing closed, two-dimensional contours and have been applied to evaluation of biological shapes. Using EFDs, we converted the contours of 17 body soap bottle shapes into multivariate Fourier coefficients and performed a PCA on the Fourier coefficients to extract major morphological features of body soap bottles. The principal components (PCs) were found to be related to the roundness of the bottles, their vertical location of the center of gravity, and form of the shoulder of the bottles. Participants rated their impressions of the bottle contours on a seven-point semantic differential scale. The first PC of bottle shapes was linked to impressions of “beautiful” and “refined.” Both second and third PCs were related to impressions of “active” and “unique.” Moreover, bottle shapes corresponding to each impression within the set of impressions were reconstructed using inverse Fourier transformations. The reconstructed bottle shapes were assessed to determine if they conveyed the intended impressions.