A hybrid geometric-feature algorithm for 2D shape similarity

In this paper, we address the problem of quantifying similarity between planar 2D shapes, which is relevant to studies of internal representations in cognitive, developmental, and neurological research. We designed a set of test shapes arranged along a visually defined perceptual similarity gradient and used them to evaluate classical geometric methods for shape comparison, including Procrustes and Chamfer distance, as well as a convolutional neural network (CNN)-inspired feature-based method. Based on the limitations identified for these individual methods, we developed a hybrid Geometric-Feature Similarity (GFS) algorithm that combines geometric alignment, global contour properties, and convolutional feature-based descriptors into a unified weighted similarity score. By combining global geometric information with local structural features, the GFS algorithm more accurately reproduces human perceptual judgments of shape similarity than either geometric or feature-based methods alone. Requiring neither network training nor large labelled datasets, the proposed algorithm provides an efficient and interpretable tool for a broad range of studies involving quantitative shape comparison.