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.
Vlachou, M. E., Thomas, E., Blouin, J.
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