EquArchNets: Equivariant Neural Networks-Based Approach for Foot Arch Classification Toward Variations in Foot Orientation

Flat feet and high arches are common foot deformities that significantly affect human foot health. The early recognition has a substantial positive impact on interventions for abnormal arches. The previous research has focused on classifying foot arch types using machine learning methods based on plantar pressure images. However, due to angular deviation and the asymmetry between the left and right feet caused by individual differences, traditional convolutional neural networks (CNNs) struggle to achieve high performance, particularly when addressing variations in foot orientation in plantar pressure images. In addition, objectively assessing these deep learning models is challenging due to the lack of publicly available image datasets for arch classification. To evaluate existing methods, this study collected 2327 plantar pressure images from 1126 participants, which were classified by two graders into the categories of high arches, flat feet, and normal feet. The proposed data augmentation method aligns more closely with assessing the generalization and robustness of these models. A series of improved models referred to as EquArchNets, has been proposed to address the issue of rotation invariance in CNNs for foot arch classification tasks. These models incorporate equivariant modules into traditional CNNs, and their parameters are optimized accordingly. Experimental results indicate that in the task of arch classification based on orientation-varied plantar pressure images, our enhanced framework achieves better performance in terms of accuracy, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${F}1$ </tex-math></inline-formula> score, and precision, with maximum increases of 4.02%, 4.12%, and 5.06%, respectively. In addition, the minimum number of parameters in the optimized model is only 40.41% of the original.