Benchmarking Point Cloud Feature Extraction with Smooth Overlap of Atomic Positions (SOAP): A Pixel-Wise Approach for MNIST Handwritten Data

In this study, we introduce a novel application of the Smooth Overlap of Atomic Positions (SOAP) descriptor for pixel-wise image feature extraction and classification as a benchmark for SOAP point cloud feature extraction, using MNIST handwritten digits as a benchmark. By converting 2D images into 3D point sets, we compute pixel-centered SOAP vectors that are intrinsically invariant to translation, rotation, and mirror symmetry. We demonstrate how the descriptor’s hyperparameters—particularly the cutoff radius—significantly influence classification accuracy, and show that the high-dimensional SOAP vectors can be efficiently compressed using PCA or autoencoders with minimal loss in predictive performance. Our experiments also highlight the method’s robustness to positional noise, exhibiting graceful degradation even under substantial Gaussian perturbations. Overall, this approach offers an effective and flexible pipeline for extracting rotationally and translationally invariant image features, potentially reducing reliance on extensive data augmentation and providing a robust representation for further machine learning tasks.