An in depth look at the Procrustes-Wasserstein distance: properties and barycenters
Authors: Davide Adamo, Marco Corneli, Manon Vuillien, Emmanuelle Vila
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We benchmark our method against existing OT approaches, demonstrating superior performance in scenarios requiring precise alignment and shape preservation. We finally show the usefulness of the PW barycenters in an archaeological context. Our results highlight the potential of PW in boosting 2D and 3D point cloud analysis for machine learning and computational geometry applications. |
| Researcher Affiliation | Academia | 1Universit e Cˆote d Azur, UMR 7264 CEPAM, CNRS, Nice, France 2Universit e Cˆote d Azur, Inria, CNRS, Laboratoire J.A. Dieudonn e, Maasai team, Nice, France 3Universit Lumi ere Lyon II, UMR 5133 Arch eorient CNRS, Lyon, France. |
| Pseudocode | Yes | Algorithm 1 PW problem Algorithm 2 Procrustes-Wasserstein barycenter (PWB) For completeness, we provide Algorithm 3 in the supplementary material, detailing the procedure for the optimization with respect to p. |
| Open Source Code | Yes | The code is available at https: //github.com/Davide Adamo98/PW-bary. |
| Open Datasets | Yes | We consider the MNIST dataset of handwritten digits with specific focus on the first five digits, from 0 to 4 (Figure 3, left). |
| Dataset Splits | No | The paper does not provide specific train/test/validation dataset splits. For the MNIST dataset, it mentions taking "10 images for each digit class" resulting in 50 point clouds for clustering, but this describes a subset selection rather than a split for reproducibility of supervised experiments. It also describes data generation (50 clouds with added noise/perturbations) but not a split of an existing dataset. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory amounts, or detailed computer specifications) used for running its experiments. |
| Software Dependencies | No | The paper mentions "The OT solvers used in the implementations are based on the POT toolbox (Flamary et al., 2021)", but it does not specify a version number for the POT toolbox or any other software dependencies. |
| Experiment Setup | Yes | In this section, we inspect several initialization strategies of Γ0 (Algorithm 1) for PW in the context of 2D/3D point cloud matching. To initialize the centroids, we adopt a strategy inspired by k-means++ as follows. This technique allows the model to compute interpolations that best capture morphological changes and are less influenced by overall distortions. We resort to a volume-based normalization which consists in two key steps. First, we set to the origin the volumetric center of mass. Second, we constrain the shape to have a unit volume. |