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On the stability of scale-space metrics

arXiv 2606.27605 ↗First posted 25 Jun 2026math.NA cs.CV cs.NAcited by 0

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Abstract (arXiv)

We study the stability of a classical family of metrics defined over functions' Gaussian scale-space representations, focusing on the comparison of images (functions of two variables). These metrics have precedents both in harmonic analysis, specifically the theory of Besov spaces, and in classical methods of image processing; special cases are also known to be metrically equivalent to certain Wasserstein distances. We quantify these metrics' robustness to geometric deformations, and introduce rotationally-invariant versions that are stable to changes in angle when comparing tomographic projections. We also describe computationally efficient algorithms for evaluating the metrics from finite samples, and prove their robustness to additive noise. The results are illustrated through numerical experiments.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 11 of its 52 references that are in the map. First posted on arXiv 25 Jun 2026.

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References · 11

  1. 2013Deep Scattering Spectrumcited by 52
  2. 2013Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EMcited by 17
  3. 2015Hierarchical Coupled Geometry Analysis for Neuronal Structure and Activity Pattern Discoverycited by 10
  4. 2019Earthmover-based manifold learning for analyzing molecular conformation spacescited by 8
  5. 2023Alignment of Density Maps in Wasserstein Distancecited by 8
  6. 2020Wasserstein K-Means for Clustering Tomographic Projectionscited by 6
  7. 2017Data-Driven Tree Transforms and Metricscited by 5
  8. 2025Fast rigid alignment of heterogeneous images in sliced Wasserstein distancecited by 4
  9. 2016Mahalanobis Distance for Class Averaging of Cryo-EM Imagescited by 3
  10. 2025Joint Hierarchical Representation Learning of Samples and Features via Informed Tree-Wasserstein Distancecited by 2
  11. 2023Cramer Type Distances for Learning Gaussian Mixture Models by Gradient Descentcited by 1

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