mlsanityData to 14 Oct 2026

Alignment of Density Maps in Wasserstein Distance

arXiv 2305.12310 ↗First posted 21 May 2023eess.IV q-bio.QM stat.MLcited by 8

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Abstract (arXiv)

In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance between the density maps after a rigid transformation. The induced loss function enjoys a more benign landscape than its Euclidean counterpart and Bayesian optimization is employed for computation. Numerical experiments show improved accuracy and efficiency over existing algorithms on the alignment of real protein molecules. In the context of aligning heterogeneous pairs, we illustrate a potential need for new distance functions.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 13 of its 42 references that are in the map. First posted on arXiv 21 May 2023.

Builds on

13 of 42 references.

References · 13

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  2. 2018A Tutorial on Bayesian Optimizationcited by 744
  3. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 192
  4. 2013Manopt, a Matlab toolbox for optimization on manifoldscited by 113
  5. 2016Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiationcited by 94
  6. 2021Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernelscited by 24
  7. 2022Wassmap: Wasserstein Isometric Mapping for Image Manifold Learningcited by 15
  8. 2020Manifold learning with arbitrary normscited by 10
  9. 2019Earthmover-based manifold learning for analyzing molecular conformation spacescited by 8
  10. 2020Centering noisy images with application to cryo-EMcited by 7
  11. 2022AlignOT: An optimal transport based algorithm for fast 3D alignment with applications to cryogenic electron microscopy density mapscited by 7
  12. 2020Wasserstein K-Means for Clustering Tomographic Projectionscited by 6
1 more
  1. 2022Three-Dimensional Alignment of Density Maps in Cryo-Electron Microscopycited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 4; 2026: 2.

8 papers.

  1. 2024Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Explorationcited by 8
  2. 2025Fast rigid alignment of heterogeneous images in sliced Wasserstein distancecited by 4
  3. 2023Robust Point Matching with Distance Profilescited by 1
  4. 2025Quantization-based Bounds on the Wasserstein Metriccited by 0
  5. 2025Quantifying the noise sensitivity of the Wasserstein metric for imagescited by 0
  6. 2025The Joint Gromov Wasserstein Objective for Multiple Object Matchingcited by 0
  7. 2026On the stability of scale-space metricscited by 0
  8. 2026Cluster-Aware Matching via Laplacian Optimal Transportcited by 0