AlignOT: An Optimal Transport Based Algorithm for Fast 3D Alignment With Applications to Cryogenic Electron Microscopy Density Maps

Riahi, Aryan Tajmir; Woollard, Geoffrey; Poitevin, Frédéric; Condon, Anne; Duc, Khanh Dao

doi:10.1109/tcbb.2023.3327633

Cited by 1 publication

(5 citation statements)

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“…(17) proposes using Kullback-Leibler divergence as the loss function which is later optimized with gradient descent, but no simulations are presented. Setting d as an entropic regularization of the 2-Wasserstein distance, the recent work (18) solves ( 2) with stochastic gradient descent by iteratively computing the optimal transport plans. Improved results are obtained over Chimera but the algorithm still requires the initial alignment to be within certain range of the true one.…”

Section: Related Workmentioning

confidence: 99%

“…Our proposed method differs from Refs. (18,19) by employing Bayesian optimization and not involving explicit calculation of transport plans. For this reason, exhaustive search-based methods are also popular and appear necessary.…”

Section: Related Workmentioning

confidence: 99%

“…In Section 4.3, we compare the performance of Algorithm 1 with the two recent works. (18,26) The algorithmic complexity is discussed in Section 4.4. Our code is available at https:// github.com/RuiyiYang/BOTalign.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…(26), which exploits common line-based methods for fast projection matching, and Ref. (18), which considers an entropic regularization of 2-Wasserstein loss in (6) and employs stochastic gradient descent for optimization. In the following comparison, we shall also consider translation recovery.…”

Section: Comparison With Existing Algorithmsmentioning

confidence: 99%

“…Lastly, AlignOT stands for the algorithm in Ref. (18) with n = 500 in their topology representing network step and maximum number of iteration N = 500 in their stochastic gradient descent. Again, we repeat the experiments 50 times for each molecule and the results are shown in Figure 7 and Table 1.…”

Section: Comparison With Existing Algorithmsmentioning

confidence: 99%

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Alignment of density maps in Wasserstein distance

Singer,

Yang

2024

Biol. Imaging

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In this article, 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. Impact StatementThis article proposes a fast algorithm for aligning three-dimensional volumes represented as density maps with a particular focus on applications in cryogenic electron microscopy. The algorithm achieves both improved accuracy and efficiency over existing methods on the alignment of real protein molecules. The article also demonstrates a potential need for new distance functions for the alignment of heterogeneous pairs of volumes.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Comparison With Existing Algorithmsmentioning

confidence: 99%

Section: Comparison With Existing Algorithmsmentioning

confidence: 99%

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