Global Divergences Between Measures: From Hausdorff Distance to Optimal Transport

Feydy, Jean; Trouvé, Alain

doi:10.1007/978-3-030-04747-4_10

Cited by 35 publications

(59 citation statements)

References 7 publications

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“…the unbiased Sinkhorn divergence that was recently shown to define a positive, definite and convex loss function for measure-fitting applications -see [6] for a proof in the balanced setting, extended in [14] to the general case. Generalizing ideas introduced by [7], we can write S ε,ρ in dual form as…”

Section: Methodsmentioning

confidence: 99%

Fast and Scalable Optimal Transport for Brain Tractograms

Feydy¹,

Roussillon

Trouvé³

et al. 2019

Lecture Notes in Computer Science

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We present a new multiscale algorithm for solving regularized Optimal Transport problems on the GPU, with a linear memory footprint. Relying on Sinkhorn divergences which are convex, smooth and positive definite loss functions, this method enables the computation of transport plans between millions of points in a matter of minutes. We show the effectiveness of this approach on brain tractograms modeled either as bundles of fibers or as track density maps. We use the resulting smooth assignments to perform label transfer for atlas-based segmentation of fiber tractograms. The parameters-blur and reachof our method are meaningful, defining the minimum and maximum distance at which two fibers are compared with each other. They can be set according to anatomical knowledge. Furthermore, we also propose to estimate a probabilistic atlas of a population of track density maps as a Wasserstein barycenter. Our CUDA implementation is endowed with a user-friendly PyTorch interface, freely available on the PyPi repository (pip install geomloss) and at www.kernel-operations.io/geomloss.

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Section: Methodsmentioning

confidence: 99%

Fast and Scalable Optimal Transport for Brain Tractograms

Feydy¹,

Roussillon

Trouvé³

et al. 2019

Lecture Notes in Computer Science

Self Cite

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“…. , q M ) in R D [40]. This property is most desirable when the shapes to register are fully observed, with a dense sampling: as detailed in Suppl.…”

Section: Robot: a Convenient Representation Of The Optimal Transport ...mentioning

confidence: 99%

“…Unfortunately, we never succeeded in converging to a competitive level of accuracy. We believe that this is due to the complex geometric structure of the lung vascular trees, which are significantly more intricate than the clean point clouds and surface meshes on which these methods are usually tested [36,40].…”

Section: A42 Experiments On Lung Vascular Treesmentioning

confidence: 99%

“…( 4) as a plug-in replacement for nearest neighbor (NN) projection. At an affordable computational cost, our RobOT layer enforces a local conservation of the point density: this geometric prior is relevant for many registration tasks and mitigates accumulation artifacts that are commonly found in nearest neighbor projections [35,40].…”

Section: A43 Experiments On Kittimentioning

confidence: 99%

“…b) Alternatively, a second approach is to rely on convolutional kernel norms such as the Energy Distance [94], which are also known as Maximum Mean Discrepancies (MMD) in statistics [48]. These loss functions are common in imaging science [88] and computational anatomy [21,115] but are prone to vanishing gradients [39,40]. c) Finally, a third type of approach is to rely on optimal transport (OT) theory [87] and solutions of the earth mover's problem [97].…”

Section: Introductionmentioning

confidence: 99%

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Accurate Point Cloud Registration with Robust Optimal Transport

Shen

Feydy

Liu

et al. 2021

Preprint

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This work investigates the use of robust optimal transport (OT) for shape matching. Specifically, we show that recent OT solvers improve both optimization-based and deep learning methods for point cloud registration, boosting accuracy at an affordable computational cost. This manuscript starts with a practical overview of modern OT theory. We then provide solutions to the main difficulties in using this framework for shape matching. Finally, we showcase the performance of transport-enhanced registration models on a wide range of challenging tasks: rigid registration for partial shapes; scene flow estimation on the Kitti dataset; and nonparametric registration of lung vascular trees between inspiration and expiration. Our OT-based methods achieve state-of-the-art results on Kitti and for the challenging lung registration task, both in terms of accuracy and scalability. We also release PVT1010, a new public dataset of 1,010 pairs of lung vascular trees with densely sampled points. This dataset provides a challenging use case for point cloud registration algorithms with highly complex shapes and deformations. Our work demonstrates that robust OT enables fast pre-alignment and fine-tuning for a wide range of registration models, thereby providing a new key method for the computer vision toolbox. Our code and dataset are available online at: https://github.com/uncbiag/robot.

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Personalized surgical recommendations and quantitative therapeutic insights for patients with metastatic breast cancer: Insights from deep learning

Zhu,

Zhang,

Wang

et al. 2024

Cancer Innovation

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BackgroundThe role of surgery in metastatic breast cancer (MBC) is currently controversial. Several novel statistical and deep learning (DL) methods promise to infer the suitability of surgery at the individual level.ObjectiveThe objective of this study was to identify the most applicable DL model for determining patients with MBC who could benefit from surgery and the type of surgery required.MethodsWe introduced the deep survival regression with mixture effects (DSME), a semi‐parametric DL model integrating three causal inference methods. Six models were trained to make individualized treatment recommendations. Patients who received treatments in line with the DL models' recommendations were compared with those who underwent treatments divergent from the recommendations. Inverse probability weighting (IPW) was used to minimize bias. The effects of various features on surgery selection were visualized and quantified using multivariate linear regression and causal inference.ResultsIn total, 5269 female patients with MBC were included. DSME was an independent protective factor, outperforming other models in recommending surgery (IPW‐adjusted hazard ratio [HR] = 0.39, 95% confidence interval [CI]: 0.19–0.78) and type of surgery (IPW‐adjusted HR = 0.66, 95% CI: 0.48–0.93). DSME was superior to other models and traditional guidelines, suggesting a higher proportion of patients benefiting from surgery, especially breast‐conserving surgery. The debiased effect of patient characteristics, including age, tumor size, metastatic sites, lymph node status, and breast cancer subtypes, on surgery decision was also quantified.ConclusionsOur findings suggested that DSME could effectively identify patients with MBC likely to benefit from surgery and the specific type of surgery needed. This method can facilitate the development of efficient, reliable treatment recommendation systems and provide quantifiable evidence for decision‐making.

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Global Divergences Between Measures: From Hausdorff Distance to Optimal Transport

Cited by 35 publications

References 7 publications

Fast and Scalable Optimal Transport for Brain Tractograms

Fast and Scalable Optimal Transport for Brain Tractograms

Accurate Point Cloud Registration with Robust Optimal Transport

Personalized surgical recommendations and quantitative therapeutic insights for patients with metastatic breast cancer: Insights from deep learning

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