Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOptimal-transport-based metric for SMLM
78
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We propose the use of Flat Metric to assess the performance of reconstruction methods for single-molecule localization microscopy (SMLM) in scenarios where the ground-truth is available. Flat Metric is intimately related to the concept of optimal transport between measures of different mass, providing solid mathematical foundations for SMLM evaluation and integrating both localization and detection performance. In this paper, we provide the foundations of Flat Metric and validate this measure by applying it to controlled synthetic examples and to data from the SMLM 2016 Challenge.
rate research
Read More
Regularization in Optimal Transport (OT) problems has been shown to critically affect the associated computational and sample complexities. It also has been observed that regularization effectively helps in handling noisy marginals as well as marginals with unequal masses. However, existing works on OT restrict themselves to $phi$-divergences based regularization. In this work, we propose and analyze Integral Probability Metric (IPM) based regularization in OT problems. While it is expected that the well-established advantages of IPMs are inherited by the IPM-regularized OT variants, we interestingly observe that some useful aspects of $phi$-regularization are preserved. For example, we show that the OT formulation, where the marginal constraints are relaxed using IPM-regularization, also lifts the ground metric to that over (perhaps un-normalized) measures. Infact, the lifted metric turns out to be another IPM whose generating set is the intersection of that of the IPM employed for regularization and the set of 1-Lipschitz functions under the ground metric. Also, in the special case where the regularization is squared maximum mean discrepancy based, the proposed OT variant, as well as the corresponding Barycenter formulation, turn out to be those of minimizing a convex quadratic subject to non-negativity/simplex constraints and hence can be solved efficiently. Simulations confirm that the optimal transport plans/maps obtained with IPM-regularization are intrinsically different from those obtained with $phi$-regularization. Empirical results illustrate the efficacy of the proposed IPM-regularized OT formulation. This draft contains the main paper and the Appendices.
Generalizing knowledge to unseen domains, where data and labels are unavailable, is crucial for machine learning models. We tackle the domain generalization problem to learn from multiple source domains and generalize to a target domain with unknown statistics. The crucial idea is to extract the underlying invariant features across all the domains. Previous domain generalization approaches mainly focused on learning invariant features and stacking the learned features from each source domain to generalize to a new target domain while ignoring the label information, which will lead to indistinguishable features with an ambiguous classification boundary. For this, one possible solution is to constrain the label-similarity when extracting the invariant features and to take advantage of the label similarities for class-specific cohesion and separation of features across domains. Therefore we adopt optimal transport with Wasserstein distance, which could constrain the class label similarity, for adversarial training and also further deploy a metric learning objective to leverage the label information for achieving distinguishable classification boundary. Empirical results show that our proposed method could outperform most of the baselines. Furthermore, ablation studies also demonstrate the effectiveness of each component of our method.
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regularization is added to the problem, the transportation plan can be efficiently computed with the Sinkhorn algorithm. Thanks to this breakthrough, optimal transport has been progressively extended to machine learning and statistical inference by introducing additional application-specific terms in the problem formulation. It is however challenging to design efficient optimization algorithms for optimal transport based extensions. To overcome this limitation, we devise a general forward-backward splitting algorithm based on Bregman distances for solving a wide range of optimization problems involving a differentiable function with Lipschitz-continuous gradient and a doubly stochastic constraint. We illustrate the efficiency of our approach in the context of continuous domain adaptation. Experiments show that the proposed method leads to a significant improvement in terms of speed and performance with respect to the state of the art for domain adaptation on a continually rotating distribution coming from the standard two moon dataset.
Recently, much progress has been made in unsupervised restoration learning. However, existing methods more or less rely on some assumptions on the signal and/or degradation model, which limits their practical performance. How to construct an optimal criterion for unsupervised restoration learning without any prior knowledge on the degradation model is still an open question. Toward answering this question, this work proposes a criterion for unsupervised restoration learning based on the optimal transport theory. This criterion has favorable properties, e.g., approximately maximal preservation of the information of the signal, whilst achieving perceptual reconstruction. Furthermore, though a relaxed unconstrained formulation is used in practical implementation, we show that the relaxed formulation in theory has the same solution as the original constrained formulation. Experiments on synthetic and real-world data, including realistic photographic, microscopy, depth, and raw depth images, demonstrate that the proposed method even compares favorably with supervised methods, e.g., approaching the PSNR of supervised methods while having better perceptual quality. Particularly, for spatially correlated noise and realistic microscopy images, the proposed method not only achieves better perceptual quality but also has higher PSNR than supervised methods. Besides, it shows remarkable superiority in harsh practical conditions with complex noise, e.g., raw depth images.
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement interpolations (a.k.a. Wasserstein barycenters) between dictionary atoms; such atoms are themselves synthetic histograms in the probability simplex. Our method simultaneously estimates such atoms, and, for each datapoint, the vector of weights that can optimally reconstruct it as an optimal transport barycenter of such atoms. Our method is computationally tractable thanks to the addition of an entropic regularization to the usual optimal transportation problem, leading to an approximation scheme that is efficient, parallel and simple to differentiate. Both atoms and weights are learned using a gradient-based descent method. Gradients are obtained by automatic differentiation of the generalized Sinkhorn iterations that yield barycenters with entropic smoothing. Because of its formulation relying on Wasserstein barycenters instead of the usual matrix product between dictionary and codes, our method allows for nonlinear relationships between atoms and the reconstruction of input data. We illustrate its application in several different image processing settings.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
