相关论文: Alignment of Density Maps in Wasserstein Distance

A common task in cryo-electron microscopy (cryo-EM) data processing is to compare three-dimensional density maps of macromolecules. In this paper, we propose an algorithm for aligning three-dimensional density maps that exploits common…

Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that many datasets are naturally interpreted as probability…

In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging…

Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…

Aligning electron density maps from Cryogenic electron microscopy (cryo-EM) is a first key step for studying multiple conformations of a biomolecule. As this step remains costly and challenging, with standard alignment tools being…

A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…

As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We…

Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…

A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…

In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…

Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…

This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete…

We propose a novel objective for penalizing geometric inconsistencies to improve the depth and pose estimation performance of monocular camera images. Our objective is designed using the Wasserstein distance between two point clouds,…

We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning. By assigning vertex weights through the LPT…

We propose a novel method for comparing non-aligned graphs of different sizes, based on the Wasserstein distance between graph signal distributions induced by the respective graph Laplacian matrices. Specifically, we cast a new formulation…

Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…

Many real-world problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns in the field of computer vision. Recently, the alignment problem…

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One motivating application is drug development: morphological cell features can be…