Related papers: Image Labeling Based on Graphical Models Using Was…

Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of…

This work presents an unsupervised and semi-automatic image segmentation approach where we formulate the segmentation as a inference problem based on unary and pairwise assignment probabilities computed using low-level image cues. The…

We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs)…

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…

This paper introduces a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as nonlocal reparametrization of the assignment flow approach that was introduced in…

In this paper, we present a novel upsampling framework to enhance the spatial resolution of the depth image. In our framework, the upscaling of a low-resolution depth image is guided by a corresponding intensity images, we formulate it as a…

The Wasserstein metric has become increasingly important in many machine learning applications such as generative modeling, image retrieval and domain adaptation. Despite its appeal, it is often too costly to compute. This has motivated…

Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…

Despite signi cant progress in semi-supervised medical image segmentation, most existing segmentation networks overlook e ective methodological guidance for feature extraction and important prior information from datasets. In this paper, we…

We propose a new equilibrium enforcing method paired with a loss derived from the Wasserstein distance for training auto-encoder based Generative Adversarial Networks. This method balances the generator and discriminator during training.…

We propose a novel iterative method to adapt a a graph to d-dimensional image data. The method drives the nodes of the graph towards image features. The adaptation process naturally lends itself to a measure of feature saliency which can…

This paper uses sample data to study the problem of comparing populations on finite-dimensional parallelizable Riemannian manifolds and more general trivial vector bundles. Utilizing triviality, our framework represents populations as…

Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of…

Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…

This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…

Image super-resolution remains an important research topic to overcome the limitations of physical acquisition systems, and to support the development of high resolution displays. Previous example-based super-resolution approaches mainly…

The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global…