Related papers: Only distances are required to reconstruct submani…

The method of finding the minimal distance between smooth non crossing submanifolds in N-dimensional Euclidean space are presented. It based on solution of the equations that describe the dynamics of the pair of material points. The…

The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial…

We consider a model of D-dimensional tethered manifold interacting by excluded volume in R^d with a single point. By use of intrinsic distance geometry, we first provide a rigorous definition of the analytic continuation of its perturbative…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Exact reconstruction of an image from measurements of its Discrete Fourier Transform (DFT) typically requires all DFT coefficients to be available. However, incorporating the prior assumption that the image contains only integer values…

We present VoroUDF, an algorithm for reconstructing high-quality triangle meshes from Unsigned Distance Fields (UDFs). Our algorithm supports non-manifold geometry, sharp features, and open boundaries, without relying on error-prone…

Manifold-valued parameters routinely arise in modern statistical applications such as in medical imaging, robotics, and computer vision, to name a few. While traditional Bayesian approaches are applicable to such settings by considering an…

We introduce an estimator for distances in a compact Riemannian manifold based on graph Laplacian estimates of the Laplace-Beltrami operator. We upper bound the error in the estimate of manifold distances, or more precisely an estimate of a…

Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned…

Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to…

In many interesting cases the reconstruction of a correct phylogeny is blurred by high mutation rates and/or horizontal transfer events. As a consequence a divergence arises between the true evolutionary distances and the differences…

A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of…

The need for efficiently comparing and representing datasets with unknown alignment spans various fields, from model analysis and comparison in machine learning to trend discovery in collections of medical datasets. We use manifold learning…

For pattern recognition like image recognition, it has become clear that each machine-learning dictionary data actually became data in probability space belonging to Euclidean space. However, the distances in the Euclidean space and the…

Unsigned distance fields (UDFs) are widely used in 3D deep learning due to their ability to represent shapes with arbitrary topology. While prior work has largely focused on learning UDFs from point clouds or multi-view images, extracting…

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…

Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordant barrier. We give a suitable generalization of…

We consider the problem of recovering a $d-$dimensional manifold $\mathcal{M} \subset \mathbb{R}^n$ when provided with noiseless samples from $\mathcal{M}$. There are many algorithms (e.g., Isomap) that are used in practice to fit manifolds…

To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME)…

We reconstruct a closed denoised curve from an unstructured and highly noisy 2D point cloud. Our proposed method uses a two- pass approach: Previously recovered manifold connectivity is used for ordering noisy samples along this manifold…