Related papers: Manifold embedding for curve registration

Theoretical results from discrete geometry suggest that normed spaces can abstractly embed finite metric spaces with surprisingly low theoretical bounds on distortion in low dimensions. In this paper, inspired by this theoretical insight,…

We propose a method for tracing implicit real algebraic curves defined by polynomials with rank-deficient Jacobians. For a given curve $f^{-1}(0)$, it first utilizes a regularization technique to compute at least one witness point per…

Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…

We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in…

We consider the problem of classification of an object given multiple observations that possibly include different transformations. The possible transformations of the object generally span a low-dimensional manifold in the original signal…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

We address the problem of estimating topological features from data in high dimensional Euclidean spaces under the manifold assumption. Our approach is based on the computation of persistent homology of the space of data points endowed with…

Many algorithms for surface registration risk producing significant errors if surfaces are significantly nonisometric. Manifold learning has been shown to be effective at improving registration quality, using information from an entire…

Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with…

Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…

We address the problem of testing hypotheses about a specific value of the Fr\'echet mean in metric spaces, extending classical mean testing from Euclidean spaces to more general settings. We extend an Euclidean testing procedure…

We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…

Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable…

One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Raw images are in the form of triangulated surfaces and the first step is to create a standardised…

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of…

This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…

We consider the problem of learning a manifold from a teacher's demonstration. Extending existing approaches of learning from randomly sampled data points, we consider contexts where data may be chosen by a teacher. We analyze learning from…

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…

We consider a smooth closed orientable submanifold $M \subset \mathbb{R}^D$ with narrow cycles. We embed $M$ into a scaled oriented Grassmannian bundle via the Gauss map in order to enlarge the scale of these cycles. Under mild assumptions,…

We establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold $(N^{n+1}, \bar g)$ through regularity study of a degenerate fully nonlinear curvature equation in general…