Related papers: Geometric medians in reconciliation spaces
In this paper, we define the geometric median of a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to calculate the median in practical cases, we also…
The geometric median as well as the Frechet mean of points in an Hadamard space are important in both theory and applications. Surprisingly, no algorithms for their computation are hitherto known. To address this issue, we use a split…
We present a novel 3D pose refinement approach based on differentiable rendering for objects of arbitrary categories in the wild. In contrast to previous methods, we make two main contributions: First, instead of comparing real-world images…
With the progress of measurement apparatus and the development of automatic sensors it is not unusual anymore to get thousands of samples of observations taking values in high dimension spaces such as functional spaces. In such large…
In this paper, we propose a class of median-based matrix information geometry (MIG) detectors with a manifold filter and apply them to signal detection in nonhomogeneous environments. As customary, the sample data is assumed to be modeled…
The spatial resolution of a detector, using a reference detector telecscope, can be measured applying the geometric mean method, with tracks reconstructed from hits of all the detectors, including ($\sigma_\mathrm{in}$) and excluding…
We consider the topological and geometric reconstruction of a geodesic subspace of $\mathbb{R}^N$ both from the \v{C}ech and Vietoris-Rips filtrations on a finite, Hausdorff-close, Euclidean sample. Our reconstruction technique leverages…
We use the geometric mean to parametrize metrics in the Hassan-Rosen ghost-free bimetric theory and pose the initial-value problem. The geometric mean of two positive definite symmetric matrices is a well-established mathematical notion…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
Modern high-resolution satellite sensors collect optical imagery with ground sampling distances (GSDs) of 30-50cm, which has sparked a renewed interest in photogrammetric 3D surface reconstruction from satellite data. State-of-the-art…
Poisson Surface Reconstruction is a widely-used algorithm for reconstructing a surface from an oriented point cloud. To facilitate applications where only partial surface information is available, or scanning is performed sequentially, a…
We propose a means of computing fitted frames on the boundary and in the interior of objects and using them to provide the basis for producing geometric features from them that are not only alignment-free but most importantly can be made to…
Recently, deep metric learning techniques received attention, as the learned distance representations are useful to capture the similarity relationship among samples and further improve the performance of various of supervised or…
We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue…
Phylogenetic reconciliation seeks to explain host-symbiont co-evolution by mapping parasite trees onto host trees through events such as cospeciation, duplication, host switching, and loss. Finding an optimal reconciliation that ensures…
We present a rigorous mathematical treatment of Ruppeiner geometry, by considering degenerate Hessian metrics defined on radiant manifolds. A manifold $M$ is said to be radiant if it is endowed with a symmetric, flat connection $\bar\nabla$…
Hessian recovery has been commonly used in mesh adaptation for obtaining the required magnitude and direction information of the solution error. Unfortunately, a recovered Hessian from a linear finite element approximation is nonconvergent…
This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures…
Despite significant progress in single image-based 3D human mesh recovery, accurately and smoothly recovering 3D human motion from a video remains challenging. Existing video-based methods generally recover human mesh by estimating the…
Estimation procedures based on recursive algorithms are interesting and powerful techniques that are able to deal rapidly with (very) large samples of high dimensional data. The collected data may be contaminated by noise so that robust…