Related papers: Geometric medians in reconciliation spaces
This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…
The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different…
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…
We introduce an evolutionary algorithm called recombinator-$k$-means for optimizing the highly non-convex kmeans problem. Its defining feature is that its crossover step involves all the members of the current generation, stochastically…
In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…
Variational and Bayesian methods are two approaches that have been widely used to solve image reconstruction problems. In this paper, we propose original connections between Hamilton--Jacobi (HJ) partial differential equations and a broad…
The Gromov-Hausdorff distance ($d_\mathrm{GH}$) provides a natural way of quantifying the dissimilarity between two given metric spaces. It is known that computing $d_\mathrm{GH}$ between two finite metric spaces is NP-hard, even in the…
The 21-cm emission from atomic hydrogen (HI) is one of the most important tracers of the structure and dynamics of the interstellar medium. Thanks to Galactic rotation, the line is Doppler shifted and, assuming a model for the velocity…
In this paper we introduce the limit, unique solution of the nonlinear equations, geodesic property, tolerance relations and pinch on the spectral geometric mean for two positive definite operators. We show that the spectral geometric mean…
We consider a region $M$ in $\mathbb{R}^n$ with boundary $\partial M$ and a metric $g$ on $M$ conformal to the Euclidean metric. We analyze the inverse problem, originally formulated by Dix, of reconstructing $g$ from boundary measurements…
Recent cosmological observations have achieved high-precision measurements of the Universe's expansion history, prompting the use of nonparametric methods such as Gaussian processes (GP) regression. We apply GP regression for reconstructing…
In coded aperture snapshot spectral imaging (CASSI) system, the real-world hyperspectral image (HSI) can be reconstructed from the captured compressive image in a snapshot. Model-based HSI reconstruction methods employed hand-crafted priors…
Compressed Sensing MRI (CS-MRI) has provided theoretical foundations upon which the time-consuming MRI acquisition process can be accelerated. However, it primarily relies on iterative numerical solvers which still hinders their adaptation…
We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions…
We define geometric matrix midranges for positive definite Hermitian matrices and study the midrange problem from a number of perspectives. Special attention is given to the midrange of two positive definite matrices before considering the…
For an ordered set $W=\{w_1,w_2,...,w_k\}$ of vertices and a vertex $v$ in a connected graph $G$, the ordered $k$-vector $r(v|W):=(d(v,w_1),d(v,w_2),...,d(v,w_k))$ is called the (metric) representation of $v$ with respect to $W$, where…
We present a novel method that integrates subspace modeling with an adaptive generative image prior for high-dimensional MR image reconstruction. The subspace model imposes an explicit low-dimensional representation of the high-dimensional…
The end-to-end Human Mesh Recovery (HMR) approach has been successfully used for 3D body reconstruction. However, most HMR-based frameworks reconstruct human body by directly learning mesh parameters from images or videos, while lacking…
Recently, deep generative adversarial networks for image generation have advanced rapidly; yet, only a small amount of research has focused on generative models for irregular structures, particularly meshes. Nonetheless, mesh generation and…
The Genome Median Problem is an important problem in phylogenetic reconstruction under rearrangement models. It can be stated as follows: given three genomes, find a fourth that minimizes the sum of the pairwise rearrangement distances…