Search Results for author:
Found 21 papers, 7 papers with code
Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor
The block tensor of trifocal tensors provides crucial geometric information on the three-view geometry of a scene.
Moment-based metrics for molecules computable from cryo-EM images
Further, we introduce a metric between a stack of projection images and a molecular structure, which is invariant to rotations and reflections and does not require performing 3-D reconstruction.
Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applications
Covering numbers are a powerful tool used in the development of approximation algorithms, randomized dimension reduction methods, smoothed complexity analysis, and others.
Condition numbers in multiview geometry, instability in relative pose estimation, and RANSAC
In this paper we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry.
The G-invariant graph Laplacian
In this work, we consider data sets whose data points lie on a manifold that is closed under the action of a known unitary matrix Lie group G. We propose to construct the graph Laplacian by incorporating the distances between all the pairs of points generated by the action of G on the data set.
Diffusion Maps for Group-Invariant Manifolds
In this article, we consider the manifold learning problem when the data set is invariant under the action of a compact Lie group $K$.
Moment Estimation for Nonparametric Mixture Models Through Implicit Tensor Decomposition
We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions.
Snapshot of Algebraic Vision
In this survey article, we present interactions between algebraic geometry and computer vision, which have recently come under the header of algebraic vision.
Tensor Moments of Gaussian Mixture Models: Theory and Applications
In this work, we develop theory and numerical methods for \emph{implicit computations} with moment tensors of GMMs, reducing the computational and storage costs to $\mathcal{O}(n^2)$ and $\mathcal{O}(n^3)$, respectively, for general covariance matrices, and to $\mathcal{O}(n)$ and $\mathcal{O}(n)$, respectively, for diagonal ones.
On the Instability of Relative Pose Estimation and RANSAC's Role
In this paper we study the numerical instabilities of the 5- and 7-point problems for essential and fundamental matrix estimation in multiview geometry.
Landscape analysis of an improved power method for tensor decomposition
In this work, we consider the optimization formulation for symmetric tensor decomposition recently introduced in the Subspace Power Method (SPM) of Kileel and Pereira.
Symmetry Breaking in Symmetric Tensor Decomposition
In this note, we consider the highly nonconvex optimization problem associated with computing the rank decomposition of symmetric tensors.
Manifold learning with arbitrary norms
Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality.
Subspace power method for symmetric tensor decomposition
This algorithm calculates one new CP component at a time, alternating between applying the shifted symmetric higher-order power method (SS-HOPM) to a certain modified tensor, constructed from a matrix flattening of the original tensor; and using appropriate deflation steps.
Numerical Analysis Numerical Analysis Optimization and Control
Earthmover-based manifold learning for analyzing molecular conformation spaces
In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction.
On the Expressive Power of Deep Polynomial Neural Networks
We study deep neural networks with polynomial activations, particularly their expressive power.
A clever elimination strategy for efficient minimal solvers
We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers.
Minimal Problems for the Calibrated Trifocal Variety
We determine the algebraic degree of minimal problems for the calibrated trifocal variety in computer vision.
Distortion Varieties
The distortion varieties of a given projective variety are parametrized by duplicating coordinates and multiplying them with monomials.
The Chow Form of the Essential Variety in Computer Vision
The Chow form of the essential variety in computer vision is calculated.
Rigid Multiview Varieties
The multiview variety from computer vision is generalized to images by $n$ cameras of points linked by a distance constraint.
