# Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applications

no code implementations9 Nov 2023,

We prove an upper bound on the covering number of real algebraic varieties, images of polynomial maps and semialgebraic sets.

# 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

We introduce the G-invariant graph Laplacian that generalizes the graph Laplacian by accounting for the action of the group on the data set.

# Diffusion Maps for Group-Invariant Manifolds

no code implementations28 Mar 2023,

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

1 code implementation25 Oct 2022,

We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions.

0

# Snapshot of Algebraic Vision

no code implementations20 Oct 2022,

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.

0

# 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 optimization problem associated with computing the rank decomposition of a symmetric tensor.

# 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.

0

# Subspace power method for symmetric tensor decomposition and generalized PCA

1 code implementation9 Dec 2019,

We introduce the Subspace Power Method (SPM) for calculating the CP decomposition of low-rank even-order real symmetric tensors.

Numerical Analysis Numerical Analysis Optimization and Control

1

# 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.

1

# On the Expressive Power of Deep Polynomial Neural Networks

We study deep neural networks with polynomial activations, particularly their expressive power.

8

# 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

no code implementations18 Nov 2016

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.

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