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Found 20 papers, 7 papers with code
On the Expressive Power of Deep Polynomial Neural Networks
We study deep neural networks with polynomial activations, particularly their expressive power.
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.
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.
Subspace power method for symmetric tensor decomposition and generalized PCA
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
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.
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.
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.
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.
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.
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.
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.
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.
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 $K$.
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.
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.
Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applications
We prove an upper bound on the covering number of real algebraic varieties, images of polynomial maps and semialgebraic sets.
