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Found 14 papers, 3 papers with code
Geometry of Linear Convolutional Networks
We study the family of functions that are represented by a linear convolutional neural network (LCN).
Symmetry Breaking in Symmetric Tensor Decomposition
In this note, we consider the optimization problem associated with computing the rank decomposition of a symmetric tensor.
Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks
We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks.
Pure and Spurious Critical Points: a Geometric Study of Linear Networks
The critical locus of the loss function of a neural network is determined by the geometry of the functional space and by the parameterization of this space by the network's weights.
Gradient Dynamics of Shallow Univariate ReLU Networks
We show that the gradient dynamics of such networks are determined by the gradient flow in a non-redundant parameterization of the network function.
Coordinate-Free Carlsson-Weinshall Duality and Relative Multi-View Geometry
We present a coordinate-free description of Carlsson-Weinshall duality between scene points and camera pinholes and use it to derive a new characterization of primal/dual multi-view geometry.
On the Expressive Power of Deep Polynomial Neural Networks
We study deep neural networks with polynomial activations, particularly their expressive power.
On the Solvability of Viewing Graphs
A set of fundamental matrices relating pairs of cameras in some configuration can be represented as edges of a "viewing graph".
Consistent sets of lines with no colorful incidence
We consider incidences among colored sets of lines in $\mathbb{R}^d$ and examine whether the existence of certain concurrences between lines of $k$ colors force the existence of at least one concurrence between lines of $k+1$ colors.
Changing Views on Curves and Surfaces
Visual events in computer vision are studied from the perspective of algebraic geometry.
General models for rational cameras and the case of two-slit projections
The rational camera model recently introduced in [19] provides a general methodology for studying abstract nonlinear imaging systems and their multi-view geometry.
Congruences and Concurrent Lines in Multi-View Geometry
We present a new framework for multi-view geometry in computer vision.
Consistency of Silhouettes and Their Duals
Silhouettes provide rich information on three-dimensional shape, since the intersection of the associated visual cones generates the "visual hull", which encloses and approximates the original shape.
The Joint Image Handbook
Given multiple perspective photographs, point correspondences form the "joint image", effectively a replica of three dimensional space distributed across its two-dimensional projections.
