In this survey article, we present interactions between algebraic geometry and computer
vision, which have recently come under the header of algebraic vision. The subject has …

We resolve a basic problem on subspace distances that often arises in applications: How
can the usual Grassmann distance between equidimensional subspaces be extended to …

We study deep neural networks with polynomial activations, particularly their expressive
power. For a fixed architecture and activation degree, a polynomial neural network defines …

Many problems in computer vision can be formulated as geometric estimation problems ie
given a collection of measurements (eg point correspondences) we wish to fit a model (eg …

We seek to determine a real algebraic variety from a fixed finite subset of points. Existing
methods are studied and new methods are developed. Our focus lies on aspects of topology …

The most widely used algorithm in the cluster partitioning method is the K-Means algorithm.
Historically K-Means is still the best grouping algorithm among other grouping algorithms …

The Euclidean distance degree of an algebraic variety is a well-studied topic in applied
algebra and geometry. It has direct applications in geometric modeling, computer vision, and …

Metric algebraic geometry combines concepts from algebraic geometry and differential
geometry. Building on classical foundations, it offers practical tools for the 21st century …

We study the joint image of lines incident to points, meaning the set of image tuples obtained
from fixed cameras observing a varying 3D point-line incidence. We prove a formula for the …

We present an algebraic study of line correspondences for pinhole cameras, in contrast to
the thoroughly studied point correspondences. We define the line multiview variety as the …