Related papers: Tensors, Differential Geometry and Statistical Sha…
We present a technique for estimating the shape and reflectance of an object in terms of its surface normals and spatially-varying BRDF. We assume that multiple images of the object are obtained under fixed view-point and varying…
Tensor networks, a class of variational quantum many-body wave functions have attracted considerable research interest across many disciplines, including classical machine learning. Recently, Aizpurua et al. demonstrated explainable anomaly…
Photometric Stereo methods seek to reconstruct the 3d shape of an object from motionless images obtained with varying illumination. Most existing methods solve a restricted problem where the physical reflectance model, such as Lambertian…
Image relighting is the task of showing what a scene from a source image would look like if illuminated differently. Inverse graphics schemes recover an explicit representation of geometry and a set of chosen intrinsics, then relight with…
We derive a numerically stable method to compute an image representation of an unknown linear system only from data, leveraging a continuous-time version of Willems et al.'s fundamental lemma. To this end, we use derivatives approximated by…
A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this learning problem and improves upon current approaches by an…
This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…
We consider denoising and deblurring problems for tensors. While images can be discretized as matrices, the analogous procedure for color images or videos leads to a tensor formulation. We extend the classical ROF functional for variational…
One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are…
We present a novel convolutional neural network architecture for photometric stereo (Woodham, 1980), a problem of recovering 3D object surface normals from multiple images observed under varying illuminations. Despite its long history in…
Weak gravitational lensing is normally assumed to have only two principle effects: a magnification of a source and a distortion of the sources shape in the form of a shear. However, further distortions are actually present owing to changes…
Predicting masked from visible parts of an image is a powerful self-supervised approach for visual representation learning. However, the common practice of masking random patches of pixels exhibits certain failure modes, which can prevent…
Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered…
The distortion varieties of a given projective variety are parametrized by duplicating coordinates and multiplying them with monomials. We study their degrees and defining equations. Exact formulas are obtained for the case of one-parameter…
For each relative $\operatorname{GL}(V)$-invariant tensor $I\in \Lambda^{p_1+1}V^{\vee}\otimes .. \otimes \Lambda^{p_n+1}V^{\vee}$ we construct a $\operatorname{GL}(V)$-invariant weighted differential form $\eta$ on $(\mathbb{P} V)^{n}$.…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
Determinantal varieties -- the sets of bounded-rank matrices or tensors -- have attracted growing interest in low-rank optimization. The tangent cone to low-rank sets is widely studied and underpins a range of geometric methods. The…
We introduce an algorithm to decide isomorphism between tensors. The algorithm uses the Lie algebra of derivations of a tensor to compress the space in which the search takes place to a so-called densor space. To make the method practicable…