Related papers: Rigid Multiview Varieties
Depictions of similar human body configurations can vary with changing viewpoints. Using only 2D information, we would like to enable vision algorithms to recognize similarity in human body poses across multiple views. This ability is…
Linear projections from P^k to P^h appear in computer vision as models of images of dynamic or segmented scenes. Given multiple projections of the same scene, the identification of many enough correspondences between the images allows, in…
The generalization ability of imitation learning policies for robotic manipulation is fundamentally constrained by the diversity of expert demonstrations, while collecting demonstrations across varied environments is costly and difficult in…
We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem…
Multi-view image generation attracts particular attention these days due to its promising 3D-related applications, e.g., image viewpoint editing. Most existing methods follow a paradigm where a 3D representation is first synthesized, and…
We study how a smooth irreducible algebraic variety $X$ of dimension $n$ embedded in $\mathbb{C} \mathbb{P}^{m}$ (with $m \geq n+2$), which degree is $d$, can be recovered using two projections from unknown points onto unknown hyperplanes.…
A set of orthonormal polynomials is proposed for image reconstruction from projection data. The relationship between the projection moments and image moments is discussed in detail, and some interesting properties are demonstrated.…
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane $\mathbb{P}^2$. They appear in the study of resonance and characteristic varieties of complex hyperplane arrangement complements…
We study the notion of consistency between a 3D shape and a 2D observation and propose a differentiable formulation which allows computing gradients of the 3D shape given an observation from an arbitrary view. We do so by reformulating view…
We present bounds for the degree and the height of the polynomials arising in some central problems in effective algebraic geometry including the implicitation of rational maps and the effective Nullstellensatz over a variety. Our treatment…
Reconstructing the geometry and appearance of objects from photographs taken in different environments is difficult as the illumination and therefore the object appearance vary across captured images. This is particularly challenging for…
A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in…
In this work, we derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. The core of our approach is the formulation of the residual covariances as a combination of geometric and photometric…
Every convex polygon with $n$ vertices is a linear projection of a higher-dimensional polytope with at most $147\,n^{2/3}$ facets.
The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined…
Object Re-IDentification (ReID), one of the most significant problems in biometrics and surveillance systems, has been extensively studied by image processing and computer vision communities in the past decades. Learning a robust and…
Platforms such as robots, security cameras, drones and satellites are used in multi-view imaging for three-dimensional (3D) recovery by stereoscopy or tomography. Each camera in the setup has a field of view (FOV). Multi-view analysis…
Incidence varieties are spaces of $n$-tuples of points in the projective plane that satisfy a given set of collinearity conditions. We classify the components of incidence varieties and realization moduli spaces associated to configurations…
We introduce a theory of multigraded Cayley-Chow forms associated to subvarieties of products of projective spaces. Two new phenomena arise: first, the construction turns out to require certain inequalities on the dimensions of projections;…
Multiview camera setups have proven useful in many computer vision applications for reducing ambiguities, mitigating occlusions, and increasing field-of-view coverage. However, the high computational cost associated with multiple views…