Related papers: A Hilbert Scheme in Computer Vision
Multi-camera 3D object detection for autonomous driving is a challenging problem that has garnered notable attention from both academia and industry. An obstacle encountered in vision-based techniques involves the precise extraction of…
Recovering high-fidelity 3D hand geometry from images is a critical task in computer vision, holding significant value for domains such as robotics, animation and VR/AR. Crucially, scalable applications demand both accuracy and deployment…
We present a method to map 2D image observations of a scene to a persistent 3D scene representation, enabling novel view synthesis and disentangled representation of the movable and immovable components of the scene. Motivated by the…
Recent work in unsupervised multi-object segmentation shows impressive results by predicting motion from a single image despite the inherent ambiguity in predicting motion without the next image. On the other hand, the set of possible…
World models enable agents to plan by imagining future states, but existing approaches operate from a single viewpoint, typically egocentric, even when other perspectives would make planning easier; navigation, for instance, benefits from a…
In the past 20 years, compactifications of the families of curves in algebraic varieties X have been studied via stable maps, Hilbert schemes, stable pairs, unramified maps, and stable quotients. Each path leads to a different enumeration…
We propose a scalable neural network framework to reconstruct the 3D mesh of a human body from multi-view images, in the subspace of the SMPL model. Use of multi-view images can significantly reduce the projection ambiguity of the problem,…
We introduce a multi-scale framework for low-level vision, where the goal is estimating physical scene values from image data---such as depth from stereo image pairs. The framework uses a dense, overlapping set of image regions at multiple…
This paper proposes a novel algorithm of discovering the structure of a kaleidoscopic imaging system that consists of multiple planar mirrors and a camera. The kaleidoscopic imaging system can be recognized as the virtual multi-camera…
We study the problem of visibility in polyhedral terrains in the presence of multiple viewpoints. We consider a triangulated terrain with $m>1$ viewpoints (or guards) located on the terrain surface. A point on the terrain is considered…
Human vision possesses a special type of visual processing systems called peripheral vision. Partitioning the entire visual field into multiple contour regions based on the distance to the center of our gaze, the peripheral vision provides…
We denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth, irreducible and non-degenerate curve of degree $d$ and genus $g$ in $\mathbb{P}^r.$ In…
Understanding the geometry and pose of objects in 2D images is a fundamental necessity for a wide range of real world applications. Driven by deep neural networks, recent methods have brought significant improvements to object pose…
We tackle the task of synthesizing novel views of an object given a few input images and associated camera viewpoints. Our work is inspired by recent 'geometry-free' approaches where multi-view images are encoded as a (global) set-latent…
Here we study the problem of generalizing one of the main tools of Groebner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the…
We introduce an atlas of algebro-geometric objects associated with image formation in pinhole cameras. The nodes of the atlas are algebraic varieties or their vanishing ideals related to each other by projection or elimination and…
In this paper, we propose a novel method for joint recovery of camera pose, object geometry and spatially-varying Bidirectional Reflectance Distribution Function (svBRDF) of 3D scenes that exceed object-scale and hence cannot be captured…
Image feature matching is a fundamental part of many geometric computer vision applications, and using multiple images can improve performance. In this work, we formulate multi-image matching as a graph embedding problem then use a Graph…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
Camera calibration is the foundation of 3D vision. Generic camera calibration can yield more accurate results than parametric cam era calibration. However, calibrating a generic camera model using printed calibration boards requires far…