Related papers: A Hilbert Scheme in Computer Vision
We present an algebraic study of the projection of plane curves and twisted cubics in space onto multiple images of pinhole cameras. The Zariski closure of the image of the projection of conics is a conic multiview varieties. Extending…
Camera-controllable image editing aims to synthesize novel views of a given scene under varying camera poses while strictly preserving cross-view geometric consistency. However, existing methods typically rely on fragmented geometric…
The aim of this paper is to investigate an attempt to build a binary classification algorithm using principles of geometry such as vectors, planes, and vector algebra. The basic idea behind the proposed algorithm is that a hyperplane can be…
We systematically compile an exhaustive catalogue of multiview varieties and anchored multiview varieties arising from projections of points and lines in 1, 2, and 3-dimensional projective space. We say that two such varieties are…
Multimodal referring segmentation aims to segment target objects in visual scenes, such as images, videos, and 3D scenes, based on referring expressions in text or audio format. This task plays a crucial role in practical applications…
We recursively compute the Gromov-Witten invariants of the Hilbert scheme of two points in the plane. By studying the space of stable maps and computing virtual contributions, we use these invariants to enumerate hyperelliptic plane curves…
3D object detection from visual sensors is a cornerstone capability of robotic systems. State-of-the-art methods focus on reasoning and decoding object bounding boxes from multi-view camera input. In this work we gain intuition from the…
The ultimate goal of many image-based modeling systems is to render photo-realistic novel views of a scene without visible artifacts. Existing evaluation metrics and benchmarks focus mainly on the geometric accuracy of the reconstructed…
We investigate the defining ideal of a set of points X in multi-projective space with a special emphasis on the case that X is in generic position, that is, X has the maximal Hilbert function. When X is in generic position, we determine the…
Detecting objects in 3D space using multiple cameras, known as Multi-Camera 3D Object Detection (MC3D-Det), has gained prominence with the advent of bird's-eye view (BEV) approaches. However, these methods often struggle when faced with…
Let X and Y be smooth varieties of dimensions n-1 and n over an arbitrary algebraically closed field, f:X-> Y a finite map that is birational onto its image. Suppose that f is curvilinear; that is, at every point of X, the Jacobian has rank…
In this work we deal with the recently introduced concept of weaving frames. We extend the concept to include multi-window frames and present the first sufficient criteria for a family of multi-window Gabor frames to be woven. We give a…
Human has an incredible ability to effortlessly perceive the viewpoint difference between two images containing the same object, even when the viewpoint change is astonishingly vast with no co-visible regions in the images. This remarkable…
The geometry of binocular projection is analyzed, with reference to the primate visual system. In particular, the effects of coordinated eye movements on the retinal images are investigated. An appropriate oculomotor parameterization is…
The Hilbert scheme of $n$ points in the affine plane contains the open subscheme parametrizing $n$ distinct points in the affine plane, and the closed subscheme parametrizing ideals of codimension $n$ supported at the origin of the affine…
Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…
We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…
A configuration of lattice vectors is supernormal if it contains a Hilbert basis for every cone spanned by a subset. We study such configurations from various perspectives, including triangulations, integer programming and Groebner bases.…
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
Vision-based motion estimation and 3D reconstruction, which have numerous applications (e.g., autonomous driving, navigation systems for airborne devices and augmented reality) are receiving significant research attention. To increase the…