Related papers: A Hilbert Scheme in Computer Vision
Self-supervised detection and segmentation of foreground objects aims for accuracy without annotated training data. However, existing approaches predominantly rely on restrictive assumptions on appearance and motion. For scenes with dynamic…
In this work, we address the problem of refining the geometry of local image features from multiple views without known scene or camera geometry. Current approaches to local feature detection are inherently limited in their keypoint…
In multiview geometry when correspondences among multiple views are unknown the image points can be understood as being unlabeled. This is a common problem in computer vision. We give a novel approach to handle such a situation by regarding…
Consider a component of the Hilbert scheme whose general point corresponds to a degree d genus g smooth irreducible and nondegenerate curve in a projective variety X. We give lower bounds for the dimension of such a component when X is P^3,…
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In Chapter 1 we discuss the equations defining the Hilbert…
The importance of wild video based image set recognition is becoming monotonically increasing. However, the contents of these collected videos are often complicated, and how to efficiently perform set modeling and feature extraction is a…
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…
Camera calibration is a fundamental prerequisite for reliable geometric perception, yet classical approaches rely on controlled acquisition setups that are impractical for in-the-wild imagery. Recent learning-based methods have shown…
We consider the notion of mixed multiplicities for multigraded modules by using Hilbert series, and this is later applied to study the projective degrees of rational maps. We use a general framework to determine the projective degrees of a…
Foundation models are vital tools in various Computer Vision applications. They take as input a single RGB image and output a deep feature representation that is useful for various applications. However, in case we have multiple views of…
The multiview variety associated to a collection of $N$ cameras records which sequences of image points in $\mathbb{P}^{2N}$ can be obtained by taking pictures of a given world point $x\in\mathbb{P}^3$ with the cameras. In order to…
Estimating positions of world points from features observed in images is a key problem in 3D reconstruction, image mosaicking,simultaneous localization and mapping and structure from motion. We consider a special instance in which there is…
We consider the multigraded Hilbert scheme corresponding to the Hilbert function of a finite number of points in general position in a smooth projective complex toric variety. We develop several criteria for a point of that parameter space…
Visual events in computer vision are studied from the perspective of algebraic geometry. Given a sufficiently general curve or surface in 3-space, we consider the image or contour curve that arises by projecting from a viewpoint.…
A multi-view image sequence provides a much richer capacity for object recognition than from a single image. However, most existing solutions to multi-view recognition typically adopt hand-crafted, model-based geometric methods, which do…
We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our construction is widely applicable, it provides explicit…
In this work, we aim to improve the 3D reasoning ability of Transformers in multi-view 3D human pose estimation. Recent works have focused on end-to-end learning-based transformer designs, which struggle to resolve geometric information…
Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to…
Change in viewpoint is one of the major factors for variation in object appearance across different images. Thus, view-invariant object recognition is a challenging and important image understanding task. In this paper, we propose a method…
Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…