Related papers: A Hilbert Scheme in Computer Vision
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
The vanishing ideal I of a subspace arrangement is an intersection of linear ideals. We give a formula for the Hilbert polynomial of I if the subspaces meet transversally. We also give a formula for the Hilbert series of a product J of the…
In this paper, we present a new framework for reducing the computational complexity of geometric vision problems through targeted reweighting of the cost functions used to minimize reprojection errors. Triangulation - the task of estimating…
$V$ is a complete intersection scheme in a multiprojective space if it can be defined by an ideal $I$ with as many generators as $\textrm{codim}(V)$. We investigate the multigraded regularity of complete intersections scheme in…
Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have…
Previous multi-view normal integration methods typically sample a single ray per pixel, without considering the spatial area covered by each pixel, which varies with camera intrinsics and the camera-to-object distance. Consequently, when…
We propose Multi-view Pyramid Transformer (MVP), a scalable multi-view transformer architecture that directly reconstructs large 3D scenes from tens to hundreds of images in a single forward pass. Drawing on the idea of ``looking broader to…
This note is devoted to the study of the links between the Hilbert function of a subscheme X of the projective space, and its geometric properties. We will assume that X is arithmetically Cohen-Macaulay, which allows us to characterize its…
This paper presents Omni-View, which extends the unified multimodal understanding and generation to 3D scenes based on multiview images, exploring the principle that "generation facilitates understanding". Consisting of understanding model,…
We call the scheme parameterizing homogeneous ideals with fixed initial ideal the Gr\"obner scheme. We introduce a Bia{\l}ynicki-Birula decomposition of the Hilbert scheme $\mathrm{Hilb}^{P}_n$ for any Hilbert polynomial $P$ such that the…
This paper proposes an end-to-end learning framework for multiview stereopsis. We term the network SurfaceNet. It takes a set of images and their corresponding camera parameters as input and directly infers the 3D model. The key advantage…
Image classification is an essential task in computer vision, which aims to categorise a set of images into different groups based on some visual criteria. Existing methods, such as convolutional neural networks, have been successfully…
The objective of this work is set-based face recognition, i.e. to decide if two sets of images of a face are of the same person or not. Conventionally, the set-wise feature descriptor is computed as an average of the descriptors from…
Mixture models are well-established learning approaches that, in computer vision, have mostly been applied to inverse or ill-defined problems. However, they are general-purpose divide-and-conquer techniques, splitting the input space into…
A fundamental question in computer vision is whether a set of point pairs is the image of a scene that lies in front of two cameras. Such a scene and the cameras together are known as a chiral reconstruction of the point pairs. In this…
We propose a neural inverse rendering approach that jointly reconstructs geometry, spatially varying reflectance, and lighting conditions from multi-view images captured under varying directional lighting. Unlike prior multi-view…
The modern approaches for computer vision tasks significantly rely on machine learning, which requires a large number of quality images. While there is a plethora of image datasets with a single type of images, there is a lack of datasets…
This paper presents new examples of elementary and non-elementary irreducible components of the Hilbert scheme of points and its nested variants. The results are achieved via a careful analysis of the deformations of a class of finite…
In computer vision, image datasets used for classification are naturally associated with multiple labels and comprised of multiple views, because each image may contain several objects (e.g. pedestrian, bicycle and tree) and is properly…
Given a birational parameterization of an algebraic surface S in the projective space, the purpose of this paper is to investigate the sets of points on S whose preimage consists in k or more points, counting multiplicities. They are…