Related papers: A Hilbert Scheme in Computer Vision
The distortion varieties of a given projective variety are parametrized by duplicating coordinates and multiplying them with monomials. We study their degrees and defining equations. Exact formulas are obtained for the case of one-parameter…
The Euclidean distance degree of an algebraic variety is a well-studied topic in applied algebra and geometry. It has direct applications in geometric modeling, computer vision, and statistics. We use non-proper Morse theory to give a…
We propose to jointly learn multi-view geometry and warping between views of the same object instances for robust cross-view object detection. What makes multi-view object instance detection difficult are strong changes in viewpoint,…
As the development of deep neural networks, 3D object recognition is becoming increasingly popular in computer vision community. Many multi-view based methods are proposed to improve the category recognition accuracy. These approaches…
Camera calibration is an essential first step in setting up 3D Computer Vision systems. Commonly used parametric camera models are limited to a few degrees of freedom and thus often do not optimally fit to complex real lens distortion. In…
We develop a Hilbert space framework for a number of general multi-scale problems from dynamics. The aim is to identify a spectral theory for a class of systems based on iterations of a non-invertible endomorphism. We are motivated by the…
Multi-view triangulation is the gold standard for 3D reconstruction from 2D correspondences given known calibration and sufficient views. However in practice, expensive multi-view setups -- involving tens sometimes hundreds of cameras --…
Hilbert schemes of zero-dimensional ideals in a polynomial ring can be covered with suitable affine open subschemes whose construction is achieved using border bases. Moreover, border bases have proved to be an excellent tool for describing…
In this paper, we give three bases for the cohomology groups of the Hilbert scheme of two points on projective space. Then, we use these bases to compute all effective and nef cones of higher codimensional cycles on the Hilbert scheme.…
Geometric camera calibration is often required for applications that understand the perspective of the image. We propose perspective fields as a representation that models the local perspective properties of an image. Perspective Fields…
Hilbert specialization is an important tool in Field Arithmetic and Arithmetic Geometry, which has usually been intended for polynomials, hence hypersurfaces, and at scalar values. In this article, first, we extend this tool to prime…
It is critical and meaningful to make image classification since it can help human in image retrieval and recognition, object detection, etc. In this paper, three-sides efforts are made to accomplish the task. First, visual features with…
Geometric calibration of cameras and projectors is an essential step that must be performed before any imaging system can be used. There are many well-known geometric calibration methods for calibrating systems comprised of multiple…
This paper provides a comprehensive survey on pioneer and state-of-the-art 3D scene geometry estimation methodologies based on single, two, or multiple images captured under the omnidirectional optics. We first revisit the basic concepts of…
Recent approaches on visual scene understanding attempt to build a scene graph -- a computational representation of objects and their pairwise relationships. Such rich semantic representation is very appealing, yet difficult to obtain from…
In this paper we introduce an effective method to construct rational deformations between couples of Borel-fixed ideals. These deformations are governed by flat families, so that they correspond to rational curves on the Hilbert scheme.…
This is a review of the problem of Mutually Unbiased Bases in finite dimensional Hilbert spaces, real and complex. Also a geometric measure of "mubness" is introduced, and applied to some recent calculations in six dimensions (partly done…
Multiview 3D evaluation assumes that the images being scored are observations of one static 3D scene. This assumption can fail in NVS and sparse-view reconstruction: inputs or generated outputs may contain artifacts, outlier frames,…
Structured light illumination is an active 3-D scanning technique based on projecting/capturing a set of striped patterns and measuring the warping of the patterns as they reflect off a target object's surface. As designed, each pixel in…
This paper studies the problem of view synthesis with certain amount of rotations from a pair of images, what we called stereo unstructured magnification. While the multi-plane image representation is well suited for view synthesis with…