Related papers: Changing Views on Curves and Surfaces
In this Book we argue that the fruitful interaction of computer vision and belief calculus is capable of stimulating significant advances in both fields. From a methodological point of view, novel theoretical results concerning the…
We give an introduction to the study of algebraic hypersurfaces, focusing on the problem of when two hypersurfaces are isomorphic or close to being isomorphic. Working with hypersurfaces and emphasizing examples makes it possible to discuss…
A class of surfaces-graphs in a Riemannian 3-space with a prescribed projection of one field of principal directions onto a surface $\Pi$ is considered. A problem of determination of such surfaces when both principal curvatures are given…
We study the geometry of surfaces in $\mathbb R^5$ by relating it to the geometry of regular and singular surfaces in $\mathbb R^4$ obtained by orthogonal projections. In particular, we obtain relations between asymptotic directions, which…
This paper studies the problem of 3D volumetric reconstruction from two views of a scene with an unknown camera. While seemingly easy for humans, this problem poses many challenges for computers since it requires simultaneously…
We study the formation of images in a reflective sphere in three configurations using caustics of the field of light rays. The optical wavefront emerging from a source point reaching a subject following passage through the optical system…
In this paper, we will study the following pattern recognition problem: Every pattern is a 3-dimensional graph, its surface can be split up into some regions, every region is composed of the pixels with the approximately same colour value…
3D reconstruction from multiple views is a successful computer vision field with multiple deployments in applications. State of the art is based on traditional RGB frames that enable optimization of photo-consistency cross views. In this…
Learning geometry, motion, and appearance priors of object classes is important for the solution of a large variety of computer vision problems. While the majority of approaches has focused on static objects, dynamic objects, especially…
In this paper alternative method for real-time 3D model rasterization is given. Surfaces are drawn in perspective-map space which acts as a virtual camera lens. It can render single-pass 360{\deg} angle of view (AOV) image of unlimited…
We provide algorithms to reconstruct rational ruled surfaces in three-dimensional projective space from the `apparent contour' of a single projection to the projective plane. We deal with the case of tangent developables and of general…
Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated.…
At any point of a surface in the four-dimensional Euclidean space we consider the geometric configuration consisting of two figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We show…
Recovering the spatial layout of the cameras and the geometry of the scene from extreme-view images is a longstanding challenge in computer vision. Prevailing 3D reconstruction algorithms often adopt the image matching paradigm and presume…
We consider curves which go around Whitney umbrella. Then we consider the geodesic and the normal curvatures, ruled surfaces generated by the normal vector and normal developable surfaces with respect to the tangent and bi-tangent vectors…
We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is…
By combining tools from different areas of mathematics, we obtain 3D visualizations of elliptic curves over different fields that faithfully capture the underlying algebra and geometry.
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
We address the problem of looking into the water from the air, where we seek to remove image distortions caused by refractions at the water surface. Our approach is based on modeling the different water surface structures at various points…
Given the complexities inherent in visual scenes, such as object occlusion, a comprehensive understanding often requires observation from multiple viewpoints. Existing multi-viewpoint object-centric learning methods typically employ random…