相关论文: Warping Peirce Quincuncial Panoramas
The spherical harmonics $Y_{\ell m}(\theta,\varphi)$ are complex-valued functions on the surface of a sphere, and have found widespread application in physics and astronomy. Every physics students knows them from quantum mechanics and…
A novel square equal-area map projection is proposed. The projection combines closed-form forward and inverse solutions with relatively low angular distortion and minimal cusps, a combination of properties not manifested by any previously…
In this work, we present an adaptation of the classical stereographic projection, originally formulated for the sphere, now considering the context of the ellipsoid and the elliptic paraboloid. We begin by constructing the stereographic…
360$^{\circ}$ panoramas are a rich medium, yet notoriously difficult to visualize in the 2D image plane. We explore how intelligent rotations of a spherical image may enable content-aware projection with fewer perceptible distortions.…
The Poincar\'e sphere is a graphical representation in a three-dimensional space for the polarization of light. Similarly, an optical element with spatially varying birefringence can be represented by a surface on a four-dimensional…
360{\deg} spherical images have advantages of wide view field, and are typically projected on a planar plane for processing, which is known as equirectangular image. The object shape in equirectangular images can be distorted and lack…
The Mercator projection is sometimes confused with another mapping technique, specifically the central cylindrical projection, which projects the Earth's surface onto a cylinder tangent to the equator, as if a light source is at the Earth's…
Learning depth from spherical panoramas is becoming a popular research topic because a panorama has a full field-of-view of the environment and provides a relatively complete description of a scene. However, applying well-studied CNNs for…
This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…
Quadratic hypersurfaces are a natural generalization of affine subspaces, and projections are elementary blocks of algorithms in optimization and machine learning. It is therefore intriguing that no proper studies and tools have been…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…
Under conditions that prevent tangential intersection, we prove quadratic convergence of a projection algorithm for the feasibility problem of finding a point in the intersection of a smooth curve and line in $\mathbb{R}^2$. This nonconvex…
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of such projective isomorphisms to five base cases by…
Monocular depth estimation is an ambiguous problem, thus global structural cues play an important role in current data-driven single-view depth estimation methods. Panorama images capture the complete spatial information of their…
We present an algorithm for converting an indoor spherical panorama into a photograph with a simulated overhead view. The resulting image will have an extremely wide field of view covering up to 4{\pi} steradians of the spherical panorama.…
As the spherical object can be seen everywhere, we should extract the ellipse image accurately and fit it by implicit algebraic curve in order to finish the 3D reconstruction. In this paper, we propose a new ellipse fitting algorithm which…
We address the problem of projecting a point onto a quadratic hypersurface, more specifically a central quadric. We show how this problem reduces to finding a given root of a scalar-valued nonlinear function. We completely characterize one…
Being able to edit panoramic images is crucial for creating realistic 360{\deg} visual experiences. However, existing perspective-based image editing methods fail to model the spatial structure of panoramas. Conventional cube-map…
The projection onto the intersection of sets generally does not allow for a closed form even when the individual projection operators have explicit descriptions. In this work, we systematically analyze the projection onto the intersection…