相关论文: Flat Maps that improve on the Winkel Tripel

Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the…

In this paper we describe a mathematically interesting but relatively minor improvement to the Gott-Goldberg-Vanderbei (GGV) map projection. This new projection can be described as what one would get by making a spherical rubber ball…

It is useful to have mathematical criteria for evaluating errors in map projections. The Chebyshev criterion for minimizing rms (root mean square) local scale factor errors for conformal maps has been useful in developing conformal map…

Choropleth maps are among the most common visualization techniques used to present geographical data. These maps require an equal-area projection but there are no clear criteria for selecting one. We collaborated with 20 social scientists…

Foreground map evaluation is crucial for gauging the progress of object segmentation algorithms, in particular in the filed of salient object detection where the purpose is to accurately detect and segment the most salient object in a…

In this paper we give a classification of tilings of the sphere by congruent quadrilaterals with exactly two equal edges. The tilings are the earth map tilings, $(p,q)$-earth map tilings and their flip modifications, and quadrilateral…

Scattered lights from terrestrial exoplanets provide valuable information about the planetary surface. Applying the surface reconstruction method proposed by Fujii et al. (2010) to both diurnal and annual variations of the scattered light,…

Omnidirectional depth estimation has received much attention from researchers in recent years. However, challenges arise due to camera soiling and variations in camera layouts, affecting the robustness and flexibility of the algorithm. In…

A flat Universe model supported by recent observations has 18 possible choices for its overall topology. To detect or exclude these possibilities is one of the most important tasks in modern cosmology, but it has been very difficult for…

Observations suggest that our universe is spatially flat on the largest observable scales. Exactly six different compact orientable three-dimensional manifolds admit flat metrics. These six manifolds are therefore the most natural choices…

While feature association to a global map has significant benefits, to keep the computations from growing exponentially, most lidar-based odometry and mapping methods opt to associate features with local maps at one voxel scale. Taking…

In the first part of this paper, we consider smooth maps from a compact orientable 3-manifold without boundary to the 2-sphere. We give a geometric criterion to decide whether two given maps are homotopic, based on the sets of points where…

In this work, the dual flatness, which is connected with Statistics and Information geometry, of general $(\alpha,\beta)$-metrics (a new class of Finsler metrics) is studied. A nice characterization for such metrics to be dually flat under…

A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…

Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal…

Circle maps with a flat spot are studied which are differentiable, even on the boundary of the flat spot. Estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set are obtained. Also, a sharp transition is found…

Seiberg-Witten theory leads to a delicate interplay between Riemannian geometry and smooth topology in dimension four. In particular, the scalar curvature of any metric must satisfy certain non-trivial estimates if the manifold in question…

Accurate distance estimation from monocular cameras is essential for intelligent monitoring systems. In many deployments, image coordinates are mapped to ground positions using planar homographies initialized by manual selection of…

We focus on estimating the 3D orientation of the ground plane from a single image. We formulate the problem as an inter-mingled multi-task prediction problem by jointly optimizing for pixel-wise surface normal direction, ground plane…

The slope of the best fit line from minimizing the sum of the squared oblique errors is the root of a polynomial of degree four. This geometric view of measurement errors is used to give insight into the performance of various slope…