Related papers: Scenic Routes over Points in 2D Space
Given a set of basic areas, the territory design problem asks to create a predefined number of territories, each containing at least one basic area, such that an objective function is optimized. Desired properties of territories often…
This works presents a formulation for visual navigation that unifies map based spatial reasoning and path planning, with landmark based robust plan execution in noisy environments. Our proposed formulation is learned from data and is thus…
Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They…
The degree of symmetry of a combinatorial object, such as a lattice path, is a measure of how symmetric the object is. It typically ranges from zero, if the object is completely asymmetric, to its size, if it is completely symmetric. We…
We achieve 3D semantic scene labeling by exploring semantic relation between each point and its contextual neighbors through edges. Besides an encoder-decoder branch for predicting point labels, we construct an edge branch to hierarchically…
Working over a field ${\mathbb{k}}$ of characteristic $\ne 2$, we study what we call bisector fields, which are arrangements of paired lines in the plane that have the property that each line in the arrangement crosses the paired lines in…
A graph is a path graph if it is the intersection graph of a family of subpaths of a tree. In 1970, Renz asked for a characterizaton of path graphs by forbidden induced subgraphs. Here we answer this question by listing all graphs that are…
One distinguishing feature of rational curves is that they have algebraic parameterizations. Arc spaces are a way of describing approximations to parameterizations of all curves in some fixed space. Playing on these descriptions, this paper…
Contact path geometries are curved geometric structures on a contact manifold comprising smooth families of paths modeled on the family of all isotropic lines in the projectivization of a symplectic vector space. Locally such a structure is…
This gives some information about the conformal point and the calibrating conic, and their relationship one to the other. These concepts are useful for visualizing image geometry, and lead to intuitive ways to compute geometry, such as…
Path planning is an important component in any highly automated vehicle system. In this report, the general problem of path planning is considered first in partially known static environments where only static obstacles are present but the…
The brain transforms visual inputs into high-dimensional cortical representations that support diverse cognitive and behavioral goals. Characterizing how this information is organized and routed across the human brain is essential for…
Path graphs are intersection graphs of paths in a tree.~In this paper we give a "6\ good characterization" of path graphs, namely, we prove that path graph membership is in $NP\cap CoNP$ without resorting to existing polynomial time…
This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph…
We investigate algorithms to find short paths in spatial networks with stochastic edge weights. Our formulation of the problem of finding short paths differs from traditional formulations because we specifically do not make two of the usual…
Semantic segmentation is an important and well-known task in the field of computer vision, in which we attempt to assign a corresponding semantic class to each input element. When it comes to semantic segmentation of 2D images, the input…
A path partition (also referred to as a linear forest) of a graph $G$ is a set of vertex-disjoint paths which together contain all the vertices of $G$. An isolated vertex is considered to be a path in this case. The path partition…
The watershed is a powerful tool for segmenting objects whose contours appear as crest lines on a gradient image. The watershed transform associates to a topographic surface a partition into catchment basins, defined as attraction zones of…
Landmarks are important features of spatial cognition. Landmarks are naturally included in human route descriptions and in the past algorithms were developed to select the most salient landmarks at decision points and automatically…
Cartograms are maps in which the areas of regions (e.g., countries or provinces) are proportional to a thematic mapping variable (e.g., population or gross domestic product). A cartogram is called contiguous if it keeps geographically…