Query-points visibility constraint minimum link paths in simple polygons

We study the query version of constrained minimum link paths between two points inside a simple polygon $P$ with $n$ vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning $P$ into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points $s$, $t$ and a query point $q$. Then, the proposed solution is extended to a general case for three arbitrary query points $s$, $t$ and $q$. In the former, we propose an algorithm with $O(n)$ preprocessing time. Extending this approach for the latter case, we develop an algorithm with $O(n^3)$ preprocessing time. The link distance of a $q$-$visible$ path between $s$, $t$ as well as the path are provided in time $O(\log n)$ and $O(m+\log n)$, respectively, for the above two cases, where $m$ is the number of links

Optimal randomized incremental construction for guaranteed logarithmic planar point location

Given a planar map of $n$ segments in which we wish to efficiently locate points, we present the first randomized incremental construction of the well-known trapezoidal-map search-structure that only requires expected $O(n \log n)$ preprocessing time while deterministically guaranteeing worst-case linear storage space and worst-case logarithmic query time. This settles a long standing open problem; the best previously known construction time of such a structure, which is based on a directed acyclic graph, so-called the history DAG, and with the above worst-case space and query-time guarantees, was expected $O(n \log^2 n)$. The result is based on a deeper understanding of the structure of the history DAG, its depth in relation to the length of its longest search path, as well as its correspondence to the trapezoidal search tree. Our results immediately extend to planar maps induced by finite collections of pairwise interior disjoint well-behaved curves.Comment: The article significantly extends the theoretical aspects of the work presented in http://arxiv.org/abs/1205.543

View-Invariant Regions and Mobile Robot Self-Localization

This paper addresses the problem of mobile robot self-localization given a polygonal map and a set of observed edge segments. The standard approach to this problem uses interpretation tree search with pruning heuristics to match observed edges to map edges. Our approach introduces a preprocessing step in which the map is decomposed into 'view-invariant regions' (VIRs). The VIR decomposition captures information about map edge visibility, and can be used for a variety of robot navigation tasks. Basing self-localization search on VIRs greatly reduces the branching factor of the search tree and thereby simplifies the search task. In this paper we define the VIR decomposition and give algorithms for its computation and for self-localization search. We present results of simulations comparing standard and VIR-based search, and discuss the application of the VIR decomposition to other problems in robot navigation

Overcoming slowly decaying Kolmogorov n-width by transport maps: application to model order reduction of fluid dynamics and fluid--structure interaction problems

In this work we focus on reduced order modelling for problems for which the resulting reduced basis spaces show a slow decay of the Kolmogorov $n$-width, or, in practical calculations, its computational surrogate given by the magnitude of the eigenvalues returned by a proper orthogonal decomposition on the solution manifold. In particular, we employ an additional preprocessing during the offline phase of the reduced basis method, in order to obtain smaller reduced basis spaces. Such preprocessing is based on the composition of the snapshots with a transport map, that is a family of smooth and invertible mappings that map the physical domain of the problem into itself. Two test cases are considered: a fluid moving in a domain with deforming walls, and a fluid past a rotating cylinder. Comparison between the results of the novel offline stage and the standard one is presented.Comment: 26 pages, 11 figure

Local Stereo Matching Using Adaptive Local Segmentation

We propose a new dense local stereo matching framework for gray-level images based on an adaptive local segmentation using a dynamic threshold. We define a new validity domain of the fronto-parallel assumption based on the local intensity variations in the 4-neighborhood of the matching pixel. The preprocessing step smoothes low textured areas and sharpens texture edges, whereas the postprocessing step detects and recovers occluded and unreliable disparities. The algorithm achieves high stereo reconstruction quality in regions with uniform intensities as well as in textured regions. The algorithm is robust against local radiometrical differences; and successfully recovers disparities around the objects edges, disparities of thin objects, and the disparities of the occluded region. Moreover, our algorithm intrinsically prevents errors caused by occlusion to propagate into nonoccluded regions. It has only a small number of parameters. The performance of our algorithm is evaluated on the Middlebury test bed stereo images. It ranks highly on the evaluation list outperforming many local and global stereo algorithms using color images. Among the local algorithms relying on the fronto-parallel assumption, our algorithm is the best ranked algorithm. We also demonstrate that our algorithm is working well on practical examples as for disparity estimation of a tomato seedling and a 3D reconstruction of a face