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Efficient Visibility Computation and Simplification in Different Environments
, Ph.D. Dissertation Sharif University of Technology ; Ghodsi, Mohammad (Supervisor)
Abstract
In this thesis, we considered several types of the visibility problem. These problems include computing the visibility polygon of a point observer inside a polygonal domain, maintaining visibility polygon of a moving point observer, visibility coherence in space, maintaining visibility polygon of a moving segment observer and visibility dependent simplification. Furthermore, we considered these problems in both offline and streaming settings. These problems arise in different practical areas, such as computer graphics, machine vision, robotics, motion planning, geographic information systems (GIS) and computational geometry. We obtained effective theoretical results as well as superior...
Investigating Path Simplification Problems
,
M.Sc. Thesis
Sharif University of Technology
;
Zarei, Alireza
(Supervisor)
Abstract
A basic technique in data reduction is to approximate a collection of data by another collection of smaller size. Then, the resulted data are easier to be processed or maintained. An example of such large scale data is the ordered sequence of n points describing a path or a region boundary. We are given a sequence of points p , p , ..., p , and we consider the 1 2 n problem of approximating these points by a path with k < n line segments which error of this path is not greater than special value. Various criterions are defined to compute the path simplification error.This problem can be used in GIS, Image Processing and Computer Graphics problems. In this thesis, we consider special case...
Minimum Link Navigation
, M.Sc. Thesis Sharif University of Technology ; Zarei, Ali Reza (Supervisor)
Abstract
Finding a path between two specified points is one of the most common problem in computational geometry. The minimum-link path problem is in this category. The minimum-link path between two points is the path between these points with the minimum number of segments. Minimum-link paths have application in areas such as computer graphic, geographic information systems, robotics, image processing, cryptography and VLSI.In this thesis we study variations of the minimum link path problem. Specifically we consider the constrained minimum-link paths in which the path must passes through some given
regions. We detected a flaw in a previously presented algorithm and propose a method to fix this...
regions. We detected a flaw in a previously presented algorithm and propose a method to fix this...
Algorithms for Path Simplification
, Ph.D. Dissertation Sharif University of Technology ; Ghodsi, Mohammad (Supervisor)
Abstract
In this thesis, we present different algorithms for path simplification. We first study this problem under area measures. We present an approximation algorithm for sum-area measure and an optimal algorithm for diff-area measure. Both of these algorithms can be applied on general paths. Moreover, we study the homotopic path simplification. We present a general framework for path simplification which work for desired error measure. We first present a strongly homotopic simplification algorithm for x-monotone paths. Also, we study the strongly homotopic simplification for general paths. We present a geometric tree data structure and present an algorithm based on this data structure....
Line Simplifcation Using the Hausdorff Distance as Error Metric
, M.Sc. Thesis Sharif University of Technology ; Zarei, Alireza (Supervisor)
Abstract
Due to recent advancements and wide usage of location detection devices, huge amount of data are collected by GPS and cellular technologies which exhibits moving objects trajectories. Using this information, it is possible to track a set of objects over a long period of time, as happens for instance in studying animal migration. Always, in these situations it is undesirable or even impossible (due to process and storage limits) to store the complete stream of positioning data. Then, simplifying a trajectory as a data reduction technique is the option for resolving such problems. Moreover, there is an increasing interest in queries capturing ”aggregate” behavior of trajectories as groups like...
Path Simplification Game
, M.Sc. Thesis Sharif University of Technology ; Abam, Mohammad Ali (Supervisor)
Abstract
The problem of path simplification is an important problem in computer science. With the advances in navigation and geographical information based systems, simplification and data compression have gained considerable importance. The intends to find a path with less weight than the provided path while estimating the initial path with good accuracy and simplifying the storage and process cost of path information. This problem is not only useful in Geographical Information Systems, but it also has use cases in image processing and computer graphics and has been studied a lot in computational geometry. In this research, we introduce a simplification game that models the limited version of the...
Computing homotopic line simplification
, Article Computational Geometry: Theory and Applications ; Vol. 47, issue. 7 , 2014 , pp. 728-739 ; ISSN: 09257721 ; Daneshpajouh, S ; Deleuran, L ; Ehsani, S ; Ghodsi, M ; Sharif University of Technology
Abstract
In this paper, we study a variant of the well-known line-simplification problem. For this problem, we are given a polygonal path P=p1, p2,...,pn and a set S of m point obstacles in the plane, with the goal being to determine an optimal homotopic simplification of P. This means finding a minimum subsequence Q=q1,q2,..., qk (q1=p1 and qk=pn) of P that approximates P within a given error ε that is also homotopic to P. In this context, the error is defined under a distance function that can be a Hausdorff or Fréchet distance function, sometimes referred to as the error measure. In this paper, we present the first polynomial-time algorithm that computes an optimal homotopic simplification of P in...
Computing polygonal path simplification under area measures
, Article Graphical Models ; Volume 74, Issue 5 , September , 2012 , Pages 283-289 ; 15240703 (ISSN) ; Ghodsi, M ; Zarei, A ; Sharif University of Technology
2012
Abstract
In this paper, we consider the restricted version of the well-known 2D line simplification problem under area measures and for restricted version. We first propose a unified definition for both of sum-area and difference-area measures that can be used on a general path of n vertices. The optimal simplification runs in O(n 3) under both of these measures. Under sum-area measure and for a realistic input path, we propose an approximation algorithm of O n2 time complexity to find a simplification of the input path, where is the absolute error of this algorithm compared to the optimal solution. Furthermore, for difference-area measure, we present an algorithm that finds the optimal...
Efficient Observer-Dependent Simplification in Polygonal Domains
, Article Algorithmica (New York) ; April , 2011 , Pages 1-21 ; 01784617 (ISSN) ; Ghodsi, M ; Sharif University of Technology
Abstract
In this paper, we consider a special version of the well-known line-simplification problem for simplifying the boundary of a region illuminated by a point light source q, or its visibility polygon VP(q). In this simplification approach, we should take the position of q as an essential factor into account to determine the quality of the resulting simplification. For this purpose, we redefine the known distance- and area-distortion error criteria as the main simplification criteria to take into account the distance between the observer q and the boundary of VP(q). Based on this, we propose algorithms for simplifying VP(q). More precisely, we propose simplification algorithms of O(n2) and...
Streaming algorithms for line simplification
, Article Discrete and Computational Geometry ; Volume 43, Issue 3 , 2010 , Pages 497-515 ; 01795376 (ISSN) ; de Berg, M ; Hachenberger, P ; Zarei, A ; Sharif University of Technology
2010
Abstract
We study the following variant of the well-known line-simplification problem: we are getting a (possibly infinite) sequence of points p0,p1,p2,... in the plane defining a polygonal path, and as we receive the points, we wish to maintain a simplification of the path seen so far. We study this problem in a streaming setting, where we only have a limited amount of storage, so that we cannot store all the points. We analyze the competitive ratio of our algorithms, allowing resource augmentation: we let our algorithm maintain a simplification with 2k (internal) points and compare the error of our simplification to the error of the optimal simplification with k points. We obtain the algorithms...
Streaming algorithms for line simplification
, Article 23rd Annual Symposium on Computational Geometry, SCG'07, Gyeongju, 6 June 2007 through 8 June 2007 ; 2007 , Pages 175-183 ; 1595937056 (ISBN); 9781595937056 (ISBN) ; De Berg, M ; Hachenberger, P ; Zarei, A ; Sharif University of Technology
2007
Abstract
We study the following variant of the well-known line-simpli- ficationproblem: we are getting a possibly infinite sequence of points p 0,p1,p2,... in the plane defining a polygonal path, and as wereceive the points we wish to maintain a simplification of the pathseen so far. We study this problem in a streaming setting, where weonly have a limited amount of storage so that we cannot store all thepoints. We analyze the competitive ratio of our algorithms, allowingresource augmentation: we let our algorithm maintain a simplificationwith 2k (internal) points, and compare the error of oursimplification to the error of the optimal simplification with k points. We obtain the algorithms with O(1)...