Algorithms for security in robotics and networks

The dissertation presents algorithms for robotics and security. The first chapter gives an overview of the area of visibility-based pursuit-evasion. The following two chapters introduce two specific algorithms in that area. The algorithms are based on research done together with Dr. Giora Slutzki and Dr. Steven LaValle. Chapter 2 presents a polynomial-time algorithm for clearing a polygon by a single 1-searcher. The result is extended to a polynomial-time algorithm for a pair of 1-searchers in Chapter 3.;Chapters 4 and 5 contain joint research with Dr. Srini Tridandapani, Dr. Jason Jue and Dr. Michael Borella in the area of computer networks. Chapter 4 presents a method of providing privacy over an insecure channel which does not require encryption. Chapter 5 gives approximate bounds for the link utilization in multicast traffic

Algorithms for Optimizing Search Schedules in a Polygon

In the area of motion planning, considerable work has been done on guarding problems, where "guards", modelled as points, must guard a polygonal space from "intruders". Different variants of this problem involve varying a number of factors. The guards performing the search may vary in terms of their number, their mobility, and their range of vision. The model of intruders may or may not allow them to move. The polygon being searched may have a specified starting point, a specified ending point, or neither of these. The typical question asked about one of these problems is whether or not certain polygons can be searched under a particular guarding paradigm defined by the types of guards and intruders. In this thesis, we focus on two cases of a chain of guards searching a room (polygon with a specific starting point) for mobile intruders. The intruders must never be allowed to escape through the door undetected. In the case of the two guard problem, the guards must start at the door point and move in opposite directions along the boundary of the polygon, never crossing the door point. At all times, the guards must be able to see each other. The search is complete once both guards occupy the same spot elsewhere on the polygon. In the case of a chain of three guards, consecutive guards in the chain must always be visible. Again, the search starts at the door point, and the outer guards of the chain must move from the door in opposite directions. These outer guards must always remain on the boundary of the polygon. The search is complete once the chain lies entirely on a portion of the polygon boundary not containing the door point. Determining whether a polygon can be searched is a problem in the area of visibility in polygons; further to that, our work is related to the area of planning algorithms. We look for ways to find optimal schedules that minimize the distance or time required to complete the search. This is done by finding shortest paths in visibility diagrams that indicate valid positions for the guards. In the case of the two-guard room search, we are able to find the shortest distance schedule and the quickest schedule. The shortest distance schedule is found in O(n^2) time by solving an L_1 shortest path problem among curved obstacles in two dimensions. The quickest search schedule is found in O(n^4) time by solving an L_infinity shortest path problem among curved obstacles in two dimensions. For the chain of three guards, a search schedule minimizing the total distance travelled by the outer guards is found in O(n^6) time by solving an L_1 shortest path problem among curved obstacles in two dimensions

A Novel Approach for Extraction of Polygon Regions

This paper presents a new algorithm to find out whether a polygon exists around a reference point given within the graphical domain. The algorithm is based on creating discrete line segments and then searching them using the orientations formed at segments intersections. The computational complexity of the searching algorithm has been determined as O( n2

An End-to-End License Plate Localization and Recognition System

An end-to-end license plate recognition (LPR) system is proposed. It is composed of pre-processing, detection, segmentation and character recognition to find and recognize plates from camera based still images. The system utilizes connected component (CC) properties to quickly extract the license plate region. A novel two-stage CC filtering is utilized to address both shape and spatial relationship information to produce high precision and recall values for detection. Floating peak and valleys (FPV) of projection profiles are used to cut the license plates into individual characters. A turning function based method is proposed to recognize each character quickly and accurately. It is further accelerated using curvature histogram based support vector machine (SVM). The INFTY dataset is used to train the recognition system. And MediaLab license plate dataset is used for testing. The proposed system achieved 89.45% F-measure for detection and 87.33% accuracy for overall recognition rate which is comparable to current state-of-the-art systems

Guarding and Searching Polyhedra

Guarding and searching problems have been of fundamental interest since the early years of Computational Geometry. Both are well-developed areas of research and have been thoroughly studied in planar polygonal settings. In this thesis we tackle the Art Gallery Problem and the Searchlight Scheduling Problem in 3-dimensional polyhedral environments, putting special emphasis on edge guards and orthogonal polyhedra. We solve the Art Gallery Problem with reflex edge guards in orthogonal polyhedra having reflex edges in just two directions: generalizing a classic theorem by O'Rourke, we prove that r/2 + 1 reflex edge guards are sufficient and occasionally necessary, where r is the number of reflex edges. We also show how to compute guard locations in O(n log n) time. Then we investigate the Art Gallery Problem with mutually parallel edge guards in orthogonal polyhedra with e edges, showing that 11e/72 edge guards are always sufficient and can be found in linear time, improving upon the previous state of the art, which was e/6. We also give tight inequalities relating e with the number of reflex edges r, obtaining an upper bound on the guard number of 7r/12 + 1. We further study the Art Gallery Problem with edge guards in polyhedra having faces oriented in just four directions, obtaining a lower bound of e/6 - 1 edge guards and an upper bound of (e+r)/6 edge guards. All the previously mentioned results hold for polyhedra of any genus. Additionally, several guard types and guarding modes are discussed, namely open and closed edge guards, and orthogonal and non-orthogonal guarding. Next, we model the Searchlight Scheduling Problem, the problem of searching a given polyhedron by suitably turning some half-planes around their axes, in order to catch an evasive intruder. After discussing several generalizations of classic theorems, we study the problem of efficiently placing guards in a given polyhedron, in order to make it searchable. For general polyhedra, we give an upper bound of r^2 on the number of guards, which reduces to r for orthogonal polyhedra. Then we prove that it is strongly NP-hard to decide if a given polyhedron is entirely searchable by a given set of guards. We further prove that, even under the assumption that an orthogonal polyhedron is searchable, approximating the minimum search time within a small-enough constant factor to the optimum is still strongly NP-hard. Finally, we show that deciding if a specific region of an orthogonal polyhedron is searchable is strongly PSPACE-hard. By further improving our construction, we show that the same problem is strongly PSPACE-complete even for planar orthogonal polygons. Our last results are especially meaningful because no similar hardness theorems for 2-dimensional scenarios were previously known

Mobile 2D and 3D Spatial Query Techniques for the Geospatial Web

The increasing availability of abundant geographically referenced information in the Geospatial Web provides a variety of opportunities for developing value-added LBS applications. However, large data volumes of the Geospatial Web and small mobile device displays impose a data visualization problem, as the amount of searchable information overwhelms the display when too many query results are returned. Excessive returned results clutter the mobile display, making it harder for users to prioritize information and causes confusion and usability problems. Mobile Spatial Interaction (MSI) research into this “information overload” problem is ongoing where map personalization and other semantic based filtering mechanisms are essential to de-clutter and adapt the exploration of the real-world to the processing/display limitations of mobile devices. In this thesis, we propose that another way to filter this information is to intelligently refine the search space. 3DQ (3-Dimensional Query) is our novel MSI prototype for information discovery on today’s location and orientation-aware smartphones within 3D Geospatial Web environments. Our application incorporates human interactions (interpreted from embedded sensors) in the geospatial query process by determining the shape of their actual visibility space as a query “window” in a spatial database, e.g. Isovist in 2D and Threat Dome in 3D. This effectively applies hidden query removal (HQR) functionality in 360º 3D that takes into account both the horizontal and vertical dimensions when calculating the 3D search space, significantly reducing display clutter and information overload on mobile devices. The effect is a more accurate and expected search result for mobile LBS applications by returning information on only those objects visible within a user’s 3D field-of-view

Mobile 2D and 3D Spatial Query Techniques for the Geospatial Web

The increasing availability of abundant geographically referenced information in the Geospatial Web provides a variety of opportunities for developing value-added LBS applications. However, large data volumes of the Geospatial Web and small mobile device displays impose a data visualization problem, as the amount of searchable information overwhelms the display when too many query results are returned. Excessive returned results clutter the mobile display, making it harder for users to prioritize information and causes confusion and usability problems. Mobile Spatial Interaction (MSI) research into this “information overload” problem is ongoing where map personalization and other semantic based filtering mechanisms are essential to de-clutter and adapt the exploration of the real-world to the processing/display limitations of mobile devices. In this thesis, we propose that another way to filter this information is to intelligently refine the search space. 3DQ (3-Dimensional Query) is our novel MSI prototype for information discovery on today’s location and orientation-aware smartphones within 3D Geospatial Web environments. Our application incorporates human interactions (interpreted from embedded sensors) in the geospatial query process by determining the shape of their actual visibility space as a query “window” in a spatial database, e.g. Isovist in 2D and Threat Dome in 3D. This effectively applies hidden query removal (HQR) functionality in 360º 3D that takes into account both the horizontal and vertical dimensions when calculating the 3D search space, significantly reducing display clutter and information overload on mobile devices. The effect is a more accurate and expected search result for mobile LBS applications by returning information on only those objects visible within a user’s 3D field-of-view. ii

Abstracts for the twentyfirst European workshop on Computational geometry, Technische Universiteit Eindhoven, The Netherlands, March 9-11, 2005

This volume contains abstracts of the papers presented at the 21st European Workshop on Computational Geometry, held at TU Eindhoven (the Netherlands) on March 9–11, 2005. There were 53 papers presented at the Workshop, covering a wide range of topics. This record number shows that the field of computational geometry is very much alive in Europe. We wish to thank all the authors who submitted papers and presented their work at the workshop. We believe that this has lead to a collection of very interesting abstracts that are both enjoyable and informative for the reader. Finally, we are grateful to TU Eindhoven for their support in organizing the workshop and to the Netherlands Organisation for Scientific Research (NWO) for sponsoring the workshop

Compression of 3D models with NURBS

With recent progress in computing, algorithmics and telecommunications, 3D models are increasingly used in various multimedia applications. Examples include visualization, gaming, entertainment and virtual reality. In the multimedia domain 3D models have been traditionally represented as polygonal meshes. This piecewise planar representation can be thought of as the analogy of bitmap images for 3D surfaces. As bitmap images, they enjoy great flexibility and are particularly well suited to describing information captured from the real world, through, for instance, scanning processes. They suffer, however, from the same shortcomings, namely limited resolution and large storage size. The compression of polygonal meshes has been a very active field of research in the last decade and rather efficient compression algorithms have been proposed in the literature that greatly mitigate the high storage costs. However, such a low level description of a 3D shape has a bounded performance. More efficient compression should be reachable through the use of higher level primitives. This idea has been explored to a great extent in the context of model based coding of visual information. In such an approach, when compressing the visual information a higher level representation (e.g., 3D model of a talking head) is obtained through analysis methods. This can be seen as an inverse projection problem. Once this task is fullled, the resulting parameters of the model are coded instead of the original information. It is believed that if the analysis module is efficient enough, the total cost of coding (in a rate distortion sense) will be greatly reduced. The relatively poor performance and high complexity of currently available analysis methods (except for specific cases where a priori knowledge about the nature of the objects is available), has refrained a large deployment of coding techniques based on such an approach. Progress in computer graphics has however changed this situation. In fact, nowadays, an increasing number of pictures, video and 3D content are generated by synthesis processing rather than coming from a capture device such as a camera or a scanner. This means that the underlying model in the synthesis stage can be used for their efficient coding without the need for a complex analysis module. In other words it would be a mistake to attempt to compress a low level description (e.g., a polygonal mesh) when a higher level one is available from the synthesis process (e.g., a parametric surface). This is, however, what is usually done in the multimedia domain, where higher level 3D model descriptions are converted to polygonal meshes, if anything by the lack of standard coded formats for the former. On a parallel but related path, the way we consume audio-visual information is changing. As opposed to recent past and a large part of today's applications, interactivity is becoming a key element in the way we consume information. In the context of interest in this dissertation, this means that when coding visual information (an image or a video for instance), previously obvious considerations such as decision on sampling parameters are not so obvious anymore. In fact, as in an interactive environment the effective display resolution can be controlled by the user through zooming, there is no clear optimal setting for the sampling period. This means that because of interactivity, the representation used to code the scene should allow the display of objects in a variety of resolutions, and ideally up to infinity. One way to resolve this problem would be by extensive over-sampling. But this approach is unrealistic and too expensive to implement in many situations. The alternative would be to use a resolution independent representation. In the realm of 3D modeling, such representations are usually available when the models are created by an artist on a computer. The scope of this dissertation is precisely the compression of 3D models in higher level forms. The direct coding in such a form should yield improved rate-distortion performance while providing a large degree of resolution independence. There has not been, so far, any major attempt to efficiently compress these representations, such as parametric surfaces. This thesis proposes a solution to overcome this gap. A variety of higher level 3D representations exist, of which parametric surfaces are a popular choice among designers. Within parametric surfaces, Non-Uniform Rational B-Splines (NURBS) enjoy great popularity as a wide range of NURBS based modeling tools are readily available. Recently, NURBS has been included in the Virtual Reality Modeling Language (VRML) and its next generation descendant eXtensible 3D (X3D). The nice properties of NURBS and their widespread use has lead us to choose them as the form we use for the coded representation. The primary goal of this dissertation is the definition of a system for coding 3D NURBS models with guaranteed distortion. The basis of the system is entropy coded differential pulse coded modulation (DPCM). In the case of NURBS, guaranteeing the distortion is not trivial, as some of its parameters (e.g., knots) have a complicated influence on the overall surface distortion. To this end, a detailed distortion analysis is performed. In particular, previously unknown relations between the distortion of knots and the resulting surface distortion are demonstrated. Compression efficiency is pursued at every stage and simple yet efficient entropy coder realizations are defined. The special case of degenerate and closed surfaces with duplicate control points is addressed and an efficient yet simple coding is proposed to compress the duplicate relationships. Encoder aspects are also analyzed. Optimal predictors are found that perform well across a wide class of models. Simplification techniques are also considered for improved compression efficiency at negligible distortion cost. Transmission over error prone channels is also considered and an error resilient extension defined. The data stream is partitioned by independently coding small groups of surfaces and inserting the necessary resynchronization markers. Simple strategies for achieving the desired level of protection are proposed. The same extension also serves the purpose of random access and on-the-fly reordering of the data stream