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

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

The matrix revisited: A critical assessment of virtual reality technologies for modeling, simulation, and training

A convergence of affordable hardware, current events, and decades of research have advanced virtual reality (VR) from the research lab into the commercial marketplace. Since its inception in the 1960s, and over the next three decades, the technology was portrayed as a rarely used, high-end novelty for special applications. Despite the high cost, applications have expanded into defense, education, manufacturing, and medicine. The promise of VR for entertainment arose in the early 1990\u27s and by 2016 several consumer VR platforms were released. With VR now accessible in the home and the isolationist lifestyle adopted due to the COVID-19 global pandemic, VR is now viewed as a potential tool to enhance remote education. Drawing upon over 17 years of experience across numerous VR applications, this dissertation examines the optimal use of VR technologies in the areas of visualization, simulation, training, education, art, and entertainment. It will be demonstrated that VR is well suited for education and training applications, with modest advantages in simulation. Using this context, the case is made that VR can play a pivotal role in the future of education and training in a globally connected world

History of Computer Art

A large text presents the history of Computer Art. The history of the artistic uses of computers and computing processes is reconstructed from its beginnings in the fifties to its present state. It points out hypertextual, modular and generative modes to use computing processes in Computer Art and features examples of early developments in media like cybernetic sculptures, video tools, computer graphics and animation (including music videos and demos), video and computer games, pervasive games, reactive installations, virtual reality, evolutionary art and net art. The functions of relevant art works are explained more detailed than is usual in such histories. From October 2011 to December 2012 the chapters have been published successively in German (The English translation started in August 2013 and was completed in June 2014)

Automatic video segmentation employing object/camera modeling techniques

Practically established video compression and storage techniques still process video sequences as rectangular images without further semantic structure. However, humans watching a video sequence immediately recognize acting objects as semantic units. This semantic object separation is currently not reflected in the technical system, making it difficult to manipulate the video at the object level. The realization of object-based manipulation will introduce many new possibilities for working with videos like composing new scenes from pre-existing video objects or enabling user-interaction with the scene. Moreover, object-based video compression, as defined in the MPEG-4 standard, can provide high compression ratios because the foreground objects can be sent independently from the background. In the case that the scene background is static, the background views can even be combined into a large panoramic sprite image, from which the current camera view is extracted. This results in a higher compression ratio since the sprite image for each scene only has to be sent once. A prerequisite for employing object-based video processing is automatic (or at least user-assisted semi-automatic) segmentation of the input video into semantic units, the video objects. This segmentation is a difficult problem because the computer does not have the vast amount of pre-knowledge that humans subconsciously use for object detection. Thus, even the simple definition of the desired output of a segmentation system is difficult. The subject of this thesis is to provide algorithms for segmentation that are applicable to common video material and that are computationally efficient. The thesis is conceptually separated into three parts. In Part I, an automatic segmentation system for general video content is described in detail. Part II introduces object models as a tool to incorporate userdefined knowledge about the objects to be extracted into the segmentation process. Part III concentrates on the modeling of camera motion in order to relate the observed camera motion to real-world camera parameters. The segmentation system that is described in Part I is based on a background-subtraction technique. The pure background image that is required for this technique is synthesized from the input video itself. Sequences that contain rotational camera motion can also be processed since the camera motion is estimated and the input images are aligned into a panoramic scene-background. This approach is fully compatible to the MPEG-4 video-encoding framework, such that the segmentation system can be easily combined with an object-based MPEG-4 video codec. After an introduction to the theory of projective geometry in Chapter 2, which is required for the derivation of camera-motion models, the estimation of camera motion is discussed in Chapters 3 and 4. It is important that the camera-motion estimation is not influenced by foreground object motion. At the same time, the estimation should provide accurate motion parameters such that all input frames can be combined seamlessly into a background image. The core motion estimation is based on a feature-based approach where the motion parameters are determined with a robust-estimation algorithm (RANSAC) in order to distinguish the camera motion from simultaneously visible object motion. Our experiments showed that the robustness of the original RANSAC algorithm in practice does not reach the theoretically predicted performance. An analysis of the problem has revealed that this is caused by numerical instabilities that can be significantly reduced by a modification that we describe in Chapter 4. The synthetization of static-background images is discussed in Chapter 5. In particular, we present a new algorithm for the removal of the foreground objects from the background image such that a pure scene background remains. The proposed algorithm is optimized to synthesize the background even for difficult scenes in which the background is only visible for short periods of time. The problem is solved by clustering the image content for each region over time, such that each cluster comprises static content. Furthermore, it is exploited that the times, in which foreground objects appear in an image region, are similar to the corresponding times of neighboring image areas. The reconstructed background could be used directly as the sprite image in an MPEG-4 video coder. However, we have discovered that the counterintuitive approach of splitting the background into several independent parts can reduce the overall amount of data. In the case of general camera motion, the construction of a single sprite image is even impossible. In Chapter 6, a multi-sprite partitioning algorithm is presented, which separates the video sequence into a number of segments, for which independent sprites are synthesized. The partitioning is computed in such a way that the total area of the resulting sprites is minimized, while simultaneously satisfying additional constraints. These include a limited sprite-buffer size at the decoder, and the restriction that the image resolution in the sprite should never fall below the input-image resolution. The described multisprite approach is fully compatible to the MPEG-4 standard, but provides three advantages. First, any arbitrary rotational camera motion can be processed. Second, the coding-cost for transmitting the sprite images is lower, and finally, the quality of the decoded sprite images is better than in previously proposed sprite-generation algorithms. Segmentation masks for the foreground objects are computed with a change-detection algorithm that compares the pure background image with the input images. A special effect that occurs in the change detection is the problem of image misregistration. Since the change detection compares co-located image pixels in the camera-motion compensated images, a small error in the motion estimation can introduce segmentation errors because non-corresponding pixels are compared. We approach this problem in Chapter 7 by integrating risk-maps into the segmentation algorithm that identify pixels for which misregistration would probably result in errors. For these image areas, the change-detection algorithm is modified to disregard the difference values for the pixels marked in the risk-map. This modification significantly reduces the number of false object detections in fine-textured image areas. The algorithmic building-blocks described above can be combined into a segmentation system in various ways, depending on whether camera motion has to be considered or whether real-time execution is required. These different systems and example applications are discussed in Chapter 8. Part II of the thesis extends the described segmentation system to consider object models in the analysis. Object models allow the user to specify which objects should be extracted from the video. In Chapters 9 and 10, a graph-based object model is presented in which the features of the main object regions are summarized in the graph nodes, and the spatial relations between these regions are expressed with the graph edges. The segmentation algorithm is extended by an object-detection algorithm that searches the input image for the user-defined object model. We provide two objectdetection algorithms. The first one is specific for cartoon sequences and uses an efficient sub-graph matching algorithm, whereas the second processes natural video sequences. With the object-model extension, the segmentation system can be controlled to extract individual objects, even if the input sequence comprises many objects. Chapter 11 proposes an alternative approach to incorporate object models into a segmentation algorithm. The chapter describes a semi-automatic segmentation algorithm, in which the user coarsely marks the object and the computer refines this to the exact object boundary. Afterwards, the object is tracked automatically through the sequence. In this algorithm, the object model is defined as the texture along the object contour. This texture is extracted in the first frame and then used during the object tracking to localize the original object. The core of the algorithm uses a graph representation of the image and a newly developed algorithm for computing shortest circular-paths in planar graphs. The proposed algorithm is faster than the currently known algorithms for this problem, and it can also be applied to many alternative problems like shape matching. Part III of the thesis elaborates on different techniques to derive information about the physical 3-D world from the camera motion. In the segmentation system, we employ camera-motion estimation, but the obtained parameters have no direct physical meaning. Chapter 12 discusses an extension to the camera-motion estimation to factorize the motion parameters into physically meaningful parameters (rotation angles, focal-length) using camera autocalibration techniques. The speciality of the algorithm is that it can process camera motion that spans several sprites by employing the above multi-sprite technique. Consequently, the algorithm can be applied to arbitrary rotational camera motion. For the analysis of video sequences, it is often required to determine and follow the position of the objects. Clearly, the object position in image coordinates provides little information if the viewing direction of the camera is not known. Chapter 13 provides a new algorithm to deduce the transformation between the image coordinates and the real-world coordinates for the special application of sport-video analysis. In sport videos, the camera view can be derived from markings on the playing field. For this reason, we employ a model of the playing field that describes the arrangement of lines. After detecting significant lines in the input image, a combinatorial search is carried out to establish correspondences between lines in the input image and lines in the model. The algorithm requires no information about the specific color of the playing field and it is very robust to occlusions or poor lighting conditions. Moreover, the algorithm is generic in the sense that it can be applied to any type of sport by simply exchanging the model of the playing field. In Chapter 14, we again consider panoramic background images and particularly focus ib their visualization. Apart from the planar backgroundsprites discussed previously, a frequently-used visualization technique for panoramic images are projections onto a cylinder surface which is unwrapped into a rectangular image. However, the disadvantage of this approach is that the viewer has no good orientation in the panoramic image because he looks into all directions at the same time. In order to provide a more intuitive presentation of wide-angle views, we have developed a visualization technique specialized for the case of indoor environments. We present an algorithm to determine the 3-D shape of the room in which the image was captured, or, more generally, to compute a complete floor plan if several panoramic images captured in each of the rooms are provided. Based on the obtained 3-D geometry, a graphical model of the rooms is constructed, where the walls are displayed with textures that are extracted from the panoramic images. This representation enables to conduct virtual walk-throughs in the reconstructed room and therefore, provides a better orientation for the user. Summarizing, we can conclude that all segmentation techniques employ some definition of foreground objects. These definitions are either explicit, using object models like in Part II of this thesis, or they are implicitly defined like in the background synthetization in Part I. The results of this thesis show that implicit descriptions, which extract their definition from video content, work well when the sequence is long enough to extract this information reliably. However, high-level semantics are difficult to integrate into the segmentation approaches that are based on implicit models. Intead, those semantics should be added as postprocessing steps. On the other hand, explicit object models apply semantic pre-knowledge at early stages of the segmentation. Moreover, they can be applied to short video sequences or even still pictures since no background model has to be extracted from the video. The definition of a general object-modeling technique that is widely applicable and that also enables an accurate segmentation remains an important yet challenging problem for further research