This is a survey on graph visualization and navigation techniques, as used in information visualization. Graphs appear in numerous applications such as web browsing, state--transition diagrams, and data structures. The ability to visualize and to navigate in these potentially large, abstract graphs is often a crucial part of an application. Information visualization has specific requirements, which means that this survey approaches the results of traditional graph drawing from a different perspective. Index Terms---Information visualization, graph visualization, graph drawing, navigation, focus+context, fish--eye, clustering. 1

In this paper we analyze in some detail the geometry of a pair of cameras, i.e. a stereo rig. Contrarily to what has been done in the past and is still done currently, for example in stereo or motion analysis, we do not assume that the intrinsic parameters of the cameras are known (coordinates of the principal points, pixels aspect ratio and focal lengths). This is important for two reasons. First, it is more realistic in applications where these parameters may vary according to the task (active vision). Second, the general case considered here, captures all the relevant information that is necessary for establishing correspondences between two pairs of images. This information is fundamentally projective and is hidden in a confusing manner in the commonly used formalism of the Essential matrix introduced by Longuet-Higgins [40]. This paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3 \Theta 3 ma...

We present a technique for building a three-dimensional description of a static scene from a dense sequence of images. These images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image. The technique utilizes knowledge of the camera motion to form and analyze slices of this solid. These slices directly encode not only the three-dimensional positions of objects, but also such spatiotemporal events as the occlusion of one object by another. For straight-line camera motions, these slices have a simple linear structure that makes them easier to analyze. The analysis computes the threedimensional positions of object features, marks occlusion boundaries on the objects, and builds a threedimensional map of "free space. " In our article, we first describe the application of this technique to a simple camera motion, and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects. 1

Algorithms for approximately optimal quantization of color images are discussed. The distortion measure used is the distance in RGB space. These algorithms are used to compute the color map for low-depth frame buffers in order to allow high-quality static images to be displayed. It is demonstrated that most color images can be very well displayed using only 256 or 512 colors. Thus frame buffers of only 8 or 9 bits can display images that normally require 15 bits or more per pixel. Work reported herein was sponsored by the IBM Corporation though a general grant agreement to MIT dated July 1, 1979. ----------------------------------------------------------------- TABLE OF CONTENTS page I. Introduction ............................................. 4 II. Frame Buffers and Colormaps .............................. 6 III. 1-Dimensional Tapered Quantization .......................17 IV. 3-Dimensional Tapered Quantization .......................27 V. Conclusions and Ideas for Further Study .......

. We address the problem of estimating three-dimensional motion, and structure from motion with an uncalibrated moving camera. We show that point correspondences between three images, and the fundamental matrices computed from these point correspondences, are sufficient to recover the internal orientation of the camera (its calibration), the motion parameters, and to compute coherent perspective projection matrices which enable us to reconstruct 3-D structure up to a similarity. In contrast with other methods, no calibration object with a known 3-D shape is needed, and no limitations are put upon the unknown motions to be performed or the parameters to be recovered, as long as they define a projective camera. The theory of the method, which is based on the constraint that the observed points are part of a static scene, thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic, is first detailed. Several algorithms are then presented, and their ...

Adults were asked to judge the self-to-object directions in a room from novel points of observation that differed from their actual point at times only by a rotation and at other times only by a translation. The results show for the rotation trials that the errors and latencies when a novel point was imagined were worse than the baseline responses from their actual points of observation, and the latencies varied as a function of the magnitude of the to-be-imagined rotation. For the translation trials, on the other hand, the errors and latencies when a novel point was imagined were comparable to the baseline responses from their actual point and did not vary significantly across the different imagined station points. The evidence indicates that subjects know the objectto-object relations directly, without going through the origin of a coordinate system. In addition, similarities in processing during imagination on the one hand, and perception and action on the other are discussed. The spatial structure of a place consists of the distances and directions relating its objects, features, and events. Observers often produce spatially coordinated action while on the move and plan actions before reaching the station points from which

When a sensor network is deployed to detect objects penetrating a protected region, it is not necessary to have every point in the deployment region covered by a sensor. It is enough if the penetrating objects are detected at some point in their trajectory. If a sensor network guarantees that every penetrating object will be detected by at least £ distinct sensors before it crosses the barrier of wireless sensors, we say the network provides £-barrier coverage. In this paper, we develop theoretical foundations for £-barrier coverage. We propose efficient algorithms using which one can quickly determine, after deploying the sensors, whether the deployment region is £-barrier covered. Next, we establish the optimal deployment pattern to achieve £-barrier coverage when deploying sensors deterministically. Finally, we consider barrier coverage with high probability when sensors are deployed randomly. The major challenge, when dealing with probabilistic barrier coverage, is to derive critical conditions using which one can compute the minimum number of sensors needed to ensure barrier coverage with high probability. Deriving critical conditions for £-barrier coverage is, however, still an open problem. We derive critical conditions for a weaker notion of barrier coverage, called weak £-barrier coverage.

We give an algorithm for triangulating n-vertex polygonal regions (with holes) so that no angle in the nal triangulation measures more than pi/2. The number of triangles in the triangulation is only O(n), improving a previous bound of O(n²), and the worst-case running time is O(n log² n). The basic technique used in the algorithm, recursive subdivision by disks, is new and may have wider application in mesh generation. We also report on an implementation of our algorithm.

This paper addresses the problem of motion estimation from profiles (also known as apparent contours) of an object rotating on a turntable in front of a sin- gle camera. Its main contribution is the development of a practical and accurate technique for solving this problem from profiles alone, which is precise enough to allow the reconstruction of the shape of the object. No correspondences be- tween points or lines are necessary, although the method proposed can be used equally when these features are available, without any further adaptation. Sym- metry properties of the surface of revolution swept out by the rotating object are exploited to obtain the image of the rotation axis and the homography relating epipolar lines in 2 views, in a robust and elegant way. These, together with ge- ometric constraints for images of rotating objects, are then used to obtain first *Corresponding author the image of the horizon, which is the projection of the plane that contains the camera centers, and then the epipoles, thus fully determining the epipolar ge- ometry of the image sequence. The estimation of the epipolar geometry by this sequential approach (image of rotation axis -- homography -- image of the hori- zon -- epipoles) avoids many of the problems usually found in other algorithms for motion recovery from profiles. In particular, the search for the epipoles, by far the most critical step, is carried out as a simple one-dimensional optimization problem. The initialization of the parameters is trivial and completely automatic for all stages of the algorithm. After the estimation of the epipolar geometry, the Euclidean motion is recovered using the fixed intrinsic parameters of the cam- era, obtained either from a calibration grid or from self-calibrati...

This thesis contains a presentation and an analysis of adaptive filtering strategies for multidimensional data. The size, shape and orientation of the filter are signal controlled and thus adapted locally to each neighbourhood according to a predefined model. The filter is constructed as a linear weighting of fixed oriented bandpass filters having the same shape but different orientations. The adaptive filtering methods have been tested on both real data and synthesized test data in 2D, e.g. still images, 3D, e.g. image sequences or volumes, with good results. In 4D, e.g. volume sequences, the algorithm is given in its mathematical form. The weighting coefficients are given by the inner products of a tensor representing the local structure of the data and the tensors representing the orientation of the filters. The procedure and filter design in estimating the representation tensor are described. In 2D, the tensor contains information about the local energy, the optimal orientation and a certainty of the orientation. In 3D, the information in the tensor is the energy, the normal to the best fitting local plane and the tangent to the best fitting line, and certainties of these orientations. In the case of time sequences, a quantitative comparison of the proposed method and other (optical flow) algorithms is presented. The estimation of control information is made in different scales. There are two main reasons for this. A single filter has a particular limited pass band which may or may not be tuned to the different sized objects to describe. Second, size or scale is a descriptive feature in its own right. All of this requires the integration of measurements from different scales. The increasing interest in wavelet theory supports the idea that a multiresolution approach is necessary. Hence the resulting adaptive filter will adapt also in size and to different orientations in different scales.