In this paper, we consider the problem of finding an optimal reconstruction from two views of a piecewise planar scene. We consider the general case of uncalibrated cameras, hence place us in a projectlye framework. In this case, there is no meaningful metric information about the object space that could be used to define optimization criteria. Taking into account that the images are then the only spaces where an optimization process makes sense, there is a need at each step of the reconstruction process, from the detection of planar structures to motion estimation and actual 3D reconstruction, of a consistent image level representation of geometric 3D structures. In our case, we need to represent camera motion and 3D points that are subject to coplanarity constraints. It is well known that camera motion between two views can be represented on the image level via the epipolar geometry (fundamental matrix). Coplanarity constraints can be expressed via a collection of 2D homographies. Unfortunately, these algebraic entities are over-parameterized in the sense that the 2D homographies must in addition obey constraints imposed by the epipolar geometry. We are thus looking for a minimal and consistent representation of motion (epipolar geometry) and structure (points+homographies) that in addition should be easy to use for minimizing reprojection error in a bundle adjustment manner. In this paper, we propose such a representation and use it to devise fast and accurate estimation methods for each step of the reconstruction process, including image point matching, plane detection and optimal triangulation of planes and points on planes. We make extensive use of the quasi-linear optimization principle. A great number of experimental results show that the new methods give sup...

In this paper, we address the problem of hand-eye calibration of a robot mounted video camera. In a first time, we derive a new linear formulation of the problem. This allows an algebraic analysis of the cases that usual approaches do not consider. In a second time, we extend this new formulation into an on-line hand-eye calibration method. This method allows to get rid of the calibration object required by the standard approaches and use unknown scenes instead. Finally, experimental results validate both methods.

The design-for-assembly technique requires realistic physically based simulation algorithms and in particular efficient geometric collision detection routines. Instead of approximating mechanical parts by large polygonal models, we work with the much smaller original CAD-data directly, thus avoiding precision and tolerance problems. We present a generic algorithm, which can decide whether two solids intersect or not. We identify classes of objects for which this algorithm can be efficiently specialized, and describe in detail how this specialization is done. These classes are objects that are bounded by quadric surface patches and conic arcs, objects that are bounded by natural quadric patches, torus patches, line segments and circular arcs, and objects that are bounded by quadric surface patches, segments of quadric intersection curves and segments of cubic spline curves. We show that all necessary geometric predicates can be evaluated by finding the roots of univariate polynomials of degree at most 4 for the first two classes, and at most 8 for the third class. In order to speed up the intersection tests we use bounding volume hierarchies. With the help of numerical optimization techniques we succeed in calculating smallest enclosing spheres and bounding boxes for a given set of surface patches fulfilling the properties mentioned above.

The power spectrum of the daily Dow Jones industrial average is calculated. It has been shown that the spectrum is P (f) 1=f 1:8, very close to that of the random walk series (1/f² noise). In contrast to some previous belief, the Dow Jones index as well as other stock prices time series are not 1/f noise. The distribution of the daily change of the Dow Jones industrial average is also calculated. Several fittings of the distribution are carried out (for both the price change and the logarithm of the price change). It has been observed that the occurrence of the big loss on Black Monday (negative change of 508) does not fit the distribution of the smaller price fluctuations (e.g., smaller than 100). This lack of scaling for the frequency of occurrence from the large stock price losses to small price fluctuations can be compared with the much better scaling law in the frequency of occurrence for global earthquakes.

As the Internet becomes more and more populous, people concern more about the copyright protection issue for digital data such as images and audio. Digital watermarking technique can hide data in images or audio to indicate the data owner or recipient. Therefore, it can protect the copyright. Motivated by copyright protection in the Internet, we propose an Internet Image Library (IIL) using watermarks to protect the copyright. With this watermarking application -- IIL in mind, we analyze and propose new watermark systems to meet this application. A lot of...

A three-dimensional complex is a partition of a three-dimensional manifold into simple cells, faces, edges and vertices. We consider here the problem of automatically producing a \nice" geometric representation (in IR m , for m 3) of an arbitrary 3D complex, given only its combinatorial description. The geometric realization is chosen by optimizing certain aesthetic criteria, measured by certain \energy functions." 1 Introduction The visualization of the geometry and topology of objects contained in spaces of dimension greater than 3 always been a challenging problem, since our visual experience is conned to an Euclidean three-dimensional world. Among these higher-dimensional objects, the 3-dimensional complexes, which include the shells of 4D polytopes, are particularly important, given their many applications { such as mechanics [15] and robotics [10], and their theoretical interest [13]. In those applications, there is often the need to visualize the structure of a 3D co...

A three-dimensional map is a partition of a 3D manifold into topological polyhedra. We consider here the problem of visualizing the topology of a three-dimensional map given only its combinatorial description. Our solution starts by automatically constructing a "nice" geometric realization of the map in R^m, for some m >= 4. The geometric realization is chosen by optimizing certain aesthetic criteria, measured by energy functions. We then project this model to R³, and display the resulting multi-celled solid object with a variety of specialized rendering techniques.

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Reconstruction of gradients from sampled data is a crucial task in volume visualization. Gradients are used, for instance, as normals for surface shading or for classi-cation in standard ray casting techniques. Using the ideal derivative reconstruction lter, which can be derived from the ideal function reconstruction lter, is impracticable because of its in nite extend. Simply truncating the lter leads to problems due to discontinuities at the edges. To overcome these problems several windows have been de ned, which are discussed in this paper with respect to gradient estimation.