In this paper, we introduce a new approach for fitting rectangular boxes and cubes given as a set of voxels in a three-dimensional voxel space. This extends our work on fitting rectangles and squares described in H. Suesse et al, (2001) to three dimensions. It is also based on our normalization method published in K. Voss et al (1997) and (1999). Here we also encounter the problem of normalizing the rotation as it is necessary for rectangles and squares, but here we have two degenerate cases to handle. The first one are cubes, the second one are rectangular boxes with two edges of equal length and the length of the third edge different from them. Our method delivers good fitting results, even if the boxes are heavily distorted for example by cutting-off vertices.

A new robust method to determine the distortion function of camera systems suffering from weak radial lens distortion is presented. It is based on single images and uses the distorted positions of collinear points. Neither information about the intrinsic camera parameters nor 3D-point-correspondences are required. The algorithm uses vanishing points of dominating directions for the iterative adjustment of collinear points and works without user interaction. The actual radial lens distortion of the most wide-angle and low-cost camera systems fits the used distortion model with two distortion coefficients sufficiently. The results of experimental measurements of different camera systems are presented and discussed.

The use of super-wide angle and fish-eye lenses causes strong distortions in the resulting images. A methodology for the correction of distortions in these cases using only single images and linearity of imaged objects is presented. Contrary to most former algorithms, the algorithm discussed here does not depend on information about the real world co-ordinates of matching points. Moreover reference points determination and camera calibration is not required in this case. The algorithm is based on circle fitting. It requires only the possibility of the extraction of distorted image points from straight lines in the 3D scene. Further, the actual distortion must approximately fit the chosen distortion model. For most fish-eye lenses appropriate distortion correction results can be obtained.

In this paper, we introduce a completely new approach to fitting rectangles and squares to given closed regions using our published ideas in Rothe et al. (1996), Voss and Suesse (1997, 1999). In these papers, we have developed a new region-based fitting method using the method of normalization. There we demonstrate the zero-parametric fitting of lines, triangles, parallelograms, circles and ellipses, and the one-parametric fitting of elliptical segments, circular segments and super-ellipses. In the present paper, we discuss this normalization idea for fitting of closed regions using rectangles and squares. As features we use the area-based low order moments. The main problem is a stable normalization of the rotation. We show that we have to solve only an one-dimensional optimization problem in the case of rectangles. In the case of squares there are no free parameters to determine. The presented algorithm is used in practice for document recognition.

Some methods for the determination of vanishing points using line segments are presented. By indicating the identity between a method using Thales' theorem and a Gaussian sphere based method we show that the knowledge of the position of the projection centre is not necessary as mostly assumed. This fact allows an accuracy improvement of a number of former methods using Gaussian sphere representation. We show by presenting some simulation experiments that the methods give very accurate results even in the case of very strong disturbances. With the knowledge of the noise value of the segment end point positions the random error can be estimated and the uncertainty of the calculated vanishing point can be determined.

This paper is an extension of the already published paper by Voss and Suesse (1997). We developed a new region-based fitting method using the method of normalization. There we demonstrated the zero-parametric fitting of lines, triangles, parallelograms, circles, and ellipses. We discuss this normalization idea for fitting of closed regions using circular segments, elliptical segments, and super-ellipses. As features, we use the area-based low order moments. We show that we have to solve only one-dimensional optimization problems in these cases.

The determination of invariant characteristics is an important problem in pattern recognition. Many invariants are known which have been obtained by the method of normalization. In this paper, we introduce a new approach of fitting planar objects by primitives using the method of normalization (e.g., fitting by lines, triangles, rectangles, circles, ellipses, super-quadrics, etc.). Objects and primitives are described by features, for example, by moments. The main advantage is that the normalization process provides us with a canonical frame of the object and the primitive. Therefore, the fit is invariant with respect to the transformation used. By this new method, an analytical fitting of non-analytical objects can be achieved, for example, fitting by polygons. Furthermore, the numerical effort can be reduced drastically by normalizing of the object and the primitive.

The determination of invariant characteristics is an important problem in pattern recognition. Many invariants are known which have been obtained by the method of normalization. In this paper, we introduce a new approach of fitting planar objects by primitives using the method of normalization (for instance: fitting by lines, triangles, rectangles, circles, ellipses, super-quadrics, etc.). Objects and primitives are described by features, for example, by moments. The main advantage is that the normalization process provides us with a canonical frame of the object and the primitive. Therefore, the fit is invariant with respect to the transformation used. By this new method, an analytical fitting of nonanalytical objects can be achieved, for example, fitting by polygons. Furthermore, the numerical effort can be reduced drastically by normalizing of the object and the primitive.

The determination of invariant characteristics is an important problem in pattern recognition. Many invariants are known, which have been obtained either by normalization or by other methods. This paper shows that the method of normalization is much more general and allows one to derive a lot of sets of invariants from the second list as well. To this end, the normalization method is generalized and is presented in such a way that it is easy to apply, thus unifying and simplifying the determination of invariants. Furthermore, this paper discusses the advantages and disadvantages of the invariants obtained by normalization. Their main advantage is that the normalization process provides us with a standard position of the object. Because of the generality of the method, also new invariants are obtained such as normalized moments more stable than known ones, Legendre descriptors and Zernike descriptors to affine transformations, two-dimensional Fourier descriptors and affine moment invariants obtained by combining Hu's moment invariants and normalized moments.

In this paper, a net model for decentralized control of user accesses to a distributed database is proposed. It is developed in detail for the restricted case of updating distributed copies of a single database. Predicate/transition-nets, a first-order extension of Petri nets, are shown to provide suitable means for concise representation of complex decentralized systems and for their rigorous formal analysis. It will be demonstrated in the present paper how these net models can be constructed and interpreted in a quite natural manner and how they can be analyzed by linear algebraic methods. By this, it will be shown that the modeled distributed database system is deadlock-free and guarantees a consistent database as well as a fair and effective service to the users.

In this paper a net model for decentralized control of user accesses to a distributed database is proposed and devel oped in detail for a restricted case. Predicate/transition-nets, a first-order extension of Petri nets, are shown to provide suitable means for concise representa tion of complex decentralized systems and for their rigorous formal analysis. It will be demonstrated in the present paper how these net models can be constructed and in terpreted in a quite natural manner and how they can be analyzed by linear algebraic methods. by this, it will be shown that the modelled distributed database system is deadlockfree and guarantees a consistent database as well as a fair and effective service to the users.