Klaus Voss

The method of normalization to determine invariants

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 Hus moment invariants and normalized moments.

A new algorithm to correct fish-eye- and strong wide-angle-lens-distortion from single images

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.

Automatic Lens Distortion Calibration Using Single Views

We present a new robust method to determine the distortion function of camera systems suffering from radial lens distortion. It is based on single images and uses the distorted positions of collinear points. Neither information about the intrinsic camera parameters nor 3D-pointcorrespondences are required. The algorithm 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 algorithm iteratively determines the distortion coefficients and the unknown co-ordinates of the principal point which is assumed to be identical with the symmetry point of the radial distortion. The results of experimental measurements of two different camera systems are presented and discussed.

Affine Point Pattern Matching

This paper presents a general solution for the problem of affine point pattern matching (APPM). Formally, given two sets of two-dimensional points (x,y) which are related by a general affine transformation (up to small deviations of the point coordinates and maybe some additional outliers). Then we can determine the six parameters aik of the transformation using new Hu point-invariants which are invariant with respect to affine transformations. With these invariants we compute a weighted point reference list. The affine parameters can be calculated using the method of the least absolute differences (LAD method) and using linear programming. In comparison to the least squares method, our approach is very robust against noise and outliers. The algorithm works in O(n) average time and can be used for translation and/or rotations, isotropic and non-isotropic scalings, shear transformations and reflections.

Automatic correction of weak radial lens distortion in single views of urban scenes using vanishing points

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.

A new one-parametric fitting method for planar objects

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.

A new efficient algorithm for fitting of rectangles and squares

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.

Invariant fitting of planar objects by primitives

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.

Shift Detection by Restoration

In this paper an approach is presented for robust shift detection of two given images. The new unifying idea is that we determine a shifted delta impulse using some well-known restoration techniques, e.g. the Wiener filtering, constraint restoration, entropy restoration, and Baysian restoration. The used restoration techniques imply the robustness of the presented method. Our approach is a generalization of the matched filtering approach. Additionally, we describe in the paper the problem of calculating an evaluation measure of the restored delta impulse image. This measure is the basis for the uncertainty of the detected shift. The unifying approach of shift detection by restoration (SDR-method) could be tested successfully, for example using a series of fundus image pairs which are of practical interest and which contain also small rotations, scalings and even deformations

Shift detection by restoration

In this paperan approachis presentedfor robustshift detectionof two givenimages.Thenew unifying ideais thatwedetermineashifteddeltaimpulse usingsomewell-known restorationtechniques, e.g. theWienerfiltering, constraintrestoration,entropy restoration,andBaysianrestoration.The usedrestorationtechniquesimply the robustnessof the presentedmethod. Our approachis a generalizationof the matchedfiltering approach.Additionally, we describein the paperthe problemof calculatingan evaluation measureof the restoreddeltaimpulseimage. This measureis the basisfor the uncertaintyof the detectedshift. The unifying approachof shift detection by restoration(SDR-method)couldbetestedsuccessfullyfor aseriesof practicalapplications.