This is a thesis written for a master's degree at the Computer Vision Laboratory, University of Linköping. An abstract outer product is defined and used as a bridge to reach 2:nd and 4:th order Tensors. Some applications of these in geometric analysis of range data are discussed and illustrated. In idealized setups, simple geometric objects, like spheres or polygons, are successfully detected. Finally, the generalization to n:th order Tensors for storing and analysing geometric information is discussed..

We derive the equation linking the Weyl Tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl Tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime.

This thesis describes new methods for automatic crack detection in pavements. Cracks in pavements can be used as an early indication for the need of reparation.Automatic crack detection is preferable compared to manual inventory; the repeatability can be better, the inventory can be done at a higher speed and can be done without interruption of the traffic.The automatic and semi-automatic crack detection systems that exist today use Image Analysis methods. There are today powerful methods available in the area of Computer Vision. These methods work in higher dimensions with greater complexity and generate measures of local signal properties, while Image Analyses methods for crack detection use morphological operations on binary images.Methods for digitalizing video data on VHS-cassettes and stitching images from nearby frames have been developed.Four methods for crack detection have been evaluated, and two of them have been used to form a crack detection and classification program implemented in the calculation program Matlab.One image set was used during the implementation and another image set was used for validation. The crack detection system did perform correct detection on 99.2 percent when analysing the images which were used during implementation.

Asymptotically flat spaces are widely studied because it is one natural way of describing an isolated system in general relativity. In this thesis we study what happens to the Lanczos potential at spacelike infinity in such spacetimes. By transformations of the Weyl-Lanczos equation, we derive expressions for the limiting equations on both the timelike unit hyperboloid, and the timelike unit cylinder. Finally the Newman-Penrose formalism is used to get a component version of the equations..