Stationary processes for object detection and non-rigid structure-from-motion

Stationary processes are random variables whose value is a signal and whose distribution is invariant to translation in the domain of the signal. They are intimately connected to convolution, and therefore to the Fourier transform, since the covariance matrix of a stationary process is a Toeplitz matrix, and Toeplitz matrices are the expression of convolution as a linear operator. This thesis utilises this connection in the study of i) efficient training algorithms for object detection and ii) trajectory-based non-rigid structure-from-motion.

Automated Discovery of Structured Process Models: Discover Structured vs. Discover and Structure

This paper addresses the problem of discovering business process models from event logs. Existing approaches to this problem strike various tradeoffs between accuracy and understandability of the discovered models. With respect to the second criterion, empirical studies have shown that block-structured process models are generally more understandable and less error-prone than unstructured ones. Accordingly, several automated process discovery methods generate block-structured models by construction. These approaches however intertwine the concern of producing accurate models with that of ensuring their structuredness, sometimes sacrificing the former to ensure the latter. In this paper we propose an alternative approach that separates these two concerns. Instead of directly discovering a structured process model, we first apply a well-known heuristic technique that discovers more accurate but sometimes unstructured (and even unsound) process models, and then transform the resulting model into a structured one. An experimental evaluation shows that our “discover and structure” approach outperforms traditional “discover structured” approaches with respect to a range of accuracy and complexity measures.

A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers

Diffusion in a composite slab consisting of a large number of layers provides an ideal prototype problem for developing and analysing two-scale modelling approaches for heterogeneous media. Numerous analytical techniques have been proposed for solving the transient diffusion equation in a one-dimensional composite slab consisting of an arbitrary number of layers. Most of these approaches, however, require the solution of a complex transcendental equation arising from a matrix determinant for the eigenvalues that is difficult to solve numerically for a large number of layers. To overcome this issue, in this paper, we present a semi-analytical method based on the Laplace transform and an orthogonal eigenfunction expansion. The proposed approach uses eigenvalues local to each layer that can be obtained either explicitly, or by solving simple transcendental equations. The semi-analytical solution is applicable to both perfect and imperfect contact at the interfaces between adjacent layers and either Dirichlet, Neumann or Robin boundary conditions at the ends of the slab. The solution approach is verified for several test cases and is shown to work well for a large number of layers. The work is concluded with an application to macroscopic modelling where the solution of a fine-scale multilayered medium consisting of two hundred layers is compared against an “up-scaled” variant of the same problem involving only ten layers.