Effective resultant-based methods for point-cloud registration 

Nowdays, robots are equipped with 3D sensors that generate point clouds that need to be processed in real-time, in order to to identify their surroundings.  Input data from different sensors must be aligned so that they may be registered in a common 3D frame.  We are interested

in efficiently addressing the points-to-points, points-to-line, and points-to-plane registration problems in a unified way.  We formulate the problem as a homogeneous, zero-dimensional polynomial system that we solve using resultant methods. This allows for closed-form solution templates that may be applied in an efficient way.  Challenges include the derivation of resultant matrices that are fast to compute and solve as well as the a priori identification of extraneous solutions.  The talk in based on joint work with Laurent Busé, Ezio Malis and Jana Vrablikova.

Marcel Celaya

On random graphs models

The theory of random graphs was founded by Erdős and Rényi in the late 1950s.  Since then, several random graph models have been analysed to answer questions of mathematical concern. During the last few decades, increasing interest in the field has been devoted to finding models that describe the complexity of real-world networks. In this talk I will start with the classical preferential attachment model and present new results for a generalized preferential attachment model with triangles. I also would like to show a model of a random simplicial complex which is a generalization of the preferential attachment model with triangles. This last part is a work in progress.

Martin Helmer