Computing relaxations for the three-dimensional stable matching problem with cyclic preferences.

Constraint programming has proven to be a successful framework for determining whether a given instance of the three-dimensional stable matching problem with cyclic preferences (3dsm-cyc) admits a solution. If such an instance is satisfiable, constraint models can even compute its optimal solution for several different objective functions. On the other hand, the only existing output for unsatisfiable 3dsm-cyc instances is a simple declaration of impossibility.

A collection of Constraint Programming models for the three-dimensional stable matching problem with cyclic preferences.

We introduce five constraint models for the 3-dimensional stable matching problem with cyclic preferences and study their relative performances under diverse configurations. While several constraint models have been proposed for variants of the two-dimensional stable matching problem, we are the first to present constraint models for a higher number of dimensions. We show for all five models how to capture two different stability notions, namely weak and strong stability.

Unsupervised markerless 3-DOF motion tracking in real time using a single low-budget camera.

Motion tracking is a critical task in many computer vision applications. Existing motion tracking techniques require either a great amount of knowledge on the target object or specific hardware. These requirements discourage the wide spread of commercial applications based on motion tracking.