Closed-Form Hierarchical Finite Element Models for Part-Based Object Detection

In this work we address part-based object detection under variability of part shapes and spatial relations. Our approach bases on the hierarchical finite element modeling concept of Engel and Tönnies [ET09a, ET09b]. They model object parts by elastic materials, which adapt to image structures via image-derived forces. Spatial part relations are realized through additional layers of elastic material forming an elastic hierarchy. We present a closed-form solution to this concept, reformulating the hierarchical optimization problem into the optimization of a non-hierarchical finite element model. This allows us to apply standard finite element techniques to hierarchical problems and to provide an efficient framework for part-based object detection. We demonstrate our approach at the example of lumbar column detection in magnetic resonance imaging on a data set of 49 subjects. Given a rough model initialization, our approach solved the detection problem reliably in 45 out of 49 cases, showing computation times of only a few seconds per subject.