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

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Date
2013
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The Eurographics Association
Abstract
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.
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@inproceedings{
:10.2312/PE.VMV.VMV13.137-144
, booktitle = {
Vision, Modeling & Visualization
}, editor = {
Michael Bronstein and Jean Favre and Kai Hormann
}, title = {{
Closed-Form Hierarchical Finite Element Models for Part-Based Object Detection
}}, author = {
Rak, Marko
and
Engel, Karin
and
Tönnies, Klaus D.
}, year = {
2013
}, publisher = {
The Eurographics Association
}, ISBN = {
978-3-905674-51-4
}, DOI = {
/10.2312/PE.VMV.VMV13.137-144
} }
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