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Optimal rotation alignment of 3D objects using a GPU-based similarity function

Michael Martinek, Roberto Grosso
University of Erlangen, Department of Computer Science, Erlangen, Germany
Computers & Graphics, Vol. 33, No. 3. (June 2009), pp. 291-298.

@article{martinek2009optimal,

   title={Optimal rotation alignment of 3d objects using a gpu-based similarity function},

   author={Martinek, M. and Grosso, R.},

   journal={Computers & Graphics},

   volume={33},

   number={3},

   pages={291–298},

   issn={0097-8493},

   year={2009},

   publisher={Elsevier}

}

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In this paper, we address the challenging task of finding the best alignment between two 3D objects by solving a global optimization problem in the space of rotations SO(3). The objective function to be optimized is a newly developed rotation-variant similarity measure, which is obtained directly from the object’s geometry and is entirely implemented on the GPU. By exploiting the modern GPU’s parallel architecture, we can process considerably greater amounts of data than a CPU implementation can do in the same amount of time. This allows us to create a similarity measure which combines speed and accuracy. The actual problem of rotation alignment is then solved by finding the global maximum of this similarity function in the space of rotations. A special rotation representation allows for an efficient local optimization on the manifold SO(3). Furthermore, unwanted local maxima can be avoided by a heuristic global optimization procedure which exploits rotational symmetry. Due to this common sense heuristics, the global search can be gradually reduced to a lower-dimensional problem up to a 1D line search to handle objects with high rotational symmetry. We show that our method is superior to existing normalization techniques such as PCA and provides a high degree of precision despite remarkably short runtimes.
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