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On Second Order Operators and Quadratic Operators
Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Computer Vision.ORCID iD: 0000-0002-6096-3648
2008 (English)In: Proceedings - International Conference on Pattern Recognition, IEEE , 2008, 1-4 p.Conference paper (Refereed)
Abstract [en]

In pattern recognition, computer vision, and image processing, many approaches are based on second order operators. Well-known examples are second order networks, the 3D structure tensor for motion estimation, and the Harris corner detector. A subset of second order operators are quadratic operators. It is lesser known that every second order operator can be written as a weighted quadratic operator. The contribution of this paper is to propose an algorithm for converting an arbitrary second order operator into a quadratic operator. We apply the method to several examples from image processing and machine learning. The advantages of the alternative implementation by quadratic operators is two-fold: The underlying linear operators allow new insights into the theory of the respective second order operators and replacing second order networks with sums of squares of linear networks reduces significantly the computational burden when the trained network is in operation phase.

Place, publisher, year, edition, pages
IEEE , 2008. 1-4 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-44876DOI: 10.1109/ICPR.2008.4761685Local ID: 78097ISBN: 978-1-4244-2175-6 (online)ISBN: 978-1-4244-2174-9 (print)OAI: diva2:265738
International Conference on Pattern Recognition
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2016-05-04

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Felsberg, Michael
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