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On the Equivalence of Normalized Convolution and Normalized Differential Convolution, Vol. 5
n/a.
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9091-4724
1994 (English)In: IEEE International Conference on Acoustics, Speech, and Signal Processing, 1994, 1994, 457-460 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper establishes an algebraic relation between two methods recently reported; normalized convolution and normalized differential convolution. These are general methods for filtering incomplete or uncertain data and are based on the separation of both data and operator into a signal part and a certainty part. General filtering can be performed without preprocessing input data with an interpolation step. The methods allow both data and operators to be scalars, vectors or tensors of higher order. Normalized differential convolution has been used in a wide range of applications. Examples are estimation of gradient estimation in irregularly sampled data, estimation of differential invariants in sparse image flow fields and image edge effect reduction. It was previously shown that normalized convolution produces a description of the neighbourhood which is optimal in a least square sense. The algebraic relation to normalized differential convolution presented in this paper proves that the latter method is also optimal in the same sense as well.

Place, publisher, year, edition, pages
1994. 457-460 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-21661DOI: 10.1109/ICASSP.1994.389389ISBN: 0-7803-1775-0 (print)OAI: oai:DiVA.org:liu-21661DiVA: diva2:245982
Conference
IEEE International Conference on Acoustics, Speech, and Signal Processing, 19-22 April, 1994. ICASSP-94
Available from: 2009-10-08 Created: 2009-10-05 Last updated: 2013-08-28

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Nordberg, KlasKnutsson, Hans

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  • nn-NB
  • sv-SE
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Output format
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  • asciidoc
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