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Simple filter design for first and second order derivatives by a double filtering approach
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Visual Information and Interaction. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computerized Image Analysis and Human-Computer Interaction.ORCID iD: 0000-0003-1054-2754
2014 (English)In: Pattern Recognition Letters, ISSN 0167-8655, E-ISSN 1872-7344, Vol. 42, 65-71 p.Article in journal (Refereed) Published
Abstract [en]

Spline filters are usually implemented in two steps, where in the first step the basis coefficients are computed by deconvolving the sampled function with a factorized filter and the second step reconstructs the sampled function. It will be shown how separable spline filters using different splines can be constructed with fixed kernels, requiring no inverse filtering. Especially, it is discussed how first and second order derivatives can be computed correctly using cubic or trigonometric splines by a double filtering approach giving filters of length 7.

Place, publisher, year, edition, pages
Elsevier, 2014. Vol. 42, 65-71 p.
Keyword [en]
Cubic and trigonometric splines; Convolution filters; Separable kernels; First and second order derivatives
National Category
Computer Vision and Robotics (Autonomous Systems)
Research subject
Computerized Image Processing
Identifiers
URN: urn:nbn:se:uu:diva-218920DOI: 10.1016/j.patrec.2014.01.014ISI: 000333451300008OAI: oai:DiVA.org:uu-218920DiVA: diva2:697995
Note

Highlights

• We show how to compute image derivatives using fitted splines.

• Trigonometric splines are more exact than cubic splines using kernels of length 4.

• Double filtering can be combined into a single kernel of length 7.

• Pre blurring can be incorporated using approximating splines.

• Matlab code is provided.

Available from: 2014-01-31 Created: 2014-02-19 Last updated: 2017-12-06Bibliographically approved

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Hast, Anders

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