Symmetric counterparts of classical 1D haar filters for improved image reconstruction via discrete back-projection

Matthew Ceko, Imants Svalbe

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

1 Citation (Scopus)

Abstract

A discrete 2D p:q lattice is comprised of known pixel values spaced at regular p:q intervals, where p, q are relatively prime integers. The lattice has zero values elsewhere. Sets of new symmetric convolution masks were constructed recently whose purpose is to interpolate values for all locations around each lattice point. These symmetric masks were found to outperform the traditional asymmetric masks that interpolate in proportion to the area each pixel shares within a p:q neighbourhood. The 1D projection of these new 2D symmetric masks can also be used when reconstructing images via filtered back-projection (FBP). Here the 1D symmetric filters are shown to outperform the traditional Haar filters that are built from the area-based masks. Images reconstructed using FBP with symmetric filters have errors up to 10% smaller than with Haar filters, and prove to be more robust under Poisson noise.
Original languageEnglish
Title of host publicationMathematical Morphology and Its Applications to Signal and Image Processing
Subtitle of host publication13th International Symposium, ISMM 2017 Fontainebleau, France, May 15–17, 2017 Proceedings
EditorsJesús Angulo, Santiago Velasco-Forero, Fernand Meyer
Place of PublicationCham Switzerland
PublisherSpringer
Pages68-80
Number of pages13
Volume10225 LNCS
ISBN (Electronic)9783319572406
ISBN (Print)9783319572390
DOIs
Publication statusPublished - 2017
EventInternational Symposium on Mathematical Morphology, 2017 - MINES ParisTech, Fontainebleau, France
Duration: 15 May 201717 May 2017
Conference number: 13th
http://cmm.ensmp.fr/ismm2017/

Publication series

NameLecture Notes in Computer Science
PublisherSpringer International Publishing AG
Volume10225
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Symposium on Mathematical Morphology, 2017
Abbreviated titleISMM 2017
CountryFrance
CityFontainebleau
Period15/05/1717/05/17
OtherThe International Symposium on Mathematical Morphology (ISMM) has established itself as the main scientific event in the field. The goal of the conference is to bring together researchers, students, and practitioners of mathematical morphology and related methodologies, to present and discuss new advances in the field, be they purely theoretical developments or novel applications, where real life imaging problems can be tackled with morphological tools.
Internet address

Cite this

Ceko, M., & Svalbe, I. (2017). Symmetric counterparts of classical 1D haar filters for improved image reconstruction via discrete back-projection. In J. Angulo, S. Velasco-Forero, & F. Meyer (Eds.), Mathematical Morphology and Its Applications to Signal and Image Processing: 13th International Symposium, ISMM 2017 Fontainebleau, France, May 15–17, 2017 Proceedings (Vol. 10225 LNCS, pp. 68-80). (Lecture Notes in Computer Science; Vol. 10225). Cham Switzerland: Springer. https://doi.org/10.1007/978-3-319-57240-6_6
Ceko, Matthew ; Svalbe, Imants. / Symmetric counterparts of classical 1D haar filters for improved image reconstruction via discrete back-projection. Mathematical Morphology and Its Applications to Signal and Image Processing: 13th International Symposium, ISMM 2017 Fontainebleau, France, May 15–17, 2017 Proceedings. editor / Jesús Angulo ; Santiago Velasco-Forero ; Fernand Meyer. Vol. 10225 LNCS Cham Switzerland : Springer, 2017. pp. 68-80 (Lecture Notes in Computer Science).
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abstract = "A discrete 2D p:q lattice is comprised of known pixel values spaced at regular p:q intervals, where p, q are relatively prime integers. The lattice has zero values elsewhere. Sets of new symmetric convolution masks were constructed recently whose purpose is to interpolate values for all locations around each lattice point. These symmetric masks were found to outperform the traditional asymmetric masks that interpolate in proportion to the area each pixel shares within a p:q neighbourhood. The 1D projection of these new 2D symmetric masks can also be used when reconstructing images via filtered back-projection (FBP). Here the 1D symmetric filters are shown to outperform the traditional Haar filters that are built from the area-based masks. Images reconstructed using FBP with symmetric filters have errors up to 10{\%} smaller than with Haar filters, and prove to be more robust under Poisson noise.",
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Ceko, M & Svalbe, I 2017, Symmetric counterparts of classical 1D haar filters for improved image reconstruction via discrete back-projection. in J Angulo, S Velasco-Forero & F Meyer (eds), Mathematical Morphology and Its Applications to Signal and Image Processing: 13th International Symposium, ISMM 2017 Fontainebleau, France, May 15–17, 2017 Proceedings. vol. 10225 LNCS, Lecture Notes in Computer Science, vol. 10225, Springer, Cham Switzerland, pp. 68-80, International Symposium on Mathematical Morphology, 2017, Fontainebleau, France, 15/05/17. https://doi.org/10.1007/978-3-319-57240-6_6

Symmetric counterparts of classical 1D haar filters for improved image reconstruction via discrete back-projection. / Ceko, Matthew; Svalbe, Imants.

Mathematical Morphology and Its Applications to Signal and Image Processing: 13th International Symposium, ISMM 2017 Fontainebleau, France, May 15–17, 2017 Proceedings. ed. / Jesús Angulo; Santiago Velasco-Forero; Fernand Meyer. Vol. 10225 LNCS Cham Switzerland : Springer, 2017. p. 68-80 (Lecture Notes in Computer Science; Vol. 10225).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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Ceko M, Svalbe I. Symmetric counterparts of classical 1D haar filters for improved image reconstruction via discrete back-projection. In Angulo J, Velasco-Forero S, Meyer F, editors, Mathematical Morphology and Its Applications to Signal and Image Processing: 13th International Symposium, ISMM 2017 Fontainebleau, France, May 15–17, 2017 Proceedings. Vol. 10225 LNCS. Cham Switzerland: Springer. 2017. p. 68-80. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-319-57240-6_6