### 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 language | English |
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Title of host publication | Mathematical Morphology and Its Applications to Signal and Image Processing |

Subtitle of host publication | 13th International Symposium, ISMM 2017 Fontainebleau, France, May 15–17, 2017 Proceedings |

Editors | Jesús Angulo, Santiago Velasco-Forero, Fernand Meyer |

Place of Publication | Cham Switzerland |

Publisher | Springer |

Pages | 68-80 |

Number of pages | 13 |

Volume | 10225 LNCS |

ISBN (Electronic) | 9783319572406 |

ISBN (Print) | 9783319572390 |

DOIs | |

Publication status | Published - 2017 |

Event | International Symposium on Mathematical Morphology, 2017 - MINES ParisTech, Fontainebleau, France Duration: 15 May 2017 → 17 May 2017 Conference number: 13th http://cmm.ensmp.fr/ismm2017/ |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer International Publishing AG |

Volume | 10225 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | International Symposium on Mathematical Morphology, 2017 |
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Abbreviated title | ISMM 2017 |

Country | France |

City | Fontainebleau |

Period | 15/05/17 → 17/05/17 |

Other | The 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). Springer. https://doi.org/10.1007/978-3-319-57240-6_6