### Abstract

Tomographic acquisitions can be described mathematically as discrete projective transforms. Direct reconstruction methods aim to compute an accurate inverse for such transforms. We assemble a limited set of measurements and then apply the inversion to obtain a high-fidelity image of the original object. In this work, we compare the following direct inversion techniques for sets of discrete projections: Radon-i(inverse)Radon, a least squared error method and filtered back-projection for Mojette inversion. We observe that filtered back-projection is the best of these methods, as the reconstruction errors that arise using this method depend least strongly on the image structure. We aim to improve results for the filtered back-projection method by optimizing the design of the regularizing filter and here present work towards eliminating the regularization threshold that is used as part of this method.

Original language | English |
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Title of host publication | Discrete Geometry for Computer Imagery |

Subtitle of host publication | 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings |

Editors | Nicolas Normand, Jeanpierre Guédon, Florent Autrusseau |

Publisher | Springer |

Pages | 117-128 |

Number of pages | 12 |

ISBN (Electronic) | 9783319323602 |

ISBN (Print) | 9783319323596 |

DOIs | |

Publication status | Published - 1 Jan 2016 |

Event | International Conference on Discrete Geometry for Computer Imagery 2016 - La Cité Nantes Events Center, Nantes, France Duration: 18 Apr 2016 → 20 Apr 2016 Conference number: 19th http://www.springer.com/us/book/9783319323596 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer |

Volume | 9647 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | International Conference on Discrete Geometry for Computer Imagery 2016 |
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Abbreviated title | DGCI 2016 |

Country | France |

City | Nantes |

Period | 18/04/16 → 20/04/16 |

Other | Discrete Geometry for Computer Imagery 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18-20, 2016. Proceedings |

Internet address |

## Cite this

Gopal, P., Rajwade, A., Chandran, S., & Svalbe, I. (2016). A comparison of some methods for direct 2D reconstruction from discrete projected views. In N. Normand, J. Guédon, & F. Autrusseau (Eds.),

*Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings*(pp. 117-128). (Lecture Notes in Computer Science; Vol. 9647). Springer. https://doi.org/10.1007/978-3-319-32360-2_9