A comparison of some methods for direct 2D reconstruction from discrete projected views

Preeti Gopal, Ajit Rajwade, Sharat Chandran, Imants Svalbe

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

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 languageEnglish
Title of host publicationDiscrete Geometry for Computer Imagery
Subtitle of host publication19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings
EditorsNicolas Normand, Jeanpierre Guédon, Florent Autrusseau
PublisherSpringer
Pages117-128
Number of pages12
ISBN (Electronic)9783319323602
ISBN (Print)9783319323596
DOIs
Publication statusPublished - 1 Jan 2016
EventInternational Conference on Discrete Geometry for Computer Imagery 2016 - La Cité Nantes Events Center, Nantes, France
Duration: 18 Apr 201620 Apr 2016
Conference number: 19th
http://www.springer.com/us/book/9783319323596

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume9647
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Conference on Discrete Geometry for Computer Imagery 2016
Abbreviated titleDGCI 2016
CountryFrance
CityNantes
Period18/04/1620/04/16
OtherDiscrete 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
Gopal, Preeti ; Rajwade, Ajit ; Chandran, Sharat ; Svalbe, Imants. / A comparison of some methods for direct 2D reconstruction from discrete projected views. Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings. editor / Nicolas Normand ; Jeanpierre Guédon ; Florent Autrusseau. Springer, 2016. pp. 117-128 (Lecture Notes in Computer Science).
@inproceedings{3aa73dfeb2b14551b9d02016b9aa4039,
title = "A comparison of some methods for direct 2D reconstruction from discrete projected views",
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.",
author = "Preeti Gopal and Ajit Rajwade and Sharat Chandran and Imants Svalbe",
year = "2016",
month = "1",
day = "1",
doi = "10.1007/978-3-319-32360-2_9",
language = "English",
isbn = "9783319323596",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "117--128",
editor = "Normand, {Nicolas } and Gu{\'e}don, {Jeanpierre } and Autrusseau, {Florent }",
booktitle = "Discrete Geometry for Computer Imagery",

}

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. Lecture Notes in Computer Science, vol. 9647, Springer, pp. 117-128, International Conference on Discrete Geometry for Computer Imagery 2016, Nantes, France, 18/04/16. https://doi.org/10.1007/978-3-319-32360-2_9

A comparison of some methods for direct 2D reconstruction from discrete projected views. / Gopal, Preeti; Rajwade, Ajit; Chandran, Sharat; Svalbe, Imants.

Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings. ed. / Nicolas Normand; Jeanpierre Guédon; Florent Autrusseau. Springer, 2016. p. 117-128 (Lecture Notes in Computer Science; Vol. 9647).

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

TY - GEN

T1 - A comparison of some methods for direct 2D reconstruction from discrete projected views

AU - Gopal, Preeti

AU - Rajwade, Ajit

AU - Chandran, Sharat

AU - Svalbe, Imants

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84964053924&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-32360-2_9

DO - 10.1007/978-3-319-32360-2_9

M3 - Conference Paper

SN - 9783319323596

T3 - Lecture Notes in Computer Science

SP - 117

EP - 128

BT - Discrete Geometry for Computer Imagery

A2 - Normand, Nicolas

A2 - Guédon, Jeanpierre

A2 - Autrusseau, Florent

PB - Springer

ER -

Gopal P, Rajwade A, Chandran S, Svalbe I. A comparison of some methods for direct 2D reconstruction from discrete projected views. In Normand N, Guédon J, Autrusseau F, editors, Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings. Springer. 2016. p. 117-128. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-319-32360-2_9