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Image processing on optimal volume sampling lattices: Thinking outside the box
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: 0000-0003-0893-4580
2015 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Bildbehandling på optimala samplingsgitter : Att tänka utanför ramen (Swedish)
Abstract [en]

This thesis summarizes a series of studies of how image quality is affected by the choice of sampling pattern in 3D. Our comparison includes the Cartesian cubic (CC) lattice, the body-centered cubic (BCC) lattice, and the face-centered cubic (FCC) lattice.

Our studies of the lattice Brillouin zones of lattices of equal density show that, while the CC lattice is suitable for functions with elongated spectra, the FCC lattice offers the least variation in resolution with respect to direction. The BCC lattice, however, offers the highest global cutoff frequency. The difference in behavior between the BCC and FCC lattices is negligible for a natural spectrum. We also present a study of pre-aliasing errors on anisotropic versions of the CC, BCC, and FCC sampling lattices, revealing that the optimal choice of sampling lattice is highly dependent on lattice orientation and anisotropy.

We suggest a new reference function for studies of aliasing errors on alternative sampling lattices. This function has a spherical spectrum, and a frequency content proportional to the distance from the origin, facilitating studies of pre-aliasing in spatial domain.

The accuracy of anti-aliased Euclidean distance transform is improved by application of more sofisticated methods for computing the sub-spel precision term. We find that both accuracy and precision are higher on the BCC and FCC lattices than on the CC lattice. We compare the performance of several intensity-weighted distance transforms on MRI data, and find that the derived segmentation result, with respect to relative error in segmented volume, depends neither on the sampling lattice, nor on the sampling density.

Lastly, we present LatticeLibrary, a open source C++ library for processing of sampled data, supporting a number of common image processing methods for CC, BCC, and FCC lattices. We also introduce BccFccRaycaster, a tool for visualizing data sampled on CC, BCC, and FCC lattices.

We believe that the work summarized in this thesis provide both the motivation and the tools for continuing research on application of the BCC and FCC lattices in image processing and analysis.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2015. , 98 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1314
Keyword [en]
BCC, FCC, aliasing, distance transform, segmentation
National Category
Medical Image Processing
Research subject
Computerized Image Processing
Identifiers
URN: urn:nbn:se:uu:diva-265340ISBN: 978-91-554-9406-3 (print)OAI: oai:DiVA.org:uu-265340DiVA: diva2:866471
Public defence
2015-12-18, Pol2447, Informationsteknologiskt centrum (ITC), Lägerhyddsvägen 2, hus 2, Uppsala, 10:00 (English)
Opponent
Supervisors
Available from: 2015-11-25 Created: 2015-10-27 Last updated: 2016-01-13
List of papers
1. Aliasing Properties of Voxels in Three-Dimensional Sampling Lattices
Open this publication in new window or tab >>Aliasing Properties of Voxels in Three-Dimensional Sampling Lattices
2012 (English)In: Large Scale Scientific Computing, 2012, 507-514 p.Conference paper, Published paper (Refereed)
Series
Lecture Notes in Computer Science, 7116
National Category
Medical Image Processing
Research subject
Computerized Image Processing
Identifiers
urn:nbn:se:uu:diva-265333 (URN)10.1007/978-3-642-29843-1_57 (DOI)978-3-642-29842-4 (ISBN)
Conference
LSSC 2011, June 6–10, Sozopol, Bulgaria
Available from: 2015-10-27 Created: 2015-10-27 Last updated: 2015-11-26Bibliographically approved
2. A Graph-Based Implementation of the Anti-Aliased Euclidean Distance Transform
Open this publication in new window or tab >>A Graph-Based Implementation of the Anti-Aliased Euclidean Distance Transform
2014 (English)In: Proceedings 22nd International Conference on Pattern Recognition (ICPR), 2014, 2014, 1025-1030 p.Conference paper, Published paper (Refereed)
Abstract [en]

With this paper, we present an algorithm for the anti-aliased Euclidean distance transform, based on wave front propagation, that can easily be extended to images of arbitrary dimensionality and sampling lattices. We investigate the behavior and weaknesses of the algorithm, applied to synthetic two-dimensional area-sampled images, and suggest an enhancement to the original method, with complexity proportional to the number of edge elements, that may reduce the amount and relative magnitude of the errors in the transformed image by as much as a factor of 10.

Series
International Conference on Pattern Recognition, ISSN 1051-4651
National Category
Medical Image Processing
Research subject
Computerized Image Processing
Identifiers
urn:nbn:se:uu:diva-237983 (URN)10.1109/ICPR.2014.186 (DOI)000359818001024 ()978-1-4799-5208-3 (ISBN)
Conference
22nd International Conference on Pattern Recognition (ICPR 2014), 24-28 August 2014, Stockholm, Sweden
Available from: 2014-12-08 Created: 2014-12-08 Last updated: 2015-11-26Bibliographically approved
3. Anti-Aliased Euclidean Distance Transform on 3D Sampling Lattices
Open this publication in new window or tab >>Anti-Aliased Euclidean Distance Transform on 3D Sampling Lattices
2014 (English)In: Discrete Geometry for Computer Imagery: 18th IAPR International Conference, DGCI 2014, Siena, Italy, September 10-12, 2014. Proceedings / [ed] Elena Barcucci, Andrea Frosini, Simone Rinaldi, 2014, 88-98 p.Conference paper, Published paper (Refereed)
Abstract [en]

The Euclidean distance transform (EDT) is used in many essential operations in image processing, such as basic morphology, level sets, registration and path finding. The anti-aliased Euclidean distance transform (AAEDT), previously presented for two-dimensional images, uses the gray-level information in, for example, area sampled images to calculate distances with sub-pixel precision. Here, we extend the studies of AAEDT to three dimensions, and to the Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices, which are, in many respects, considered the optimal three-dimensional sampling lattices. We compare different ways of converting gray-level information to distance values, and find that the lesser directional dependencies of optimal sampling lattices lead to better approximations of the true Euclidean distance.

Series
Lecture Notes in Computer Science, ISSN 0302-9743 ; 8668
National Category
Medical Image Processing
Research subject
Computerized Image Processing
Identifiers
urn:nbn:se:uu:diva-237982 (URN)10.1007/978-3-319-09955-2_8 (DOI)000358195100008 ()978-3-319-09954-5 (ISBN)978-3-319-09955-2 (ISBN)
Conference
Discrete Geometry for Computer Imagery, 18th IAPR International Conference, DGCI 2014, Siena, Italy, September 10-12, 2014
Available from: 2014-12-08 Created: 2014-12-08 Last updated: 2015-11-26Bibliographically approved
4. Pre-aliasing and anisotropy on the CC, BCC, and FCC sampling lattices
Open this publication in new window or tab >>Pre-aliasing and anisotropy on the CC, BCC, and FCC sampling lattices
(English)Manuscript (preprint) (Other academic)
National Category
Medical Image Processing
Identifiers
urn:nbn:se:uu:diva-265338 (URN)
Available from: 2015-10-27 Created: 2015-10-27 Last updated: 2015-11-26
5. Fuzzy Segmentation of Synthetic and MRI Volume Data sampled on Optimal Lattices
Open this publication in new window or tab >>Fuzzy Segmentation of Synthetic and MRI Volume Data sampled on Optimal Lattices
2016 (English)Article in journal (Other academic) Submitted
National Category
Medical Image Processing
Research subject
Computerized Image Processing
Identifiers
urn:nbn:se:uu:diva-265336 (URN)
Available from: 2015-10-27 Created: 2015-10-27 Last updated: 2016-02-03Bibliographically approved
6. LatticeLibrary and BccFccRaycaster: Software for processing and viewing 3D data on optimal sampling lattices
Open this publication in new window or tab >>LatticeLibrary and BccFccRaycaster: Software for processing and viewing 3D data on optimal sampling lattices
Show others...
2016 (English)In: SoftwareX, ISSN 2352-7110, Vol. 5, 16-24 p.Article in journal (Refereed) Published
National Category
Medical Image Processing
Research subject
Computerized Image Processing
Identifiers
urn:nbn:se:uu:diva-265337 (URN)10.1016/j.softx.2016.01.002 (DOI)
Available from: 2016-03-15 Created: 2015-10-27 Last updated: 2016-12-28Bibliographically approved

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