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Generalizing the mean intercept length tensor for gray-level images
Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Medical and Health Sciences, Radiology. Linköping University, Faculty of Health Sciences.ORCID iD: 0000-0001-5765-2964
Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9267-2191
Linköping University, Center for Medical Image Science and Visualization (CMIV). Linköping University, Department of Medical and Health Sciences, Radiology. Linköping University, Faculty of Health Sciences. Östergötlands Läns Landsting, Center for Diagnostics, Department of Radiology in Linköping.ORCID iD: 0000-0002-7750-1917
2012 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 39, no 7, 4599-4612 p.Article in journal (Refereed) Published
Abstract [en]

Purpose: The mean intercept length tensor is the most used technique to estimate microstructure orientation and anisotropy of trabecular bone. This paper proposes an efficient extension of this technique to gray-scale images based on a closed formulation of the mean intercept length tensor and a generalization using different angular convolution kernels.

Methods: First, the extended Gaussian image is computed for the binary or gray-scale image. Second, the intercepts are computed for all possible orientations through an angular convolution with the half-cosine function. Finally, the tensor is computed by means of the covariance matrix. The complexity of the method is O(n + m) in contrast with O(nm) of traditional implementations, where n is the number of voxels in the image and m is the number of orientations used in the computations. The method is generalized by applying other angular convolution kernels instead of the half-cosine function. As a result, the anisotropy of the tensor can be controlled while keeping the eigenvectors intact.

Results: The proposed extension to gray-scale yields accurate results for reliable computations of the extended Gaussian image and, unlike the traditional methodology, is not affected by artifacts generated by discretizations during the sampling of different orientations.

Conclusions: Experiments show that the computations on both binary and gray-scale images are correlated, and that computations in gray-scale are more robust, enabling the use of the mean intercept length tensor to clinical examinations of trabecular bone. The use of kernels based on the von Mises-Fisher distribution is promising as the anisotropy can be adjusted with a parameter in order to improve its power to predict mechanical properties of trabecular bone.

Place, publisher, year, edition, pages
American Association of Physicists in Medicine , 2012. Vol. 39, no 7, 4599-4612 p.
Keyword [en]
fabric tensors, mean intercept length tensor, extended Gaussian image, trabecular bone, shape analysis
National Category
Medical Image Processing
Identifiers
URN: urn:nbn:se:liu:diva-79754DOI: 10.1118/1.4730502ISI: 000306893000055OAI: oai:DiVA.org:liu-79754DiVA: diva2:544192
Note

funding agencies|Swedish Research Council (VR)|2006-5670|

Available from: 2012-08-13 Created: 2012-08-13 Last updated: 2017-12-07Bibliographically approved

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Moreno, RodrigoBorga, MagnusSmedby, Örjan

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