Scale-Specific Multifractal Medical Image Analysis
Name
CMMM.2013.262931.pdf
Size
6.17 MB
Format
Adobe PDF
Checksum (MD5)
a823dd55a3891a034e4ba762e8d8ef04
Author(s)
Braverman, Boris
Tambasco, Mauro
Date Issued
2013
Journal
Computational and Mathematical Methods in Medicine
Publisher
Hindawi Publishing Corporation
Citation
Braverman, Boris, and Mauro Tambasco. “Scale-Specific Multifractal Medical Image Analysis.” Computational and Mathematical Methods in Medicine 2013 (2013): 1–11.
Version
Final published version
Abstract
Fractal geometry has been applied widely in the analysis of medical images to characterize the irregular complex tissue structures that do not lend themselves to straightforward analysis with traditional Euclidean geometry. In this study, we treat the nonfractal behaviour of medical images over large-scale ranges by considering their box-counting fractal dimension as a scale-dependent parameter rather than a single number. We describe this approach in the context of the more generalized Rényi entropy, in which we can also compute the information and correlation dimensions of images. In addition, we describe and validate a computational improvement to box-counting fractal analysis. This improvement is based on integral images, which allows the speedup of any box-counting or similar fractal analysis algorithm, including estimation of scale-dependent dimensions. Finally, we applied our technique to images of invasive breast cancer tissue from 157 patients to show a relationship between the fractal analysis of these images over certain scale ranges and pathologic tumour grade (a standard prognosticator for breast cancer). Our approach is general and can be applied to any medical imaging application in which the complexity of pathological image structures may have clinical value.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Research Laboratory of Electronics
MIT-Harvard Center for Ultracold Atoms
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1155/2013/262931
