Scale-Specific Multifractal Medical Image Analysis
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 larg...
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2015
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| Online Access: | http://hdl.handle.net/1721.1/96102 https://orcid.org/0000-0001-5193-2711 |
| _version_ | 1811091372723142656 |
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| author | Braverman, Boris Tambasco, Mauro |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Braverman, Boris Tambasco, Mauro |
| author_sort | Braverman, Boris |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:01:23Z |
| format | Article |
| id | mit-1721.1/96102 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:01:23Z |
| publishDate | 2015 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | mit-1721.1/961022022-09-29T12:05:58Z Scale-Specific Multifractal Medical Image Analysis Braverman, Boris Tambasco, Mauro Massachusetts Institute of Technology. Department of Physics Massachusetts Institute of Technology. Research Laboratory of Electronics MIT-Harvard Center for Ultracold Atoms Braverman, Boris 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. Alberta Cancer Foundation Alberta Innovates-Health Solutions 2015-03-20T13:29:25Z 2015-03-20T13:29:25Z 2013 2013-06 2015-03-19T11:34:42Z Article http://purl.org/eprint/type/JournalArticle 1748-670X 1748-6718 http://hdl.handle.net/1721.1/96102 Braverman, Boris, and Mauro Tambasco. “Scale-Specific Multifractal Medical Image Analysis.” Computational and Mathematical Methods in Medicine 2013 (2013): 1–11. https://orcid.org/0000-0001-5193-2711 en http://dx.doi.org/10.1155/2013/262931 Computational and Mathematical Methods in Medicine Creative Commons Attribution http://creativecommons.org/licenses/by/2.0 Copyright © 2013 Boris Braverman and Mauro Tambasco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. application/pdf Hindawi Publishing Corporation Hindawi Publishing Corporation |
| spellingShingle | Braverman, Boris Tambasco, Mauro Scale-Specific Multifractal Medical Image Analysis |
| title | Scale-Specific Multifractal Medical Image Analysis |
| title_full | Scale-Specific Multifractal Medical Image Analysis |
| title_fullStr | Scale-Specific Multifractal Medical Image Analysis |
| title_full_unstemmed | Scale-Specific Multifractal Medical Image Analysis |
| title_short | Scale-Specific Multifractal Medical Image Analysis |
| title_sort | scale specific multifractal medical image analysis |
| url | http://hdl.handle.net/1721.1/96102 https://orcid.org/0000-0001-5193-2711 |
| work_keys_str_mv | AT bravermanboris scalespecificmultifractalmedicalimageanalysis AT tambascomauro scalespecificmultifractalmedicalimageanalysis |