Persistent Homology for Breast Tumor Classification Using Mammogram Scans
An important tool in the field of topological data analysis is persistent homology (PH), which is used to encode abstract representations of the homology of data at different resolutions in the form of persistence barcode (PB). Normally, one will obtain one PB from a digital image when using a suble...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-10-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/21/4039 |
| _version_ | 1797467409272012800 |
|---|---|
| author | Aras Asaad Dashti Ali Taban Majeed Rasber Rashid |
| author_facet | Aras Asaad Dashti Ali Taban Majeed Rasber Rashid |
| author_sort | Aras Asaad |
| collection | DOAJ |
| description | An important tool in the field of topological data analysis is persistent homology (PH), which is used to encode abstract representations of the homology of data at different resolutions in the form of persistence barcode (PB). Normally, one will obtain one PB from a digital image when using a sublevel-set filtration method. In this work, we built more than one PB representation of a single image based on a landmark selection method, known as local binary patterns (LBP), which encode different types of local texture from a digital image. Starting from the top-left corner of any 3-by-3 patch selected from an input image, the LBP process starts by subtracting the central pixel value from its eight neighboring pixel values. Then, each cell is assigned with 1 if the subtraction outcome is positive, and 0 otherwise, to obtain an 8-bit binary representation. This process will identify a set of landmark pixels to represent 0-simplices and use Vietoris–Rips filtration to obtain its corresponding PB. Using LBP, we can construct up to 56 PBs from a single image if we restrict to only using the binary codes that have two circular transitions between 1 and 0. The information within these 56 PBs contain detailed local and global topological and geometrical information, which can be used to design effective machine learning models. We used four different PB vectorizations, namely, persistence landscapes, persistence images, Betti curves (barcode binning), and PB statistics. We tested the effectiveness of the proposed landmark-based PH on two publicly available breast abnormality detection datasets using mammogram scans. The sensitivity and specificity of the landmark-based PH obtained was over 90% and 85%, respectively, in both datasets for the detection of abnormal breast scans. Finally, the experimental results provide new insights on using different PB vectorizations with sublevel set filtrations and landmark-based Vietoris–Rips filtration from digital mammogram scans. |
| first_indexed | 2024-03-09T18:52:14Z |
| format | Article |
| id | doaj.art-c3ebfbdfd72943c2be6b80731b2d6c0a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:52:14Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c3ebfbdfd72943c2be6b80731b2d6c0a2023-11-24T05:43:57ZengMDPI AGMathematics2227-73902022-10-011021403910.3390/math10214039Persistent Homology for Breast Tumor Classification Using Mammogram ScansAras Asaad0Dashti Ali1Taban Majeed2Rasber Rashid3School of Computing, The University of Buckingham, Buckingham MK18 1EG, UKIndependent Researcher, North York, ON M2R 1G4, CanadaDepartment of Computer Science and IT, Salahaddin University, Erbil 44001, IraqDepartment of Computer Science and IT, Salahaddin University, Erbil 44001, IraqAn important tool in the field of topological data analysis is persistent homology (PH), which is used to encode abstract representations of the homology of data at different resolutions in the form of persistence barcode (PB). Normally, one will obtain one PB from a digital image when using a sublevel-set filtration method. In this work, we built more than one PB representation of a single image based on a landmark selection method, known as local binary patterns (LBP), which encode different types of local texture from a digital image. Starting from the top-left corner of any 3-by-3 patch selected from an input image, the LBP process starts by subtracting the central pixel value from its eight neighboring pixel values. Then, each cell is assigned with 1 if the subtraction outcome is positive, and 0 otherwise, to obtain an 8-bit binary representation. This process will identify a set of landmark pixels to represent 0-simplices and use Vietoris–Rips filtration to obtain its corresponding PB. Using LBP, we can construct up to 56 PBs from a single image if we restrict to only using the binary codes that have two circular transitions between 1 and 0. The information within these 56 PBs contain detailed local and global topological and geometrical information, which can be used to design effective machine learning models. We used four different PB vectorizations, namely, persistence landscapes, persistence images, Betti curves (barcode binning), and PB statistics. We tested the effectiveness of the proposed landmark-based PH on two publicly available breast abnormality detection datasets using mammogram scans. The sensitivity and specificity of the landmark-based PH obtained was over 90% and 85%, respectively, in both datasets for the detection of abnormal breast scans. Finally, the experimental results provide new insights on using different PB vectorizations with sublevel set filtrations and landmark-based Vietoris–Rips filtration from digital mammogram scans.https://www.mdpi.com/2227-7390/10/21/4039topological data analysispersistent homologybreast mammogrampersistence diagram vectorizationmedical imaginglocal binary patterns |
| spellingShingle | Aras Asaad Dashti Ali Taban Majeed Rasber Rashid Persistent Homology for Breast Tumor Classification Using Mammogram Scans Mathematics topological data analysis persistent homology breast mammogram persistence diagram vectorization medical imaging local binary patterns |
| title | Persistent Homology for Breast Tumor Classification Using Mammogram Scans |
| title_full | Persistent Homology for Breast Tumor Classification Using Mammogram Scans |
| title_fullStr | Persistent Homology for Breast Tumor Classification Using Mammogram Scans |
| title_full_unstemmed | Persistent Homology for Breast Tumor Classification Using Mammogram Scans |
| title_short | Persistent Homology for Breast Tumor Classification Using Mammogram Scans |
| title_sort | persistent homology for breast tumor classification using mammogram scans |
| topic | topological data analysis persistent homology breast mammogram persistence diagram vectorization medical imaging local binary patterns |
| url | https://www.mdpi.com/2227-7390/10/21/4039 |
| work_keys_str_mv | AT arasasaad persistenthomologyforbreasttumorclassificationusingmammogramscans AT dashtiali persistenthomologyforbreasttumorclassificationusingmammogramscans AT tabanmajeed persistenthomologyforbreasttumorclassificationusingmammogramscans AT rasberrashid persistenthomologyforbreasttumorclassificationusingmammogramscans |