Fractales como una herramienta de asistencia al médico en la observación de mamogramas

Rosana  Pirchio

Authors

Rosana Pirchio Comisión Nacional de Energía Atómica, Argentina

Keywords:

fractal dimension, fractals, mammography

Abstract

Mammograms are widely used for the diagnosis of microcalcifications, nodules, and architectural distortions. Exist different tools to segment/identify on those images. The objective of this work was to use the multifractal spectrum / alpha image for segmentation of the image and the fractal dimension to classify the lesion as benign or malign. Twenty images of the Mini all Mias base of dense, glandular and fatty breast were used, which contained masses, microcalcifications and architectural distortion. The fractal dimension (method of counting cubes with threshold and prisms), the multifractal spectrum (from it the falpha image can be segmented), the alpha image and the falpha image were studied. The processing was made with the MATLAB2017a software. The best contrast for the falpha image was obtained with threshold 0.3 and microcalcifications and masses were segmented. Spiculated masses and architectural distortion of dense breasts could not be segmented. With the prism method, it was not possible to classify lesions, while with the box method it was observed that the value of the dimension depends on the improvement made to the image. The most reliable method is the threshold method, and by repeating the methodology of a single author, the correct classification was achieved. Finally, the falpha image could help the doctor in the diagnosis of a dense/glandular and fatty breast and the fractal dimension could be used to classify lesions and nevertheless would have to try more images of other database using five megapixels monitor.

References

Costa A. Hausdorff box counting fractal-dimension. Recuperado de https://bit.ly/3emYxR8

Don S., Chung D., Revathy K., Choi E., Min D. (2013). A New Approach for Mammogram Image Classification Using Fractal Properties. Cybernetics and Information Technologies, 12 (2), 69 – 83. doi:10.2478/cait-2012-0013.

Florindo, J. B. and Bruno O. M. (2018). Fractal Descriptors of Texture Images Based on the triangular Prism Dimension. Journal of Mathematical Imaging and Vision, 61(2), 140 – 159. doi: 10.1007/s10851-018-0832-y

IARC: International Agency for Research on Cancer. Recuperado de https://bit.ly/3HoLb3l

INC: Instituto Nacional del Cáncer. Recuperado de https://bit.ly/3qfoYxm.

De Goes Junior, E. S., Souza Oliviera, F. B., Ambrosio, P. E. (2014). Fractal dimension for characterization of focal breast lesions. 11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) E. Oñate, J. Oliver and A. Huerta (Eds).

FracLab. Recuperado de https://bit.ly/3yYhFy7

Guo, Q., Shao, J, and Ruiz, V. (2009). Characterization and classification of tumor lesions using computerized fractal-based texture analysis and support vector machines in digital mammograms. Int J Comput Assist Radiol Surg, 4(1):11–25. doi: 10.1007/s11548-008-0276-8

Lefebvre F., Benali H., Gilles R., Edmond K., and Di Paola R. (1995). A fractal approach to the segmentation of microcalcifications in digital mammograms. Med Phys, 22, 381 doi: 10.1118/1.597473.

Maldebrot, B.B., 1983, La geometría fractal de la naturaleza, WH Freeman, Oxford.

Moisy F. (2008). Computing a fractal dimension with Matlab: 1D, 2D and 3D Box-counting. University Paris Sud.

Moisy F., Fractal dimension using the 'box-counting' method for 1D, 2D and 3D sets. Recuperado de https://bit.ly/3ekSwUR

Nguyen, T. (2021). Hausdorff (Box-Counting) Fractal Dimension with multi-resolution calculation MATLAB Central File Exchange. Recuperado de https://bit.ly/3yTm4m7

Rangayyan, R. M., and Thanh, M. N. (2006). Fractal Analysis of Contours of Breast Masses in Mammograms. J Digit Imaging 20: 223-237. doi: 10.1007/s10278-006-0860-9

Rangayyan, R.M., Prajna, S., Ayres, F., and Desautels, J. (2008). Detection of architectural distortion in prior screening mammograms using Gabor filters, phase portraits, fractal dimension, and texture analysis. Int J Computer Assisted Radiology and Surgery, 2(6): 347–361. doi:10.1007/s11548-007-0143-z

Razi, F.A. (2021). An Analysis of COVID-19 using X-ray Image Segmentation based Graph Cut and Box Counting Fractal Dimension, Telematika, 14(1), 25-32. doi:10.35671/telematika.v14i1.1217

Rodriguez Scarso, R. S. (2019) Clasificación de tejidos mediante la característica fractal de la imagen mamográfica. Tesis en la Universidad de Mendoza, Facultad de Ingeniería, Instituto de Bioingeniería.

Sankar, D., and Thomas, T. (2010). A new fast fractal modeling approach for the detection of microcalcifications in mammograms. Journal of Digital Imaging, 23(5), 538–546.

Shanmugavadivu, P., and Sivakumar, V. (2013). Fractal-Based Detection of Microcalcification Clústeres in Digital Mammograms, journal ArXiv.

arXiv:1304.8092

Stojić T. M., Reljin I., Reljin B. (2006). Adaptation of multifractal analysis to segmentation of microcalcifications in digital mammograms. Physica A: Statistical Mechanics and its Applications, 367, 494-508. doi:0.1016/j.physa.2005.11.030

Tourassi, G. D., Delong, D. M. and Floyd, C. E. Jr. (2006). A study on the computerized fractal analysis of architectural distortion in screening mammograms. Phys Med Biol, 51, 1299–1312. doi: 10.1088/0031-9155/51/5/018

Velanovich, V. (1996). Fractal Analysis of Mammographic Lesions: A Feasibility Study Quantifying the Difference Between Benign and Malignant Masses. Am J Med Sci, 311 (5), 211-214. doi: 10.1097/00000441-199605000-00003

Wikipedia. Recuperado de https://bit.ly/32eWex7

Zhang, P., Barad, H.S., and Martinez A.B. (1989). Application of Fractal Modeling to Cell Image Analysis, Proceedings of the IEEE Energy and Information Technologies in the Southeast, IEEE.