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Frequency Support of Microcalcifications

C I M A T V Taller de Procesamiento de Imágenes. Frequency Support of Microcalcifications. Authors: Humberto Ochoa, Osslan Vergara, Vianey Cruz, Javier Vega and Efrén Gutiérrez. Universidad Autónoma de Ciudad Juárez. Guanajuato México, 21 y 22 de agosto de 2008. Outline. Introduction.

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Frequency Support of Microcalcifications

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  1. C I M A TV Taller de Procesamiento de Imágenes Frequency Support of Microcalcifications Authors: Humberto Ochoa, Osslan Vergara, Vianey Cruz, Javier Vega and Efrén Gutiérrez Universidad Autónoma de Ciudad Juárez Guanajuato México, 21 y 22 de agosto de 2008

  2. Outline • Introduction. • 2-D DFT of compactly supported signals. • Experiments. • Results. • The Discrete Wavelet Transform. • Conclusions.

  3. Characteristics of microcalcifications • Small deposit of calcium in the breast. • Detected mainly by mammography. • Very small spatial support. • Low contrast samples. • Diameter of a few pixels (from some μm up to approximately 200 μm). • Difficult to detect in a simple sight.

  4. What is a compactly supported microcalcification? • A few neighbor samples of low contrast, closely related in amplitude, and connected to surrounding tissue in the spatial domain. • Microcalcifications are believed to exist only in a high-frequency region of the frequency spectrum, while low-frequency components are believed to contain the background.

  5. Compactly supported microcalcifications

  6. 2-D DFT of compactly supported signals Let: For a compact signal we have:

  7. 2-D DFT of compactly supported signals It follows that: Approaches to zero Approaches to one

  8. 2-D DFT of compactly supported signals The samples engulfed by the intervals [d11, d12];[d21, d22] are closely related in amplitude. Therefore, if the intervals becomes larger (less compactly supported): Becomes low pass

  9. Experiments DCT Microcalcification + Surrounding noise Energy calculation Zonal filters

  10. Experiments DCT Microcalcification Energycalculation Zonal filters

  11. Results Percents of retained energy after zonal filtering for Percents of retained energy after zonal filtering for

  12. Normalized differences The depicted function will be more or less skewed for different mammograms and noise types.

  13. Frequency support of two different microcalcifications Highamplitude Short spatial support. Shortamplitude Short spatial support.

  14. DWT DWT is the most common method to detect microcalcifications. Discard the lowest frequency subband and apply a threshold to the remaining subbands; or recover the image before applying threshold. One level of DWT decomposition Decimated filter banks are limited by the inband aliasing. Undecimated filter banks are also used but they are computational extensive.

  15. DWT CDF 9/7 Original and recovered injuries after 1 and 4 levels of DWT decomposition.

  16. Conclusions • Microcalcifications are signals mostly with a large frequency support and in many cases, signals supported in the entire frequency spectrum. • Small compactly supported and short amplitude injuries could be an early sign of abnormality and could not be detected if they are assumed wrongly. For example, if the spatial support of a microcalcification is large, and its frequency support is not considered, detection could fail and the injury could be missed. • Frequency support of microcalcifications must be taken into considerations in order to have an accurate detection.

  17. References • Alqdah, M.; Rahmanramli, A.; Mahmud, R. (2005):A System of Microcalcifications Detection and Evaluation of the Radiologist: Comparative Study of the Three Main Races in Malaysia. Computers in Biology and Medicine, vol. 35, no. 10, pp. 905– 914. • Essam, A.; Rashed, E. A.; Ismail, A.; Ismail, B.; Sherif, I. (2007):Multiresolution Mammogram Analysis in Multilevel Decomposition. Pattern Recognition Letters, vol. 28, no. 2, pp. 286–292. • Kook, J. K.; Wook H. P. (1999):Statistical Textural Features for Detection of Microcalcifications in Digitized Mammograms. IEEE Transactions on Medical Imaging, vol. 18, no. 3, pp. 231–238. • Mencattini, A.; Salmeri, M.; Lojacono, R.; Frigerio, M.; Caselli, F. (2008):Mammographic Images Enhancement and Denoising for Breast Cancer Detection Using Dyadic Wavelet Processing. IEEE Transactions on Instrumentation and Measurement, vol. 57, no. 7, pp. 1422-1430.

  18. Questions Universidad Autónoma de Ciudad Juárez UACJ www.uacj.mx Cuerpo Académico de Instrumentación y Procesamiento de Señales (CAIPS) hochoa@uacj.mx

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