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

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

3. CAIPS 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. CAIPS 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. CAIPS 5 Compactly supported microcalcifications

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

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

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

10. CAIPS 10 Experiments Microcalcification DCT Zonal filters Energy calculation

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

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

13. CAIPS 13 Frequency support of two different microcalcifications High amplitude Short spatial support. Short amplitude Short spatial support.

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

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

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