1. Mammographic image analysis for breast cancer detection using complex wavelet transforms and morphological operators

2. V. Alarcón Aquino O. Starostenko R. Rosas Romero J. Rodríguez Asomoza O. J. Paz Luna K. Vázquez Muñoz L. Flores Pulido V. Alarcón Aquino O. Starostenko R. Rosas Romero J. Rodríguez Asomoza O. J. Paz Luna K. Vázquez Muñoz L. Flores Pulido

3. SIGMAP 20093 Contents Introduction Microcalcifications Wavelet Transforms Experimental Results Conclusions Introduction Microcalcifications Wavelet Transforms Experimental Results Conclusions

4. SIGMAP 20094 Introduction A mammography exam is used to aid in the diagnosis of breast diseases in women The early detection of breast cancer is difficult due that small tumors and microcalcifications are very similar to normal glandular tissue So, wavelet transform is employed in eliminate noise in mammogram’s images A mammography exam is used to aid in the diagnosis of breast diseases in women The early detection of breast cancer is difficult due that small tumors and microcalcifications are very similar to normal glandular tissue So, wavelet transform is employed in eliminate noise in mammogram’s images

5. SIGMAP 20095 Introduction A system based on fuzzy logic has been reported in (Cheng, 1998) A mathematical morphology study is reported in (Zhao, 1993) A two stages method for segmentation and detection of MC’s with matched filters (Strickland 1996) Wang (1998) detect MCs using the decimated wavelet transform and a nonlinear treshold A system based on fuzzy logic has been reported in (Cheng, 1998) A mathematical morphology study is reported in (Zhao, 1993) A two stages method for segmentation and detection of MC’s with matched filters (Strickland 1996) Wang (1998) detect MCs using the decimated wavelet transform and a nonlinear treshold

6. SIGMAP 20096 Microcalcifications The breast tissue study was performed in radiology including magnetic resonance image and nuclear medicine Using both methods it helped to decide the best theraphy for each lesion Unfortunately it is not possible improve the visualization of present elements Digital mammographs is preferred The breast tissue study was performed in radiology including magnetic resonance image and nuclear medicine Using both methods it helped to decide the best theraphy for each lesion Unfortunately it is not possible improve the visualization of present elements Digital mammographs is preferred

7. SIGMAP 20097 Microcalcifications Breast microcalcifications are commonly discovered in the radiological story of asymptomatic women These are deposits of calcium at the thickness of mamary tissue and are represented as little white dots The first sign of cancerous process. Breast microcalcifications are commonly discovered in the radiological story of asymptomatic women These are deposits of calcium at the thickness of mamary tissue and are represented as little white dots The first sign of cancerous process.

8. SIGMAP 20098 Mammography Image Analysis Society database

9. SIGMAP 20099 Microcalcifications MC’s are small deposits of calcium that appear as diminutive white dots in the mammogram Due to microcalcifications’s size, the detection of: –non-homogeneus background of mammograms (breast glandular tissue) –noise detection of MC’s is difficult MC’s are small deposits of calcium that appear as diminutive white dots in the mammogram Due to microcalcifications’s size, the detection of: –non-homogeneus background of mammograms (breast glandular tissue) –noise detection of MC’s is difficult

10. SIGMAP 200910 Wavelet Transforms Is a mathematical tool that provides building blocks with information in scale and time of a signal The process of wavelet transform of a signal is called analysis The inverse process to reconstruct the analyzed signal is called synthesis Is a mathematical tool that provides building blocks with information in scale and time of a signal The process of wavelet transform of a signal is called analysis The inverse process to reconstruct the analyzed signal is called synthesis

11. SIGMAP 200911 Discrete Wavelet Transform Is a time-scale representation of a digital signal, obtained with digital filtering techniques The signal is passed trough several filters with cut-frequencies at different scales The wavelet’s family is generated by a mother wavelet defined by: Is a time-scale representation of a digital signal, obtained with digital filtering techniques The signal is passed trough several filters with cut-frequencies at different scales The wavelet’s family is generated by a mother wavelet defined by:

12. SIGMAP 200912 Complex Wavelet Transform Is used to avoid limitations of DWT and to obtain phase information Real and imaginary coefficients are used to compute amplitude and phase information Is used to avoid limitations of DWT and to obtain phase information Real and imaginary coefficients are used to compute amplitude and phase information

13. SIGMAP 200913 Bank filter for 1D DT-CWT Analysis The form of the conjugated filters of one-dimensional DT- CWT is defined for Where: – is the set of filter – is the set – and correspond to low-pass and high-pass filter for real part – and are in the imaginary part –The synthesis bank filter is realized with the pairs and The form of the conjugated filters of one-dimensional DT- CWT is defined for Where: – is the set of filter – is the set – and correspond to low-pass and high-pass filter for real part – and are in the imaginary part –The synthesis bank filter is realized with the pairs and

14. SIGMAP 200914 Proposed Approach The five steps that conforms the method to detect MC’s are: –Mammogram’s sub-band frequency decomposition –Mammogram’s noise reduction –Suppression of bands containing low- frequencies –Dilatation of high-frequency components –Mammogram’s reconstruction Detection of Microcalcifications The five steps that conforms the method to detect MC’s are: –Mammogram’s sub-band frequency decomposition –Mammogram’s noise reduction –Suppression of bands containing low- frequencies –Dilatation of high-frequency components –Mammogram’s reconstruction Detection of Microcalcifications

15. SIGMAP 200915 Experimental Results Evaluation using the SWT and the Top-Hat Transformation In the SWT case the fourth order Daubechies wavelet is used The detection of MCs using the SWT is accomplished by setting low frequencies subbands to zero Before the reconstruction of the image Evaluation using the SWT and the Top-Hat Transformation In the SWT case the fourth order Daubechies wavelet is used The detection of MCs using the SWT is accomplished by setting low frequencies subbands to zero Before the reconstruction of the image

16. SIGMAP 200916 Experimental Results Glandular tissue that contains a set of maligns MCs using DT-CWT

17. SIGMAP 200917 Experimental Results Glandular tissue that contains a set of maligns MCs using SWT and Top Hat Transform

18. SIGMAP 200918 Experimental Results SWT complexity is high O(n2) DT-CWT O(2n) Top-Hat transformation worst method to detect MCs This is due to the fact that other tissues and breast’s glands are not filtered and appear together with MCs Which are not significantly appreciated as in the cases of the two other simulated methods SWT complexity is high O(n2) DT-CWT O(2n) Top-Hat transformation worst method to detect MCs This is due to the fact that other tissues and breast’s glands are not filtered and appear together with MCs Which are not significantly appreciated as in the cases of the two other simulated methods

19. SIGMAP 200919 Conclusions SWT detects the MCs but other details are also observed as MCs Inconvenient presented by the SWT computational complexity, O(n2) Computational complexity of the DT-CWT is O(2n) only SWT detects the MCs but other details are also observed as MCs Inconvenient presented by the SWT computational complexity, O(n2) Computational complexity of the DT-CWT is O(2n) only

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