Mammographic image analysis for breast cancer

detection using complex wavelet transforms and

morphological operators

V. Alarcón AquinoO. Starostenko

R. Rosas RomeroJ. Rodríguez Asomoza

O. J. Paz Luna K. Vázquez Muñoz

L. Flores Pulido

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Contents• Introduction• Microcalcifications• Wavelet Transforms• Experimental Results • Conclusions

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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

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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

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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

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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.

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Mammography Image Analysis Society database

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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

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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

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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:

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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

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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

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s n( ) = hn + ign( )

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hn

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h0 ,h1{ }

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gn

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g0 ,g1{ }

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h0

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h1

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g0

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g1

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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 reconstructionDetection of

Microcalcifications

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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

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Experimental Results

Glandular tissue that contains a set of maligns MCs using DT-CWT

M a m o g ra m a o r ig in a l

1 0 0 2 00 30 0 4 00 50 0 6 00 70 0 8 00 9 00 1 0 00

10 0

20 0

30 0

40 0

50 0

60 0

70 0

80 0

90 0

1 00 0

M a m o gra m a c o n m ic roc a lc ific a c io n e s u s an d o DT -CW T

5 8 0 6 00 62 0 6 4 0 6 6 0 68 0 70 0 72 0 7 40

76 0

78 0

80 0

82 0

84 0

86 0

88 0

90 0

92 0

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Experimental Results

• Glandular tissue that contains a set of maligns MCs using SWT and Top Hat

Transform

M a m og ra m a c on m ic ro c a lc ific a c io n es u s a n d o la S W T

5 8 0 6 0 0 62 0 6 4 0 6 6 0 6 8 0 70 0 7 2 0 7 40

7 6 0

7 8 0

8 0 0

8 2 0

8 4 0

8 6 0

8 8 0

9 0 0

9 2 0

M a m o gra fía u s a n do To p -Ha t fil te rin g

5 8 0 60 0 6 2 0 6 40 66 0 680 70 0 720 74 0

76 0

78 0

80 0

82 0

84 0

86 0

88 0

90 0

92 0

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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

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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

THANKS! QUESTIONS?