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Frequency Support of Microcalcifications

C I M A TV 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

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Outline

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

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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.

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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.

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Compactly supported microcalcifications

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2-D DFT of compactly supported signals

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),(11

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kkX nkN

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otherwise 0

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),( Mdddmd

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For a compact signal we have:

0 d11- d12

0 d21- d22

Let:

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2-D DFT of compactly supported signals

It follows that:

2sin

2)12221(sin

2sin

2)11211(sin ),(),( 2)2122(2)1112(

/2/221

2

1

/ddj

Y

Y/ddj

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d- d d- d 1112and1112 Approaches to zero

),( 21 kkX

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X

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2sin

2/)122d21d(sin

2sin

2/)112d11d(sin ),(X)k,k(X

Approaches to one

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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):

),( 21 kkX

Becomes low pass

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Experiments

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),(1

),(ˆ1

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k

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l

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n

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m

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nmxNM

xEn

),(),(),(ˆ nmnmxnmx

Microcalcification +

Surrounding noise

DCT

Zonal filters

Energy calculation

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Experiments

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),(1

),(ˆ1

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k

M

l

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n

M

m

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nmxNM

xEn

),(),(ˆ nmxnmx

Microcalcification

DCT

Zonal filters

Energy calculation

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Results

Percents of retained energy after zonal filtering for

Percents of retained energy after zonal filtering for),(ˆ nmx ),( nmx

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Normalized differences

a b c d e f 0

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1

Zonal filters

No

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lized

dif

fere

nc

e

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

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Frequency support of two different microcalcifications

High amplitude Short spatial support.

Short amplitude Short spatial support.

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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.

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DWT CDF 9/7

Original and recovered injuries after 1 and 4

levels of DWT decomposition.

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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.

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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.

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Questions

hochoa@uacj.mx

Cuerpo Académico de Instrumentación y Procesamiento de Señales (CAIPS)

Universidad Autónoma de Ciudad JuárezUACJ

www.uacj.mx