caips 1 frequency support of microcalcifications c i m a t v taller de procesamiento de imágenes...
DESCRIPTION
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.TRANSCRIPT
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CAIPS 1
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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CAIPS 2
Outline
• Introduction.• 2-D DFT of compactly supported signals.• Experiments.• Results.• The Discrete Wavelet Transform. • Conclusions.
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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.
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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.
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CAIPS 5
Compactly supported microcalcifications
02
46
810
1214
16
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5
10
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20
40
60
80
100
120
SamplesSamples
Am
plitu
de
0 5 100510
-10
-5
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5
10
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20
25
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SamplesSamples
Am
plitu
de
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CAIPS 6
2-D DFT of compactly supported signals
1,.,1,0 ;1,.,1,0
),(11),(
2
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kkX nkN
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For a compact signal we have:0 d11- d12
0 d21- d22
Let:
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CAIPS 7
2-D DFT of compactly supported signals
It follows that:
2sin
2)12221(sin
2sin
2)11211(sin ),(),( 2)2122(2)1112(
/2/221
21
/ddj
Y
Y/ddj
X
X
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YX e/dde/ddXkkX
d- d d- d 1112and1112 Approaches to zero),( 21 kkX
YX
Y
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X
XYX21 ,-
2sin
2/)122d21d(sin
2sin
2/)112d11d(sin ),(X)k,k(X
Approaches to one
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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):
),( 21 kkX
Becomes low pass
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CAIPS 9
Experiments
1
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),(1
),(ˆ1
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k
M
l
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n
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m
XEnlkXNM
nmxNM
xEn
),(),(),(ˆ nmnmxnmx
Microcalcification +
Surrounding noise
DCT
Zonal filters
Energy calculation
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CAIPS 10
Experiments
1
0
1
0
2
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),(1
),(ˆ1
N
k
M
l
N
n
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m
XEnlkXNM
nmxNM
xEn
),(),(ˆ nmxnmx
Microcalcification
DCT
Zonal filters
Energy calculation
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CAIPS 11
Results
Percents of retained energy after zonal filtering for
Percents of retained energy after zonal filtering for),(ˆ nmx ),( nmx
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CAIPS 12
Normalized differences
a b c d e f 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Zonal filters
Nor
mal
ized
diff
eren
ce
The depicted function will be more or less skewed for different mammograms and noise types.
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CAIPS 13
Frequency support of two different microcalcifications
High amplitude Short spatial support.
Short amplitude Short spatial support.
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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.
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CAIPS 15
DWT CDF 9/7
Original and recovered injuries after 1 and 4
levels of DWT decomposition.
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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.
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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.
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CAIPS 18
Questions
Cuerpo Académico de Instrumentación y Procesamiento de Señales (CAIPS)
Universidad Autónoma de Ciudad JuárezUACJ
www.uacj.mx