Breast Mass Segmentation in Mammography Using Plane Fitting and Dynamic Programming

Rationale and Objectives

Segmentation is an important and challenging task in a computer-aided diagnosis (CAD) system. Accurate segmentation could improve the accuracy in lesion detection and characterization. The objective of this study is to develop and test a new segmentation method that aims at improving the performance level of breast mass segmentation in mammography, which could be used to provide accurate features for classification.

Materials and Methods

This automated segmentation method consists of two main steps and combines the edge gradient, the pixel intensity, as well as the shape characteristics of the lesions to achieve good segmentation results. First, a plane fitting method was applied to a background-trend corrected region-of-interest (ROI) of a mass to obtain the edge candidate points. Second, dynamic programming technique was used to find the “optimal” contour of the mass from the edge candidate points. Area-based similarity measures based on the radiologist’s manually marked annotation and the segmented region were employed as criteria to evaluate the performance level of the segmentation method. With the evaluation criteria, the new method was compared with 1) the dynamic programming method developed by Timp and Karssemeijer, and 2) the normalized cut segmentation method, based on 337 ROIs extracted from a publicly available image database.

Results

The experimental results indicate that our segmentation method can achieve a higher performance level than the other two methods, and the improvements in segmentation performance level were statistically significant. For instance, the mean overlap percentage for the new algorithm was 0.71, whereas those for Timp’s dynamic programming method and the normalized cut segmentation method were 0.63 ( P < .001) and 0.61 ( P < .001), respectively.

Conclusions

We developed a new segmentation method by use of plane fitting and dynamic programming, which achieved a relatively high performance level. The new segmentation method would be useful for improving the accuracy of computerized detection and classification of breast cancer in mammography.

Breast cancer is one of the leading causes of death in women . Scientific evidence indicates that early detection and treatment of breast cancer can reduce the mortality and morbidity of patients . Mammography is widely considered as one of the most cost-effective methods to detect early breast cancer . Computer-aided diagnosis (CAD) systems can be useful in breast cancer screening programs with mammography by providing radiologists with a “second opinion.”

Segmentation of masses in mammography is an important and challenging task in a CAD system. Accurate segmentation could provide accurate lesion features and thus improve accuracy in lesion detection and characterization . Segmentation of masses overlapping with dense breast tissue is particularly difficult because mass boundaries may become obscured, irregular, and low in contrast. In recent years, many studies have been focused on segmentation of mass lesions in digital mammography. Petrick et al developed a segmentation method based on density-weighted contrast enhancement (DWCE), which incorporated adaptive filtering and edge detection. Zheng et al proposed a method for the detection of masses with an adaptive multi-layer topographic region growth algorithm. Comer et al used Markov random fields to segment masses in a mammogram based on texture information. Catarious et al applied an iterative routine based on gray level to do mass segmentation. Yuan et al proposed a dual-stage method for lesion segmentation on digital mammograms, which combined a radial gradient index (RGI) based segmentation method and an improved active contour model.

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Materials and methods

Dataset

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Segmentation Using Plane Fitting and Dynamic Programming

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Step 1: ROI Preprocessing

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Step 2: Detection of Edge Candidate Points by Use of Plane Fitting

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f=a⋅i+b⋅j+c, f

⋅

where −2≤i≤2 −

≤

2 and −2≤j≤2 −

≤

2 . Each pixel could thus be characterized by a set of three parameters “a,” “b,” and “c.” Because

⎧⎩⎨∂f∂i=a∂f∂j=b, {

∂

parameters “a” and “b” indicate the gradients on the vertical direction and the horizontal direction, respectively. Figure 3 e and f show the grayscale image corresponding to the vertical gradient and the horizontal gradient, respectively.

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{i=−tsinj=tcos. {

−

sin

cos

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f=−a⋅t⋅sin+b⋅t⋅cos+c, f

−

⋅

sin

⋅

cos

and consequently,

∂f∂t=−asin+bcos. ∂

∂

−

sin

cos

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Step 3: Delineation of Lesion Outline by Use of Dynamic Programming

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C(n)=dis(n,n−1)255−I(n), C

(

)

(

−

)

255

−

(

)

where dis( n , n – 1) represented the distance between the edge candidate point on the nth radial line and one edge candidate point on the (n – 1)th radial line, and I ( n ) represented the gray value of the edge candidate point on the nth radial line.

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Segmentation Using Dynamic Programming Proposed by Timp

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Segmentation Using Normalized Cut

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Segmentation Performance Evaluation

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AOM=Arearadiologist∩AreasegmentationArearadiologist∪Areasegmentation. A

log

∩

log

∪

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CM=(AOM+(1−Arearadiologist−Arearadiologist∩AreasegmentationArearadiologist)+(1−Areasegmentation−Arearadiologist∩AreasegmentationAreasegmentation))/3. C

(

−

log

−

log

∩

log

)

(

−

log

∩

)

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EM=Num(Arearadiologist∪Areasegmentation−Arearadiologist∩Areasegmentation)Num(perimeterradiologist), E

(

log

∪

−

log

∩

)

(

log

)

where Num(Arearadiologist∪Areasegmentation−Arearadiologist∩Areasegmentation) N

(

log

∪

−

log

∩

) represented the number of pixels in the mismatched area between the outline delineated by radiologists and the segmentation result, and Num ( perimeter radiologist ) represented the number of pixels on the outline delineated by the radiologists. The EM measures the accuracy of the segmentation algorithm relative to the actual size of the lesion. Unlike AOM and CM, the smaller the EM, the better the segmentation algorithm.

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Results

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Table 1

Descriptive Statistics of Performance Measures AOM, CM, and EM for the Three Segmentation Methods

Descriptive Statistics of AOM Method Min. First Qu. Median Mean Third Qu. Max. OurDp 0.098 0.665 0.736 0.712 0.803 0.921 TimpDp 0.003 0.547 0.651 0.627 0.747 0.902 Ncut 0.029 0.484 0.675 0.607 0.769 0.907

Descriptive Statistics of CM Method Min. First Qu. Median Mean Third Qu. Max. OurDp 0.399 0.766 0.816 0.801 0.867 0.946 TimpDp 0.080 0.691 0.764 0.743 0.829 0.934 Ncut 0.093 0.635 0.775 0.722 0.843 0.937

Descriptive Statistics of EM Method Min. First Qu. Median Mean Third Qu. Max. OurDp 0.614 1.487 2.093 2.762 3.154 22.191 TimpDp 0.733 1.719 2.796 3.962 4.416 43.323 Ncut 0.617 1.801 2.870 5.691 6.080 54.462

AOM, area overlap measure; CM, combined metric; EM, error metric.

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Table 2

P Values of the Two-sided Wilcoxon (rank-sum) Test for the Statistical Differences in the Three Area-based Similarity Measures (AOM, CM, and EM) of the Three Segmentation Methods

Method_P_ Value for AOM_P_ Value for CM_P_ Value for EM OurDp - TimpDp <.001 <.001 <.001 OurDp - Ncut <.001 <.001 <.001 TimpDp - Ncut 0.227 0.400 0.697

AOM, area overlap measure; CM, combined metric; EM, error metric; Ncut, normalised cut method; Our Dp, our method; Timp Dp, Timp’s method.

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Table 3

The Percentages of Masses with an Area Overlap Method of 0.6 or Higher for Five Subtlety Ratings (1: very subtle, 5: very obvious), and Five Mass Margin Types

Subtlety Rating Method 1 2 3 4 5 OurDp 80% 90% 85% 89% 86% TimpDp 60% 35% 66% 67% 70% Ncut 40% 50% 57% 58% 68%

Margin Type Method Circumscribed Spiculated Ill-defined Microlobulated Obscured OurDp 88% 78% 92% 84% 95% TimpDp 81% 48% 78% 59% 64% Ncut 56% 52% 75% 63% 64%

Ncut, normalised cut method; Our Dp, our method; Timp Dp, Timp’s method.

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Discussion

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Conclusion

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Acknowledgment

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References

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Breast Mass Segmentation in Mammography Using Plane Fitting and Dynamic Programming

Rationale and Objectives

Materials and Methods

Results

Conclusions

Materials and methods

Dataset

Segmentation Using Plane Fitting and Dynamic Programming

Step 1: ROI Preprocessing

Step 2: Detection of Edge Candidate Points by Use of Plane Fitting

Step 3: Delineation of Lesion Outline by Use of Dynamic Programming

Segmentation Using Dynamic Programming Proposed by Timp

Segmentation Using Normalized Cut

Segmentation Performance Evaluation

Results

Discussion

Conclusion

Acknowledgment

References

Further Reading

Atlas of Brain Function

Computed Radiography-based Mammography with 50-μm Pixel Size

Diffusion Tensor Tractography in the Head-and-Neck Reg ion Using a Clinical 3-T MR Scanner