A Dynamic Graph Cuts Method with Integrated Multiple Feature Maps for Segmenting Kidneys in 2D Ultrasound Images

Rationale and Objectives

Automatic segmentation of kidneys in ultrasound (US) images remains a challenging task because of high speckle noise, low contrast, and large appearance variations of kidneys in US images. Because texture features may improve the US image segmentation performance, we propose a novel graph cuts method to segment kidney in US images by integrating image intensity information and texture feature maps.

Materials and Methods

We develop a new graph cuts-based method to segment kidney US images by integrating original image intensity information and texture feature maps extracted using Gabor filters. To handle large appearance variation within kidney images and improve computational efficiency, we build a graph of image pixels close to kidney boundary instead of building a graph of the whole image. To make the kidney segmentation robust to weak boundaries, we adopt localized regional information to measure similarity between image pixels for computing edge weights to build the graph of image pixels. The localized graph is dynamically updated and the graph cuts-based segmentation iteratively progresses until convergence. Our method has been evaluated based on kidney US images of 85 subjects. The imaging data of 20 randomly selected subjects were used as training data to tune parameters of the image segmentation method, and the remaining data were used as testing data for validation.

Results

Experiment results demonstrated that the proposed method obtained promising segmentation results for bilateral kidneys (average Dice index = 0.9446, average mean distance = 2.2551, average specificity = 0.9971, average accuracy = 0.9919), better than other methods under comparison ( P < .05, paired Wilcoxon rank sum tests).

Conclusions

The proposed method achieved promising performance for segmenting kidneys in two-dimensional US images, better than segmentation methods built on any single channel of image information. This method will facilitate extraction of kidney characteristics that may predict important clinical outcomes such as progression of chronic kidney disease.

Introduction

Ultrasound (US) imaging has been widely used to examine kidneys for structural abnormalities and to measure kidney anatomic features such as renal parenchymal area that have been associated with development of end stage renal disease . utomatic segmentation of US images of kidneys will facilitate extraction and quantification of anatomic features such as renal parenchymal area and kidney echogenicity, which currently are measured manually. However, automatic segmentation of kidneys in (two-dimensional) 2D US images remains a challenging task due to high speckle noise, low contrast between foreground and background, weak boundaries, and large appearance variations of kidneys in 2D US images . A

A variety of automatic methods have been developed for segmenting kidneys in 2D US images, including active contour model (ACM)-based methods , atlas-based methods , Markov random field-based methods , watershed-based methods , machine learning-based methods , and deep learning methods . Among them, the ACM-based method is appealing because of its robustness to imaging noise, weak boundaries, and large appearance variation within kidneys. However, the existing ACM-based image segmentation methods typically adopt gradient descent flow-based optimization techniques, which often get stuck at local minima . Such a limitation can be overcome by graph cuts (GC) techniques . Particularly, GC techniques model the image segmentation task as an image labeling problem on a graph . The GC techniques can be integrated with the ACM-based methods by transforming the minimization problem of the ACM methods into a minimum-cut problem of a graph . However, speckle noise and low contrast of US images might degrade the segmentation performance if the US images are directly used as input to the segmentation algorithms.

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Materials and Methods

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Texture Feature Map Extraction

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{g=12πσxσyexp(−(x′σ2x+y′σ2y))exp(i(2πx′λ))x′=xcosθ+ysinθ,y′=−xsinθ+ycosθ, {

(

−

(

′

)

(

′

)

′

xcosθ

ysinθ

′

−

xsinθ

ycosθ

where σ x and σ y are standard deviations of the Gaussian functions along axis x and axis y respectively, θ is the direction of the Gabor filter, wavelength λ is the frequency factor, and the frequency ω=2πλ ω

λ . A Gabor filter with a small λ captures image information of high frequency and small scale, whereas a Gabor filter with a big λ captures image information of low frequency and big scale. Gabor filters in different scales, and directions can be integrated to capture multiscale image information .

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gi=argmaxj=1,…,n|fi,j(p)|,i=1,…,m, g

argmax

…

(

)

…

where the dominant direction at scale i has the maximum absolute value, ∣∣fi,gi(p)∣∣ |

(

)

| , among all directions. For every direction, we then compute the number of scales at which the direction under consideration is the dominant direction.

Dj=∑mi=1δ(|fi,j(p)|−∣∣fi,gi(p)∣∣),j=1,…,n D

∑

(

)

−

(

)

…

where function δ (∙) is 1 at zero and 0 otherwise. Finally, we identify dominant directions across all scales as

Ω={j|Dj≥0.5⋅maxj=1,..,nDj}, Ω

{

≥

0.5

⋅

max

}

where dominant directions are identified as those with filtering responses greater than half of the maximal response values to balance robustness and redundancy of the dominant directions.

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f(p)=1m∑mi=1∑j∈Ω|fi,j(p)|. f

(

)

∑

∈

(

)

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Dynamic GC-Based Image Segmentation with Integrated Multiple Feature Maps

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w(p,q)=α⋅wp(p,q)+(1−α)⋅wr(p,q), w

(

)

⋅

(

)

(

−

)

⋅

(

)

wp(p,q)=exp(−1N∑Ni=1(Ii(p)−Ii(q))2σ),wr(p,q)=exp(−(1/(1N∑Ni=1Ki(p,q)))σ), w

(

)

(

−

∑

(

)

−

(

)

(

)

(

−

(

∑

(

)

where p and q are adjacent pixels, wp(p,q) w

(

) and wr(p,q) w

(

) are image similarity measures based on pixel information and regional information respectively, α is a trade-off parameter between the two terms, Ii(p) I

(

) and Ii(q) I

(

) are image intensity value of p and q for the i th feature map, Ki(p,q) K

(

) is an image difference measure based on regional information, σ is a parameter, and i = 1, 2 corresponding to the original US image intensity and the Gabor feature map respectively. The numerator terms in both wp(p,q) w

(

) and wr(p,q) w

(

) are normalized to [0,1]. Particularly, Ki(p,q) K

(

) is defined as

Ki(p,q)=min(lp,lq)∈{(S,T),(T,S),(S,S)or(T,T)}(Ii(p)−flpi(p))2+(Ii(q)−flqi(q))2, K

(

)

min

(

)

∈

{

(

)

(

)

(

)

(

)

}

(

)

−

(

)

(

)

−

(

)

where Ii(p) I

(

) and Ii(q) I

(

) are image intensity value of p and q for the i th feature map, fSi(p) f

(

) , fTi(p) f

(

) , fSi(q) f

(

) , fTi(q) f

(

) are intensity mean of pixels of a small neighborhood of p and q corresponding to segments S and T , respectively, as illustrated in Figure 3 c, and lp∈{S,T} l

∈

{

} and lq∈{S,T} l

∈

{

} are possible segmentation labels of p and q to be updated according to the minimal value computed by Equation 7 . Particularly, Ki(p,q) K

(

) measures differences between image intensity values of pixels and mean image intensity values of their corresponding optimal segmentation results. However, if the optimal segmentation labels of p and q are the same, we set Ki(p,q)=max(u,v)∈(V,V)Ki(u,v) K

(

)

max

(

)

∈

(

)

(

) so that they will not be separated into different segments.

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Segmentation Performance Evaluation and Parameter Optimization

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Results

Optimization of the Parameters

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Experiments on Single and Multiple Feature Maps

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Experiments on Different Settings of Image Similarity Measures

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Experiments on Different Initializations

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Table 1

Intraclass Correlation Coefficients for Three Different Initializations

Dice Index Mean Distance Specificity Accuracy 0.8531 0.8329 0.8549 0.8691

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Experiments on Different Narrowbands

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Comparison with Alternative Methods

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Table 2

Segmentation Accuracy Measures of Results Obtained by Different Methods (Paired Wilcoxon Rank Sum Tests Were Adopted to Compare the Proposed Method with the Alternatives)

Dice Index Mean Distance Mean Std Median_P_ value Mean Std Median_P_ value LRAC 0.9051 0.0257 0.9093 5.12e–23 3.6527 0.9810 3.5612 8.14e–23 GAC 0.9315 0.0374 0.9465 3.99e–04 2.9888 2.0283 2.2896 1.02e–04 AMFSM 0.9024 0.0388 0.9118 2.04e–22 4.1275 1.1435 3.9175 1.51e–22 Proposed 0.9446 0.0179 0.9489 2.2551 0.5783 2.1941

Specificity Accuracy Mean Std Median_P_ value Mean Std Median_P_ value LRAC 0.9932 0.0048 0.9941 3.73e–13 0.9868 0.0053 0.9877 1.02e–22 GAC 0.9945 0.0087 0.9969 1.24e–04 0.9894 0.0085 0.9918 1.00e–03 AMFSM 0.9901 0.0065 0.9915 6.33e–21 0.9854 0.0054 0.9858 1.75e–22 Proposed 0.9971 0.0022 0.9976 0.9919 0.0031 0.9924

AMFSM, adaptive multifeature segmentation model; GAC, geodesic active contours; LRAC, localizing region-based active contours; Std, standard deviation.

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Discussion and Conclusions

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A Dynamic Graph Cuts Method with Integrated Multiple Feature Maps for Segmenting Kidneys in 2D Ultrasound Images

Rationale and Objectives

Materials and Methods

Results

Conclusions

Introduction

Materials and Methods

Texture Feature Map Extraction

Dynamic GC-Based Image Segmentation with Integrated Multiple Feature Maps

Segmentation Performance Evaluation and Parameter Optimization

Results

Optimization of the Parameters

Experiments on Single and Multiple Feature Maps

Experiments on Different Settings of Image Similarity Measures

Experiments on Different Initializations

Experiments on Different Narrowbands

Comparison with Alternative Methods

Discussion and Conclusions

References

Further Reading

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