Automatic Breast Ultrasound Image Segmentation: A Survey
Min Xian1, Yingtao Zhang3, H.D. Cheng2, 3, Fei Xu2, Boyu Zhang2, Jianrui Ding3
1

Department of Computer Science, University of Idaho, Idaho Falls, ID 83402, USA
2

3

Department of Computer Science, Utah State University, Logan, UT 84322, USA

School of Computer Science and Technology, Harbin Institute of Technology, China

Abstract
Breast cancer is one of the leading causes of cancer death among women worldwide. In clinical routine, automatic breast ultrasound (BUS) image segmentation is very challenging and essential for cancer diagnosis and
treatment planning. Many BUS segmentation approaches have been studied in the last two decades, and have
been proved to be effective on private datasets. Currently, the advancement of BUS image segmentation seems
to meet its bottleneck. The improvement of the performance is increasingly challenging, and only few new
approaches were published in the last several years. It is the time to look at the field by reviewing previous
approaches comprehensively and to investigate the future directions. In this paper, we study the basic ideas,
theories, pros and cons of the approaches, group them into categories, and extensively review each category
in depth by discussing the principles, application issues, and advantages/disadvantages.

Keyword: breast ultrasound (BUS) images; breast cancer; segmentation; benchmark; early detection;
computer-aided diagnosis (CAD)

1. Introduction
Breast cancer occurs in the highest frequency in women among all cancers, and is also one of the leading
causes of cancer death worldwide [1, 2]. Scientists do not definitely know what causes breast cancer yet, and
only know some risk factors that can increase the likelihood of developing breast cancer: getting older, genetics,
radiation exposure, dense breast tissue, alcohol consumption, etc. The key of reducing the mortality is to find
signs and symptoms of breast cancer at its early stage by clinic examination [3]. Breast ultrasound (BUS)
imaging has become one of the most important and effective modality for the early detection of breast cancer
because of its noninvasive, nonradioactive and cost-effective nature [4]; and it is most suitable for large-scale
breast cancer screening and diagnosis in low-resource countries and regions.

1 / 40

Computer-Aided Diagnosis (CAD) systems based on B-mode breast ultrasound have been developed to
overcome the considerable inter- and intra-variabilities of the breast cancer diagnosis, and have been clinically
tested their ability to improve the performance of the breast cancer diagnosis. BUS segmentation, extracting
tumor region of a BUS image, is a crucial step for a BUS CAD system. Base on the segmentation results,
quantitative features will be calculated to describe tumor shape, size, echo pattern, etc., and be input into a
classifier to determine the category of the tumors. Therefore, the precision of BUS segmentation directly affects the performance of the quantitative analysis and diagnosis of tumors. Segmentation is a common and
crucial task in medical image analysis, and many medical image segmentation tasks share essentially similar
segmentation approaches; however, comparing with medical image segmentation for other imaging modalities,
e.g., computed tomography (CT), magnetic resonance imaging (MRI), mammography, BUS image segmentation is very challenging because (1) ultrasound image has very low quality due to the speckle noise, low contrast, low single noise ratio (SNR) and artifacts; (2) large variations of breast structures exists among patients,
which make it difficult to apply the knowledge of anatomical structures; and (3) strong priors based on tumor
shape, size and echo strength are important for organ segmentation [174, 180] in other imaging modalities; but
these features vary largely across patients and are difficult to be applied to BUS image segmentation.
Automatic BUS segmentation has been studied extensively in the last two decades. We can classify
existing approaches into semi-automated and fully automated groups according to the degree of human intervention involved in segmentation process. In most semi-automated methods, radiologist needs to specify a
region of interest (ROI) including the lesion, a seed in the lesion, or an initial boundary. Fully automated
segmentation approaches need no user intervention, and usually model the knowledge of breast ultrasound and
oncology as the prior constraints. Many segmentation techniques were employed in both semi-automatic and
fully automatic approaches.
[175] is the first survey paper for BUS image segmentation published recently; however, this paper is
much more comprehensive in terms of major issue discussions, future direction prediction, theory fundamentals, application theme and the number of references. In this paper, we classify breast cancer segmentation
approaches into six main categories: (1) graph-based approaches [7, 9-13, 22-25, 27, 28, 32-34], (2) deformable models [42, 50, 52, 54-59, 61-65, 67, 69, 71, 73, 75, 76, 78-82, 85, 124, 139, 148, 166], (3) learning-based
approaches [7, 9,10, 87, 89, 91, 94, 95, 98,100, 103-107, 120], (4) thresholding [22, 109-115], (5) region
growing [54, 55, 113, 117, 118], and (6) watershed [109, 122, 123, 126-128]. As shown in Fig. 1, the first three
categories dominate BUS image segmentation approaches; and the last three categories are the classical image
2 / 40

processing approaches. The category of the others [136, 138, 139, 140, 142-146] is composed of three small
sub-categories, each contains only few literatures. Due to the challenging nature of the task, just using single
image processing technique cannot achieve desirable results; and most successful approaches employ hybrid

Number of Publications

techniques and model biological priors.
50
40
30
20
10
0

Graph-based approaches
Defromable models
Learning-based approaches
Thresholding
Region growing
Watershed
Others

Categories
Fig. 1. Distribution of automatic BUS image segmentation approaches; data come from google scholar until May 2017.

The rest of the paper is organized as follows: in section 2, the fundamental issues in BUS segmentation
are discussed, e.g., denoising, interaction, biological priors modeling, validation, and the possible problemsolving strategies; in sections 3 - 6, we review automatic BUS image segmentation methods by presenting the
principle of each category, discussing their advantages and disadvantages, and summarizing the most valuable
strategies. In section 7, we discuss the approaches of three sub-categories briefly. Section 8 gives the conclusion and the future directions.
2. Fundamental Issues of BUS Image Segmentation
BUS segmentation approaches have been studied in the last two decades extensively, and many of them
achieved good performances utilizing their own datasets. In this section, we discuss the fundamental issues in
BUS segmentation, and summarize the successful strategies employed in state-of-the-art approaches.
2.1 Denoising and Preserving Edge
In ultrasound imaging, speckle noise is inherent to coherent illumination and Rayleigh scattering caused by
tissue microstructures [147]; and it is a major difficulty in BUS image segmentation because the speckle artifacts are tissue-dependent and cannot be effectively modeled [167]. Many de-speckle approaches have been
applied, e.g., mean filter, Gaussian low-pass filter, speckle reducing anisotropic diffusion (SRAD) [148], nonlinear coherence diffusion (NCD) [149], sticks filter [60], bilateral filter [150, 151], fractional subpixel diffusion [157], nonlocal means-based speckle filter [167], etc. Mean filter and Gaussian low-pass filter are simple,
fast, and easy to implement. They are widely used in early BUS segmentation approaches [22, 52, 59, 61-63,
109, 112, 115, 123, 133, 138]; SRAD, NCD, sticks filter, and fractional subpixel diffusion are specially de-

3 / 40

signed to deal with speckle noise, and because of their excellent property in edge preservation, these approaches are employed in BUS segmentation popularly [34, 58, 65, 89, 95, 103, 105, 106, 113, 114, 124, 125,
158, 165, 166]. The mean filter and Gaussian low-pass filter have the side effect of blurring edges and are only
suitable for the approaches insensitive to image edges or gradient. For the edge-based approaches, e.g., edgebased deformable models and watershed, denoising with edge preservation approaches are preferred to avoid
the leakage of final segmentation. For more details about modern image denoising or filtering approaches,
please refer [168].
2.2 Human Intervention
Many semi-automatic approaches exist in literature; and user interactions like setting seeds, drawing initial
boundary or ROI are required in these approaches. Radiologists’ interactions could be useful in segmenting
extremely difficult BUS cases which have very poor image quality; however, these interactions make the approaches operator-dependent and the results unreproducible; furthermore, it is also impossible to apply the
semi-automatic approaches to a large-scale BUS image dataset, because of the great cost of human labor and
time. The intensity and sensitivity of interaction are two important criteria for evaluating interactive segmentation approaches [152, 153]; because user interaction has large degree of arbitrariness and different interaction
may lead to quite different results. However, no work has been done in BUS image segmentation to evaluate
the sensitivity and intensity of the approach’s interaction yet.
Fully automatic BUS image segmentation has many advantages in comparison with interactive segmentation, such as fully operator-independent, reproducible, and suitable for large scale tasks; therefore, we believe
that fully automatic segmentation is the trend in the future BUS CAD systems. Many fully automatic approaches [22, 25, 64, 98, 100, 106, 109, 115, 154] have been proposed in the last few years. In fully automatic
BUS segmentation, the key step to make an approach completely automatic is the tumor detection, which outputs ROI, rough boundary, seeds, or candidate regions to localize tumors, and initializes the subsequent segmentation steps. The approaches [54, 55, 106, 113] constructing empirical formulas to model domain priors
provided effective means for tumor detection, but the predefined reference point (RP) formulated in these
approaches limited the robustness and flexibility. One direction to improve these approaches is to model more
robust prior, e.g., adaptive RP [22]; the second direction is to improve the generality of the formulas by constructing them in a learning-based framework. Learning based fully automatic approaches [25, 64, 98, 100]
are promising and increasing popularity recently. There are two directions to improve these approaches: (1)

4 / 40

incorporating both global and local features into the learning framework; and (2) learning deep representation
of breast structure towards the better understanding of BUS image by using deep convolutional neural network.
2.3 Modeling Prior Knowledge
Many ordinary image segmentation frameworks have been applied to BUS image segmentation; however, just
applying ordinary image segmentation approaches cannot achieve good performance; and successful BUS
segmentation approaches should model domain-related priors appropriately. We summarize the major priors
that have been modeled in BUS image segmentation as follows.
Intensity distribution. It is widely used in BUS image segmentation, and the approaches can be classified
into following classes: (1) using empirical distribution to model the intensity distribution of tumor or normal
tissues, e.g., Gaussian, Raleigh, exponential model, etc; and (2) defining intensity distribution implicitly by
using histograms and classifiers. In graph-based approaches [7, 9 - 11], Gaussian distribution of tumor intensity
was usually applied to define the likelihood energy (data term). Liu et al. [67] modeled the probability density
difference between the intensity distribution of tumor/background region and estimated Rayleigh distribution
to improve the performance of Geometric Deformable Model (GDM). In [22, 54, 55], no explicit distribution
was predefined, and only histogram was applied to describe the distribution of tumor region and normal tissues.
In [25, 27, 28], supervised learning approaches are introduced to train the classifiers to output the probability
of each image region to be tumor or background.
Texture and local region statistics. Texture and other local region features have more descriptive power
than intensity, and have been studied in many works [9, 10, 64, 98]. They can distinguish tumor regions from
normal tissues with high accuracy. In [9, 10], the texture distributions were utilized to build the likelihood
energy of the graph model. Madabhushi et al. [54, 55] trained the texture histogram of tumor regions, and
incorporated it with the trained intensity distribution to determine the candidate tumor regions. Liu et al. [64,
98] extracted statistic texture from local regions (16× 16 grid), and learned a SVM classifier to localize tumors accurately.
Edge or gradient. In edge-based deformable models, [42, 50, 52, 56 - 59, 61 - 63], image gradient is
applied to constructing the external force or speed function of the evolving curve; as discussed in section 4.3,
because of the speckle noise and week boundary problems, the performance of most approaches depend on
both denoising and edge preservation techniques; [73, 75] defined the stop function of GDM for edge detection
in the frequency domain rather than in the spatial domain, which made the GDM insensitive to image contrast
and work well on weak boundaries. Xian et al. [22, 115] proposed an edge detector in the frequency domain
5 / 40

and incorporated it into a graph-based framework, which made the pairwise energy less sensitive to image
contrast and brightness.
Layer structure. The breast is composed of different layers of tissues, e.g., skin, premammary, mammary,
retromammary, and muscle layers [169]. Due to the difference of their physical properties, different layers
have different appearances in BUS images. The location and depth of these layers may have big variations and
they are difficult to detect; however, some works [22, 115, 154] had utilized the layer information for segmenting tumors.
Topological properties. Human vision system is very sensitive to the topological properties of objects,
and some works have been investigated [115, 152, 153] for both natural and medical image processing tasks.
In [152, 153], the Neutro-Connectedness (NC) is proposed to compute both the connectedness structure and
map, which has solved the problems of high interaction intensity and interaction-dependence in interactive
image segmentation successfully.
Smoothness. In graph-based models, it corresponds the smoothness term (pairwise energy), and the minimization of the energy makes the models produce a smooth boundary; however, it is important to notice that
the smoothness term also makes the models have the tendency to shrink and generate much shorter boundary
than the real boundary (“Shrink” problem [172]).
2.4 Validation: ground truth, metrics, and BUS image datasets
Most BUS image segmentation approaches discussed in this paper have been evaluated quantitatively, and two
major approaches have been utilized. The first approach is to evaluate segmentation performance by using
physical phantoms or simulation software, e.g., Field II [155, 156]. The advantage of this approach is that the
ground truth is very accurate; but the physical phantoms cannot represent the real breast anatomy exactly, and
the simulation software uses simple acquisition model and cannot represent the real BUS image acquisition
process well. The second approach for validation is to compare the segmentation result with manually delineated boundary. The problem of this approach is that the manually delineated ground truth could be flawed
because of human error; however, this problem could be solved by labeling the boundary multiple times by
same person and/or multiple radiologists. Currently, evaluating BUS image segmentation approaches through
the ground truth delineated by radiologists is widely accepted.
In Table 1, we list eight commonly used metrics; the first six are area metrics and the last two are boundary metrics. Notice that in some papers [22, 23, 115, 127, 137], the similarity index (SI) is defined as Jaccard

6 / 40

index (JI); while in paper [61], SI is defined as the Dice’s coefficient (DSC). FNR equals to (1 – TRP); therefore, it is not necessary to compute both.
Currently, there is no public BUS image benchmark with a reasonable number of clinical cases; the performance of most approaches are validated by only using the private datasets; and it is difficult to compare
different approaches objectively. Therefore, there is a pressing need for establishing a BUS image benchmark.
It will be valuable for comparing the algorithms by using a public dataset objectively, and for determining
which approach achieves better performance and what segmentation strategies should pursue.
Table 1. Quantitative metrics for BUS image segmentation
Metrics

Definition

Alias in References

True positive ratio (TPR)

|R ∩ G|⁄|G|

False negative ratio (FNR)

1 - TPR

False positive ratio (FPR)

|R ∪ G − G|⁄|G|

Error fraction

Jaccard index (JI)

|R ∩ G|⁄|R ∪ G|

Similarity Index, coincidence percentage

Dice’s coefficient (DSC)
Area error ratio (AER)

Hausdorff distance (HD)

Recall rate, overlap fraction,
None

Similarity Index, Dice similarity

2|R ∩ G|⁄(|R| + |G|)
|(R ∪ G) − (R ∩ G)|⁄|G|
max max{𝑑(𝑥, G)} , max{𝑑(𝑦, R)}
∈

∈

Difference radio, normalize residual value

None

𝑑(𝑥, 𝐶) = min{‖𝑥 − 𝑦‖}, C = R or G
Mean absolute distance (MAD)

1/2(∑

∈
( , )

∈

+∑

( , )
∈

)

Mean error distance

3. Graph-based approaches
Graph-based approaches gain increasing popularity in BUS image segmentation due to their advantages: (1)
they provide a simple way to organize task-related priors and image information in a unified framework; (2)
they are flexible and suitable for expressing soft constraints among random variables; and (3) the computation
based on graphical manipulation is very efficient [5].
Let 𝐺 = (𝒱, ℰ) be a graph comprising a set of nodes (vertices) 𝒱 = {𝑣 , 𝑣 , ⋯ , 𝑣 }, and each of them
corresponds to an image pixel/superpixel; and a set of links (edges) ℰ = 〈𝑣 , 𝑣 〉 𝑣 , 𝑣 ∈ 𝒱 , and each of
them connects two adjacent nodes according to a predefined neighborhood system 𝒩 = {𝑁 | 𝑖 =
1, ⋯ , 𝑛} where 𝑁 is the set of neighbors of node 𝑣 . Each link 〈𝑣 , 𝑣 〉 is associated with a nonnegative
weight 𝑤〈𝑣 , 𝑣 〉. The weight is usually defined as the cost of separating the two connected nodes into different classes. For state-of-the-art superpixel generation approaches, refer [177-179].
3.1 MRF-MAP approaches
Markov random field (MRF) is an undirected graphical model and provides a convenient way to model context-dependent entities (pixels/superpixels). In MRF, a site set 𝑆 = {𝑖}

indexes the node set 𝒱; each site i
7 / 40

is associated with a random variable 𝑋 ; 𝑥 = {𝑥 }
ble set 𝑋 = {𝑋 }

is the configuration (implementation) of random varia-

, and 𝑥 takes value from a label set ℒ = {𝑙 }

where m is the number of labels (clas-

ses). In BUS image segmentation, the label set is usually defined as ℒ = {𝑙 , 𝑙 } where 𝑙 denotes tumor and
𝑙 denotes non-tumor.
Let 𝑝(𝑥) be the joint probability (also called the prior distribution) denoted as 𝑝(𝑋 = 𝑥). X is said to be
a MRF on S with respect to a neighborhood system 𝒩 = {𝑁 }

if and only if it satisfies the positivity and

Markovianity:
𝑝(𝑥) = 𝑝(𝑥 |𝑥

{ } )𝑝(𝑥

= 𝑝(𝑥 |𝑥 )𝑝(𝑥
where 𝑥

{}

denotes a set of labels for sites 𝑆 − {𝑖}, and 𝑥

{ })

>0
(1)

{ })

is the set of labels for site i’s neighbors (𝑁 ).

Maximum a posteriori (MAP) is the most popular optimality criterion for MRF modeling and the optimal
(𝑥 ∗ ) is found by
𝑥 ∗ = argmax 𝑝(𝑥|𝑑) = argmax 𝑝(𝑑|𝑥)𝑝(𝑥)

(2)

where d is the observation (image), 𝑝(𝑥|𝑑) is the posterior distribution and 𝑝(𝑑|𝑥) is the likelihood distribution. The Hammersley-Clifford theorem [6] established the equivalence between MRF and Gibbs random
field (GRF), and the MAP is equivalently found by minimizing the posterior energy function
𝑥 ∗ = argmin 𝐸(𝑥|𝑑) = argmin 𝐸(𝑑|𝑥) + 𝐸(𝑥)

(3)

where 𝐸(𝑥|𝑑) = 𝐸(𝑑|𝑥) + 𝐸(𝑥), and 𝐸(𝑑|𝑥) is the likelihood energy and 𝐸(𝑥) is prior energy.
There are two major parts in the MRF-MAP modeling for BUS image segmentation: (1) defining the prior
and likelihood energies and determining the corresponding initial parameters; and (2) designing optimization
algorithm for finding the minimum of the posterior energy. Ashton and Parker [7] defined the MRF prior
energy as the Potts model
𝐸(𝑥) = ∑ ∈ 𝑉(𝑥 ) + ∑ ∈ ∑
𝑉 𝑥 ,𝑥

=

∈

𝑉 𝑥 ,𝑥

−𝛽, if 𝑥 = 𝑥
𝛽, otherwise

(4)
(5)

where 𝛽 is a positive constant. The assumption that every site s takes any label equally likely makes 𝑉(𝑥 )
a constant for all configurations; therefore, 𝐸(𝑥) is usually defined only on the pairwise term (𝑉(𝑥 , 𝑥 )).
They also assume that the intensities of a low-pass filtered image follow the Gaussian distribution, and the
likelihood energy is given by

8 / 40

𝐸(𝑑|𝑥) = ∑ ∈ ln 𝛿

+

(

(6)

)

where di is the intensity of the pixel at site i, 𝑥 is the label of site i, and 𝜇
mean and standard deviation, respectively. The parameters (𝜇

and 𝛿

are the local class

and 𝛿 ) are estimated by using a modified

adaptive k-mean method [8].
Boukerroui et al. [9] improved the method in [7] by modeling both intensity and texture distributions in
the likelihood energy. Boukerroui et al. [10] modified the method in [9] by introducing a weighting function
considering both global and local statistics. [12] improved the approach in [11] by introducing one-click user
interaction to estimate Gaussian parameters automatically. [13] introduced the tissue stiffness information of
ultrasound elastography to the method in [11] by modifying one-dimensional tumor and background Gaussian
distributions as bivariate Gaussian distributions.
The energy function of MRF-MAP can be optimized by using Simulated Annealing (SA) [14] and Iterated
Conditional Mode (ICM) [15] algorithms. Because ICM is much faster than SA, the ICM is preferred in most
BUS image segmentation approaches [7, 9, 11 - 13]. ICM takes a local greedy strategy: it starts with an initial
labeling from estimation or user interaction, then selects label for each site to minimize the energy function;
and the steps repeat until convergence. ICM is quite sensitive to the initialization (parameters) because of its
high possibility of converging to local minima, especially, for non-convex energies in high-dimensional space
[35]. A detailed comparison between ICM and other MRF energy minimization techniques can be found in
[35]. Therefore, one important issue of applying ICM is how to learn the parameters: Gibbsian parameter 𝛽
(Eq. (5)), number of classes (m), and parameters of the initial Gaussian distribution. In BUS image segmentation, the number of classes is usually set from 2 to 4; β could be set adaptively [7] or set to a constant [11-13];
and the parameters of Gaussian distribution are usually initialized by using K-means algorithm [7, 9, 10].
3.2 Graph cuts
Graph cuts was proposed to solve a special case in MRF-MAP framework [16]: the global optimization of the
binary labelling problem (ℒ = {𝑙 , 𝑙 }). It was then improved to solve the general (color image segmentation)
and multi-labeling problems [17, 18]. The main idea of graph cuts is to employ the theories and algorithms of
the min-cut (s-t cut) and max-flow for binary segmentation. The graph 𝐺
𝐺

= (𝒱 , ℰ ), 𝒱

ℰ

=

ℰ
⏟

is defined as following.

= 𝒱 ∪ {𝑠, 𝑡},

∪ {〈𝑣, 𝑠〉|𝑣 ∈ 𝒱} ∪ {〈𝑣, 𝑡〉|𝑣 ∈ 𝒱}

(7)

9 / 40

As shown in Eq. (7), graph cuts introduces two auxiliary nodes s and t representing the source and sink,
respectively; the newly added edges between each node in 𝒱 and the terminal nodes (s and t) are called the tlinks, and the original edges among neighboring nodes in ℰ are called the n-links. A cut (𝐶 ) of 𝐺

is

defined by
𝐶

= 〈𝑣 , 𝑣 〉 〈𝑣 , 𝑣 〉 ∈ 𝐺

𝑎𝑛𝑑 𝑥 ≠ 𝑥

(8)

where 𝑥 and 𝑥 are the labels for nodes 𝑣 and 𝑣 , respectively; and the default labels for nodes s and t
are l1 and l2, respectively. The cost of the cut 𝐶
𝐸(𝐶 ) = ∑〈
=∑

, 〉∈
∈𝒱 𝑥

is given by

𝑤(𝑣 , 𝑣 )
∙ 𝑤(𝑣 , 𝑡) + (1 − 𝑥 )𝑤(𝑣 , 𝑠) + 𝛽 ∑

∈𝒱, ∈

𝑥 −𝑥

𝑤 𝑣 ,𝑣

(9)

In Eq. (9), 𝑤 defines the weight of edge in ℰ ; and the cost function of a cut can be decomposed into
two terms: the data term and the smoothness term. The data term is similar to the likelihood energy of MAPMRF, which is usually modeled based on domain related knowledge (e.g., color distribution, shape and location); and the smoothness term is usually to penalize the discontinuity between neighboring nodes. The segmentation of an image is to find a cut that minimizes 𝐸(𝐶 ); the minimum s-t cut is equivalent to maximize
the flow (max-flow) from s to t according to the Ford-Fulkerson theorem [19]. If a cost function is submodular
[20], it can be represented by a graph (𝐺 ), and the function can be minimized by using the max-flow algorithm. The Boykov-Kolmogorov version [21] of the implementation of the max-flow algorithm can be downloaded from http://vision.csd.uwo.ca/code/. However, it is not for BUS segmentation; and users need to modify
the code accordingly for BUS segmentation.
Applying graph cuts for BUS image segmentation, the key issue is how to define the data and smoothness
terms. [22] proposed a fully automatic BUS image segmentation framework in which the cost function modeled the information in the frequency and space domains. The data term modeled the tumor pose, position and
intensity distribution; and the weights are given by
𝑤(𝑣 , 𝑡) = −𝑙𝑜𝑔[𝐺(𝑖) ∙ Pr(𝑑 |𝑥 = 1)]

(10)

𝑤(𝑣 , 𝑠) = −𝑙𝑜𝑔 1 − 𝐺(𝑖) ∙ Pr(𝑑 |𝑥 = 0)

(11)

where G(i) is a 2D elliptical Gaussian function to model the tumor pose and position, and is constructed based
on the results of the ROI generation [22]; and 𝑃𝑟(𝑑 |𝑥 ) defines the intensity distributions of the tumor and
nor-tumor regions. The smoothness term is constructed based on the intensity discontinuities in the space domain and the edge in the frequency domain; and the weight function is defined by
10 / 40

𝑤 𝑣 ,𝑣

= 1 − 𝐸𝐷 𝑣 , 𝑣

+𝑒

𝐷 𝑣 ,𝑣

(12)

where ED is the edge detector defined in the frequency domain, and De is the Euclidean distance between two
nodes. For details, refer [22, 23].
In [24], user needs to specify a group of foreground (tumor) regions (F) and a group of background regions
(B) to initialize the graph. The weight of any t-link is set to ∞ if the node belongs to 𝐹 ∩ 𝐵, and all other
weights of t-links are set to 0; the weight function of the smoothness term is defined by utilizing region intensity
difference and edge strength [138]. In [25], the weights of t-links were determined online by training a Probabilistic Boosting Tree (PBT) [26] classifier; and 𝑤(𝑣 , 𝑣 ) was learned offline utilizing the training set by the
PBT. Hao et al. [27] constructed a hierarchical multiscale superpixel classification framework to define the
weights in the data term. In [28], both the region-level [29] and pixel-level features were utilized to define the
weights in the data term; and all weights were learned by using a structural SVM [30].
3.3 Summary
Graph-based approaches account for the second largest portion of BUS image segmentation literature (Fig. 1).
They are among the earliest techniques for BUS image segmentation, fade away due to the successes of other
powerful approaches such as deformable models (section 3), and surge again because of the dramatic advances
of graph models and energy optimization algorithms.
MRF-MAP-ICM is a flexible framework for image multi-partition (not just tumor or non-tumor for BUS
images). Most BUS image segmentation approaches based on this framework achieve good performance by
designing better likelihood energy and obtaining better initialization. Only obtaining locally optimal solution
is the main shortcoming of these approaches. Graph cuts provides an efficient framework for image bi-partition
and MRF energy global optimization, and is the main factor to make graph-based models popular again in
BUS image segmentation. The approaches based on graph cuts focus on designing more comprehensive data
and smoothness terms to deal with low contrast, inhomogeneity, and not well-defined boundary of BUS images.
The “shrink” problem is the common disadvantage of these approaches, and the extension [18] could only find
the approximate solution of multiple labeling of graph cuts. Normalized cut (N-Cut) [31] could avoid the
problem by considering both the disconnected links and the links inside each component. [27, 32 - 34] applied
normalized cut for BUS image segmentation. However, without the data term, N-Cut cannot integrate semantic
information into the energy, and usually needs user interaction or combining with other approach to achieve
good performance; and its high computational cost is another drawback of N-Cut.

11 / 40

A detailed comparison of seven typical graph-based BUS image segmentation approaches is listed in
Table 2. As illustrated in Table 2, two approaches [25, 28] learned all parameters of graph models by using
discriminative learning. This strategy enhances the robustness of graph models. Another potentially useful
strategy is to build high-order graph models, in which every pair of nodes in the graph has an edge; and it can
be applied to represent the global correlation among nodes, and can obtain a more representative smoothness
term. An efficient approach to optimize the fully connected graph model was proposed in [36].
Table 2. Comparison of graph-based approaches
Ref.

[9]

[13]

Year

1998

2016

Category
MRF-MAPICM
MRF-MAPICM

F/S

S

S

Images

30

33

Useful Strategies
Integrate texture distribution; estimate distribution parameters locally

Disadvantages

Issues

Depend heavily on parameters estimation; assume the Gaussian distribution

2.3

of features

Integrate tissue stiffness information

Assume the Gaussian distribution of

from ultrasound elastography

features

2.3

No distribution assumption;
[23]

2012

Graph cuts

F

184

construct smoothness term in both

The “shrink” problem

2.3

spatial and frequency domains
[24]

2010

Graph cuts

S

13

[25]

2010

Graph cuts

F

347

Graph cuts on regions
Learn the data and smoothness terms
using deterministic model

Manually set the foreground and background priors; “shrink” problem
The “shrink” problem

2.3
2.3 &
2.4

Integrate features of superpixel and
[28]

2013

Graph cuts

F

469

local detection windows; learn all
model parameters by using struc-

The “shrink” problem

2.3 &
2.4

tured support vector machine [30]
[32]

2012

N-cut

S

100

No “shrink” problem

Manually select ROI

2.3

F denotes fully automatic approach and S denotes semi-automatic approach; the column of Issues shows the issues of concern of each approach discussed in Sections 2.1 – 2.4.

4. Deformable models
Deformable models (DMs) are curves/surfaces that can move toward to the object boundary under the influence of forces defined on the curve or surface by using the information of image. DMs can deal with biological
structures with significant variability, and permit user to integrate expertise to guide the segmentation when
necessary; therefore, they have been applied to BUS image segmentation extensively. DMs are proposed by
Terzopoulos [37], and then become a popular and active field after the snake approach for planar image was
proposed by Kass et al. [38]. Generally, DMs can be classified into two categories according to the curve or
surface representation during deformation: (1) the parametric DMs (PDMs) and (2) the geometric DMs
(GDMs). In PDMs, a curve or surface is represented by its parametric form explicitly. GDMs represent curves
12 / 40

and surfaces implicitly as a level set of a scalar function. It can adapt to topological changes of targets, which
is helpful for segmenting multi-objects and objects with unknown topology.
4.1 Parametric deformable models
Finding object boundaries using PDMs is formulated to minimize an energy function including internal and
external energies. The internal term controls the continuity and smoothness of curves/surfaces; and the external
energy function is calculated using image features to attract curves to object boundary. Let 𝐶(𝑝) =
(𝑥(𝑝), 𝑦(𝑝)), 𝑝 ∈ [0, 1] be a deformable curve; it moves to the optimal object boundary by minimizing
(13)

ℰ(𝐶) = ∫ (𝛼 ∙ (𝐶 ) + 𝛽 ∙ (𝐶 ) )𝑑𝑝 + ∫ 𝑃 𝐶(𝑝) 𝑑𝑝
ℰ

ℰ

( )

( )

where 𝐶 indicates the first order derivative of C that keeps the continuity of curve, and 𝐶

is the second

order derivative that controls the smoothness of curve; 𝛼 and 𝛽 are the weights; large 𝛼 will lead the
change in distances between points on curve to have high cost, and large 𝛽 will penalize more on non-smooth
curve. 𝑃 is the cost function based on image features and the general formulation of P in the original DMs
could be found in [38].
The problem of finding the curve C minimizing ℰ(𝐶) is to find the extrema of functional which satisfies
Euler-Lagrange equation [38]:
ℰ( )

= −α𝐶 + 𝛽𝐶

+ ∇𝑃 = 0

(14)

The above equation states that the functional derivative vanishes at the optimal curve. Given an initial curve
C0, we can apply the gradient descent minimization to optimize ℰ(𝐶) iteratively. At step t + 1, the pth point
on curve C is updated as
𝐶

(𝑝) = 𝐶 (𝑝) + 𝛾𝐹 𝐶 (𝑝)

(15)

where 𝛾 is the step size, F is the force on curve defined as the negative of the functional derivative
𝐹 = α(𝐶 ) − 𝛽(𝐶

) −∇𝑃

(16)

where the internal forces Fint discourage curve stretching and bending, and the external forces Fext often are
composed of multiple forces to make the models flexible enough to handle different tasks. The default PDMs
discussed above may converge poorly for real image segmentation tasks because of several limitations, e.g.,
failing to converge to concave boundaries, and poor performance if the initial curve is not close to the minimum.
Several variants [39, 70, 146] have been proposed to address the problems of the default PDMs by introducing
different external energy.
13 / 40

4.2 Geometric deformable models (GDMs)
GDMs [40, 41] are proposed to overcome the two primary limitations of PDMs: lack of topology adaptivity
and parameterization dependence. In GDMs, a 2D curve (C) at time t is represented implicitly as the zero-level
set of a scalar function (𝜙): 𝐶 = {𝐶(𝑝, 𝑡) = (𝑥, 𝑦)|𝜙(𝑥, 𝑦, 𝑡) = 0}, and the curve deformation utilizes curve’s
geometric measures such as the unit norm and curvature, and image properties.
Let 𝑣⃑(𝑝, 𝑡) and 𝑛⃑(𝑝, 𝑡) be the speed and the unit normal vector of the pth point of an evolving curve at
time t, respectively; and the partial derivative of C with respect to t can be defined as the normal component
of 𝑣⃑:
(17)

= 𝑣⃑ ∙ 𝑛⃑,
since the tangential component does not affect the geometry of an evolving curve.

Because of the curve representation by using level set function in GDMs, the deformation of curve is
realized by evolving the level set function rather than tracking the evolution of the curve, which enables the
automatic topology adaption of the embedded curve. Given a level set function 𝜙(𝑥, 𝑦, 𝑡) and a curve
{𝐶(𝑝, 𝑡)}, we have
𝜙(𝐶(𝑝, 𝑡), 𝑡) = 0, 𝑎𝑛𝑑

+ ∇𝜙

(18)

=0
∇

If 𝜙 is negative inside and positive outside, the inside-pointing unit norm can be defined as 𝑛⃑ = − |∇ |, and
we can obtain
= −∇𝜙 ∙ 𝑣⃑ ∙ 𝑛⃑ = 𝑣⃑ ∙ |∇𝜙|

(19)

Notice that the speed function 𝑣⃑ is the key of GDMs; and it is usually defined as a function of the curvature (𝜅); to avoid the final curve shrinking to a point, image related information such as gradient is usually
formulated to slow down the evolving process and to attract the evolving curve to the desired boundary. Three
important issues need to consider in implementing GDMs for BUS image segmentation:
(1) Designing the speed function. The foremost step in applying GDM is to design an appropriate speed
function that can stop the evolving curve at the desirable object contour. A commonly used speed function is
formulated as [42-44]
𝑣⃑ = 𝑔 ∙ (𝑉 + 𝜅) − 〈∇𝑔, 𝑛⃑〉

(20)

𝑔=

(21)

|∇(

∗ )|

14 / 40

where 𝑉 is a constant to speed up the curve deformation, g is the stopping function by using image gradient
to slow down and to stop the curve evolving at the high gradient locations, and the second term (〈∇𝑔, 𝑛⃑〉) makes
the stopping power stronger when there are no perfect edges. (2) Initializing the level set function. The initial
level set function is usually the signed distance from each point to the zero level set. A fast computation approach is described in [41]. (3) Reinitializing the level set function. The speed function is defined only on the
zero level set; the level function deformation requires it to be extended to all level sets; and the extensions [45]
can cause the irregularity problem of level set function. The re-initialization is applied to provide a numerical
approach to replace the level set function with newly signed distance functions. For more information about
the re-initialization, refer [45-47].
4.3 Edge-based vs. Region-based DMs
DMs provide a flexible image segmentation framework that can incorporate both low-level image features and
various prior knowledge, such as edge, local region statistics, shape, and intensity distribution. The DMs can
be classified into edge-based [38, 41, 42, 44, 48] and region-based [47, 49, 66] according to the information to
construct the external force in PDMs or speed function in GDMs. Edge-based DMs aim to attract the evolving
curve to object boundary by defining the deformation force or speed using image gradient [42-44], and the
models depend on image gradient to stop curve deformation. Region-based DMs model region features to
guide the curve deformation and can achieve better performance than edge-based models; specially, if images
have plenty of noise and weak object boundary.
4.4 Deformable models for BUS image segmentation
The application of DMs for BUS image segmentation can be divided into two stages. In the first stage, BUS
image segmentation approaches apply the ideas of PDMs, and focus on developing method to generate good
initialization. To achieve global deformation and local variation of irregular tumor, Chen et al. [50] applied
the B-snake model [51] for BUS image sequence segmentation. In [52], Chen et al. proposed a cell-based dual
snake [53] to handle the two problems of applying traditional DMs for BUS image segmentation: (1) initial
contour should be placed close to the tumor boundary; and (2) difficulty to capture highly winding tumor
boundary. In [54, 55], Madabhushi et al. proposed a fully automatic approach for BUS image segmentation
using PDM which is initialized by utilizing the boundary points produced in tumor localization step. In [56,
57], Sahiner applied PDM for 3D BUS tumor segmentation, the external forces had two terms: the first term
was defined on image gradient by using 3×3 Sobel filters, and the second term is the balloon force. In [58, 59],
Chang et al. applied DM for 3D breast ultrasound image segmentation. The sticks filter [60] was utilized to
15 / 40

enhance edge and reduce speckle noise. Huang et al. [61] proposed an automatic BUS image segmentation
approach by using the gradient vector flow (GVF) model [70]. The initial boundary was obtained by using
Watershed approach. Yap et al. [62] proposed a fully automatic approach by applying GVF model. In its initial
contour generation step, a fixed threshold was employed for candidate generation.
In the second stage, many works modified DMs to improve segmentation performance. Yezzi et al. [42]
modified traditional GDMs by having an additional term (〈∇𝑔, 𝑛⃑〉) that provided stronger stopping power at
object edges. Deng et al. [63] proposed a fast GDM method for biomedical image segmentation. It only updated
the speed function and evolved the level set functions in a small window. The experimental results showed
that it was much faster than the narrow band algorithm [52]. Liu et al. [64] proposed a fully automatic BUS
image segmentation based on texture classification and GDM. Gomez et al. [65] proposed a BUS image segmentation approach based on the active contour without edges (ACWE) model [66] which defined the stopping
term using Mumford-Shah technique and was robust to segment images with weak boundaries.
Liu et al. [67] proposed an interactive BUS image segmentation approach utilizing region-based GDMs,
in which the probability density difference between the intensity distributions (tumor and background) and the
estimated Rayleigh distribution was applied to enforce priors of intensity distribution. The approach was compared with two other GDM approaches [66, 68] using 79 BUS images. Rodtook et al. [69] modified the generalized GVF [70] approach based on a continuous force field analysis, and applied it to BUS image segmentation. Daoud et al. [71] considered the SNR and local intensity value as two important features for estimating
tumor boundary, and built a two-fold termination criterion based on the two features in discrete dynamic DMs
[72]. Gao et al. [73] proposed a level set approach for BUS image segmentation based on the method in [47]
by redefining the edge-based stop function using phase congruency [74] which is invariant to intensity magnitude, and integrated GVF model into the level set framework. Cai et al. [75] proposed a phase-based DM in
which the local region statistics [49] was introduced to solve the inhomogeneous intensity problem, and the
phase-based edge indicator is used to replace the gradient-based edge operator. Lin et al. [76] modified the
local region-based level set approach [77] by using additional constrained energies centered at four markers
specified by radiologist. [78] proposed a fully automatic robust region-based level set approach with contour
points classification (low contrast class and high contrast class). For the points in the low contrast class, both
the global and local region-based energies [66, 77] were used; while for the high contrast class, only the local
region-based [77] energy was utilized. [79] adopted the region-based approach in [78], proposed a learning

16 / 40

based approach (multivariate linear regression and support vector regression) to produce the parameters adaptively. Yuan et al. [80] proposed a new level set based DM approach; the local divergence and a smoothing
kernel were introduced to improve the speed function. Kuo et al. [81, 82] utilized user interaction to generate
the volume of interest (VOI), applied the radial-gradient index [83] to estimate the initial lesion boundary, and
implemented the region-based DM [48, 49] iteratively to find the final contour. The stopping criterion was
defined as (𝐼 ̅

− 𝐼 ̅ ) − (𝐼 ̅

− 𝐼 ̅ ) = 0 [84], where 𝐼 ̅ and 𝐼 ̅

were the mean intensities inside and

outside the segmented regions at step t, respectively.
Table 3. Comparison of BUS image segmentation approaches based on deformable models
Ref.

Year

Category

F/S

Images

Useful Strategies

[55]

2003

PDMs

F

90

[58]

[57]

[62]

[64]

[67]

2003

2004

2007

2009

2010

PDMs

PDMS

PDMS

PDMs

GDMs

F

S

F

F

S

8(3D)

Disadvantages

Issues

Use the balloon force to increase the attraction

Fixed RP; difficult to set the

2.2 &

range

strength of the balloon force

2.3

Define the external force using local texture features

Validated only on a small dataset,

2.2 &

and sensitive to initialization

2.3
2.3

102

Use the balloon force to increase the attraction

No quantitative evaluation of the

(3D)

range

segmentation

360

Use GVF to extend the attraction range and to han-

Fixed threshold and RP; no quan-

2.2 &

dle concave boundaries

titative evaluation

2.3

Use a well-trained texture classifier to detect tumor

Predefined rules to exclude false

2.2 &

ROI

classified regions

2.3

Model the difference between the regional intensity

Slow; sensitive to initialization

2.3

Redefine the edge-based stopping function using

Validated only on a small dataset;

2.3

phase information

sensitive to noise

Use both local statistics and phase information to

Slow

2.3

Slow and sensitive to initialization

2.2 &

103

79

distribution and the estimated prior distribution
[73]

[75]

2012

2013

PDMs

GDMs

S

S

20

168

define the speed function; and handle weak boundary and inhomogeneity problems better
[78]

2013

GDMs

F

861

Region-based GDM and solve the inhomogeneity
problem better

[81]

2014

GDMs

S

98(3D)

2.3

Use Region-based GDM and handle inhomogeneity

Slow and need user interaction to

problem

extract VOI

2.3

F denotes fully automatic approach and S denotes semi-automatic approach; the column of Issues shows the issues of concern of each approach discussed in Sections 2.1 – 2.4.

4.5 Summary
DM is the most popular approach applied to BUS image segmentation. For PDMs, the explicit curve or surface
representation allows direct model interaction and can lead to fast implementation. The results of most PDMs
are sensitive to initialization, and different initial curve or surface may converge to different local minimal
locations and lead to quite different results; consequently, many variants of PDMs extend the attraction range
17 / 40

to avoid local minima. The curves/surfaces of PDMs do not split and merge during the deforming process,
which makes PDMs unable to adapt to topological change and to segment multiple objects with single initialization. GDMs apply level set functions to represent curves and surfaces implicitly, and inspire great progress
in the related fields. There are two advantages of GDMs: (1) they can allow shapes to change topology during
the evolving process, which makes them suitable for segmenting multiple objects and time-varying objects;
and (2) the numerical computation of the curve and surface propagation can be implemented without parameterizing the objects. GDMs transfer the n-dimensional curve/surface deformation into n+1-dimensional level
set function, which needs to extend the speed function to all level set functions and increases the computational
cost greatly. Table 3 presents a detailed comparison of 10 typical DMs-based BUS image segmentation approaches. Due to the advantages, GDMs become more popular than traditional PDMs in BUS image segmentation; and most successful approaches focus on improving the performance of GDMs to deal with the weak
boundary and inhomogeneity of BUS images. There are two useful strategies: (1) redefining the stopping
function (𝑔), and making it independent of image gradient; and (2) redesigning the speed function by using
regional statistics.
5. Learning-based approaches
Image segmentation can also be viewed as a classification problem, i.e., classifying pixels or superpixels into
different categories. Therefore, it is quite common to apply machine learning approaches to image segmentation tasks. Both supervised and unsupervised learning approaches have been employed in BUS image segmentation.
5.1 Unsupervised learning approaches
K-means and Fuzzy C-means (FCM) are two popular unsupervised learning (clustering) approaches. Because
K-means can be viewed as a special case of FCM, we only present the theoretical background of FCM in this
section. FCM was proposed in [85] and improved in [86]. Let 𝐷 = {𝑑 , ⋯ 𝑑 } be a finite set of data (pixels
or superpixels), 𝐿𝐶𝑠 = {𝑐𝑡 }

be a list of C cluster centers; and FCM partitions set D into C clusters by

minimizing the following objective function:
𝑚𝑖𝑛 ∑

∑

(𝑢 )

𝑑 − 𝑐𝑡

(22)

In Eq. (22), 𝑢 ∈ [0,1] is the membership value representing the degree of data point 𝑥 belonging to cluster 𝑗, and is given by
(23)

𝑢 =
∑

18 / 40

where m (𝑚 ∈ 𝑅 and 𝑚 ≥ 1) is the fuzzifier, and determines the degree of cluster fuzziness; a large m leads
fuzzier cluster (smaller 𝑢 ); if m = 1, 𝑢

takes values 0 or 1, which implies a hard partition (K-means); and

m is usually set to 2 if no domain knowledge is introduced. The cluster centers are computed on all data points
and weighted by their membership values:
𝑐𝑡 =

∑
∑

(24)

The objective function (Eq. (22)) is optimized iteratively to find the local minimum in two simple steps: (1)
decide the number of clusters (C) and assign the initial membership values (𝑢 ); and (2) iteratively update the
cluster centers (Eq. (24)) and the membership values (Eq. (23)) until the membership values’ change between
two iterations is less than a predefined threshold.
The main advantage of the FCM is that each data point can belong to every cluster with a corresponding
membership value rather than just belongs to one cluster as in K-means, and FCM can achieve better performance for overlapped data points. However, like K-means, the FCM algorithm can only find the local minima
and the results depend on the initialization. In [7, 9, 10], K-means was utilized to estimate the parameters of
distributions in graph-based models, and the predefined number of clusters should be set. Xu et al. [87] proposed a BUS image segmentation method using the spatial FCM (sFCM) [88] with local texture and intensity
features. Lo et al. [89] applied FCM to generate image regions in four clusters, then extracted the morphology,
location, and size features of each region; and finally trained a linear regression model [90] to produce the
tumor likelihoods for all regions. The region with the highest likelihood is considered as a tumor. Moon et al.
[91] applied FCM to image regions produced by using the mean shift method [92]; and [91] trained a linear
regression model to estimate the tumor likelihoods of candidate regions utilizing seven quantitative features
which were extracted according to the American College of Radiology (ACR) Breast Imaging Reporting and
Data System (BI-RADS) [93]. [89, 91] did not discuss how to initialize the membership values for FCM. To
deal with the blur boundary and uncertainty in BUS images, Shan et al. [94, 95] extended the FCM and proposed the neutrosophic l-means (NLM) clustering which takes the indeterminacy of membership into consideration, and can handle the uncertainty in BUS images much better.
5.2 Supervised learning approaches
5.2.1 Support vector machine (SVM)
SVM is one of the most popular supervised-learning models in machine learning, and can be utilized for both
linear classification (linear SVM) and non-linear classification (kernel SVM) [96, 99] by mapping its inputs to

19 / 40

high dimensional spaces. Let {(𝑑 , 𝑥 )}

be a training dataset of n points where 𝑥 is either 1 or -1, indi-

cating the class of data point 𝑑 ; and SVM aims to find a hyperplane which can separate the training samples
by a gap as wide as possible. Let w be the normal vector to the hyperplane, and {𝜁 = 𝑚𝑎𝑥(0, 1 − 𝑥 (𝑤 ∙ 𝑑 +
𝑏))}

be slack variables for the soft margins; then the problem can be formulated as a constrained quadratic

optimization problem [97]
𝑚𝑖𝑛

∑

𝜁 + 𝜆‖𝑤‖

𝑠. 𝑡. ∀ 𝑖, 𝑥 (𝑑 ∙ 𝑤 + 𝑏) ≥ 1 − 𝜁 𝑎𝑛𝑑 𝜁 ≥ 0

(25)

Finally, w and b learned from the training dataset can be used to classify new data by computing 𝑥 =
𝑠𝑔𝑛(𝑑 ∙ 𝑤 + 𝑏). Liu et al. [98] trained a kernel SVM classifier [99] using the local image features to classify
small image lattices (16 × 16) into tumor or non-tumor classes; the radius basis function (RBF) was utilized;
and 18 features, including 16 features from co-occurrence matrix and the mean and variance of the intensities,
were extracted from a lattice. Jiang et al. [100] proposed two-step BUS segmentation approach. First, a set of
candidate tumor regions were produced by using Adaboost classifier [101] and 24 Haar-like features [102];
and a SVM classifier was trained using the quantized intensity features produced by K-means clustering to
determine the false positive and true positive regions. Second, random walk [173] was applied to generate the
final tumor boundary by placing seed at the center of each true region.
5.2.2 Artificial Neural network (ANN)
ANN is another popular supervised learning approach for BUS image segmentation. A typical ANN has three
layers: an input layer, a hidden layer and an output layer, interconnected by weighted links, e.g., 𝑤 =
[𝑤 , , ⋯ , 𝑤

,

]

is the weight vector of the links between the jth hidden units and the input units, and 𝑤 =

[𝑤

,

]

is the weight vector between the kth unit in the output layer and the hidden units. The units

,

,⋯,𝑤

in the layers are usually called ‘neurons’. The input neurons represent the feature vector 𝑥 = [𝑥 , ⋯ , 𝑥 ] ;
hj is the output of the jth hidden neuron; and 𝑧 = [𝑧 , ⋯ , 𝑧 ] yielded in the output layers will be used for
classification. The output of the kth neuron in the output layer (𝑧 ) is
𝑧 =𝜑 ∑

𝑤

,

∙𝜑

𝑤

∙𝑥

(26)

where 𝜑(∙) is the activation function of a neuron (in hidden or output layers), and converts a neuron’s
weighted input to its output value; and the preferred activation function should be non-linear and differentiable
such as the sigmoid and hyperbolic tangent functions.
Huang et al. [103] proposed an ANN-based method to segment 3D BUS images by processing 2D image
slices. First, thresholding was applied to generate candidate regions; then five region features (average gray
20 / 40

level intensity, entropy, ratio of region size to slice size, ratio of region size to the size of its bounding box,
and the distance from the region center to image center), were used as the inputs of NN. The number of hidden
unites and output units was not discussed. [104] trained an ANN to generate the threshold for BUS image
segmentation. Two feature extraction approaches were proposed: 1) using 128 × nkey SIFT features where
nkey is the number of key points; and 2) exacting 4 texture features (contrast, correlation, energy and homogeneity) of a 40×40 region. The ANN has 3 layers, 60 nodes in hidden layer, and one node in the output layer.
The stop criterion is 10-7 of the MSE. Shan et al. [105, 106] trained an ANN using three new features: the phase
in the max-energy orientation (PMO) based on phase congruency, radial distance (RD) and the joint probability
of intensity and texture [30]. The NN had 6 hidden units and 1 output unit.
5.2.3 Naive Bayesian classifiers (NBCs)
NBCs are a family of probabilistic classifiers based on the strong independence assumption: given the
class variable, each feature is independent of other features in the feature vector. By using the strong independence assumption and the Bayes’ theorem, the conditional distribution over the class variable is
𝑝(𝑥 |𝑑) = 𝑝(𝑥 ) ∏
where 𝑑 = [𝑑 , ⋯ , 𝑑 ]

𝑝(𝑑 |𝑥 ) , 𝑘 = 1, ⋯ , 𝐾

is the vector of n independent features, and 𝑥 = [𝑥 , ⋯ 𝑥 ]

(27)
is K class labels; 𝑍 =

𝑝(𝑥) is a constant if the values of the feature variables are known; and 𝑝(𝑥 ) is the prior distribution of 𝑥 .
NBC commonly combines the conditional distribution and the MAP decision rule to construct the classifier:
𝑥 = argmax 𝑝(𝑥 ) ∏

𝑝(𝑑 |𝑥 )

(28)

Applying NBC, the first thing is to calculate the prior by assuming equiprobable classes (𝑝(𝑙 ) = 𝑝(𝑙 ), 𝑖 ≠ 𝑗)
or by estimating from the training set; and then one must assume the conditional distribution (𝑝(𝑥 |𝑙 )) over
feature variables or learn a nonparametric model from training set.
Yang et al. [107] proposed a whole breast tumor detection method by classifying slice pixels into tumor
(x1) or normal tissue (x2) by using NBC. Two features, local (5 × 5 mask) intensity mean and stick filter [60]
output, were utilized; the class priors were assumed to be equiprobable, and the conditional distribution of
each feature (𝑥 ) was assumed to be Rayleigh distribution:
𝑝(𝑥 |𝑙 ) =

𝑒

⁄

, 𝑘 = 1, 2

(29)

where 𝜎 is the Rayleigh parameter and can be estimated from training data. NBC produced a set of suspected
lesions, and a two-phase lesion selection method based on region shape features and region continuity and
volume size were applied for final tumor region decision [108].
21 / 40

Table 4. Comparison of learning-based BUS image segmentation approaches
Ref.

Year

Category

[7, 9,

95, 98,

Adaptive

10]

2003

K-means

[89]

2014

FCM

[91]

[98]

2014

2010

FCM

SVM

F/S

Images

S

< 10

Advantages
Achieved better performance than
the standard K-means on images
with local intensity variations

F

F

F

58

148

112

[100]

2012

SVM

F

112

[103]

2008

ANN

F

93 (3D)

High sensitive rate

High sensitive rate

Disadvantages
Sensitive to initialization; only used for estimating distribution parameters
Sensitive to initialization; high false positive rate
Sensitive to initialization; used fixed threshold

Utilized local texture features to

Only produced rough tumor boundaries; de-

classify local lattices and achieved

pended on post processing rules to refine

high precision and recall ratio

the results

Balanced sensitivity and specific-

Slow; depended on random walk to gener-

ity

ate the final boundary
Depended on fixed threshold to produce

Fully automatic

candidate regions; relatively low performance

Issues

2.3

2.2 &
2.3
2.2 &
2.3
2.2 &
2.3
2.2 &
2.3
2.2 &
2.3

Achieved good performance by
[106]

2012

ANN

F

120

using the phase information, ra-

Depended on fixed reference point to gener-

dial distance and the joint distri-

ate the initial ROI

2.2 &
2.3

bution of texture and intensity
Depended on the assumption of intensity
[107]

2012

NBC

F

31

Achieved high sensitive ratio

distribution; depended on post selection to
reduce FPR

2.2 &
2.3

F denotes fully automatic approach and S denotes semi-automatic approach; the column of Issues shows the issues of concern of each approach discussed in Sections 2.1 – 2.4.

5.3 Summary
Unsupervised learning is simple and fast, and has been widely utilized in many BUS image segmentation
approaches. However, because of the challenging nature of BUS image segmentation, unsupervised approaches are only employed as a preprocessing step to generate candidate image regions and more sophisticated methods are usually employed to perform the final segmentation; for example, in [7, 9, 10], K-means
was utilized to estimate the initial parameters of intensity or texture distributions. Supervised learning provides
a good framework to integrate different levels of features and to learn the knowledge between the inputs and
target outputs. Many BUS image segmentation approaches achieve good performance by using supervised
learning approaches. Most of them design features using domain knowledge (feature engineering) to improve
the performance. They can be integrated with other segmentation techniques, e.g., in [25, 28], supervised
learning approaches learned the parameters of the graph-based models from the training data; and they also
22 / 40

can be used to perform segmentation alone, e.g., in [120], a well-trained ANN was applied to perform tumor
segmentation. One common disadvantage of the supervised learning approaches is that they cannot produce
accurate tumor boundary, and refinement is usually necessary. Table 4 presents a detailed comparison of 10
learning-based BUS image segmentation approaches.
Learning-based approaches thrive in BUS image segmentation in the last decade and we believe new deep
learning techniques [162] such as deep convolutional neural networks (CNNs) and recurrent neural network
(RNN) will make great progress in segmenting BUS images in the near future. For more details about applying
deep learning to medical image analysis, refer the survey paper [171].
6. Classical Approaches: thresholding, region growing, and watershed
In this section, we will discuss some classical segmentation approaches applied to BUS image segmentation,
and they are usually combined with other methods to achieve good performance.
6.1 Thresholding
Thresholding is the most intuitive, simple and fast segmentation approach, and enjoys the popularity in BUS
image segmentation. It groups image pixels directly into regions by using a single threshold (two classes) or
multiple thresholds (multiple classes) based on pixel features (e.g., intensity, color, local mean, standard deviation, etc). Let th be the threshold that segments image pixels into two classes. When th is a constant over
entire image, the method is called global thresholding; if th is changing over the local features, the method is
referred as adaptive/local thresholding. Global thresholding is fast and works well when the intensity distributions of objects and background are sufficiently distinct; however, if the object-background contrast is low,
image is noisy, and/or illumination varies across the image, global thresholding cannot achieve good performance. However, global thresholding is often used as a pre-segmentation step in BUS image segmentation.
There are three main approaches to select the global threshold. The first approach is to choose an empirical
value as the threshold for the whole dataset [109-111]; the second approach is to select the threshold for each
image based on domain related rules [112, 113]; and the third is to generate the threshold automatically based
on statistical-decision theory [22, 114, 115].
6.2 Region growing
Region growing extracts regions from a set of pixels (seeds) and grows seeds to bigger regions utilizing predefined growth criteria. Seed generation: the seeds can be placed by user interactively [116, 117] or generated
automatically [54, 55, 113, 118]. [54, 55] selected a seed (𝑝∗ ) automatically from a set of candidate pixels by
formulating empirical rules [55]:
23 / 40

,

𝑝∗ = argmax

∙ℐ ∙

(30)

where 𝑖 and 𝑡 are the intensity and texture values of pixel p, respectively; Γ(𝑖 , 𝑡 ) is pixel p’s value of
joint intensity and texture probability; ℐ refers to the local mean value of Γ around p; 𝑌 is the row position
(origin at the lower-left of image) of p and avoids selecting seed from the shadowing region appearing at the
bottom of BUS image; and 𝑑

is the distance between p and image center. [118] used this method for seed

generation. For each pixel p adjacent to the seed region, if p satisfied (growing criterion): ℐ /ℐ

∗

∈ [𝛽 , 𝛽 ];

p will be added to the seed region, where 𝛽 and 𝛽 are selected by experiment. The growing process will
stop until no more pixel satisfying the condition
Shan et al. [113] proposed another automatic seed generation approach. Thresholding was used to generate a group of candidate regions; and the region ranking criteria based on region location, size, and local
feature, were utilized to determine a true tumor region (𝑟 ∗ ):
( )

𝑟 ∗ = argmax

∙

(31)

( )

where 𝐴(𝑟) is the number of pixels in region r; 𝑑 is the distance between the center of r and a fixed reference point (center of the top half of image); 𝑟 is the center of region r; and 𝑣𝑎𝑟(𝑟 ) is the local variance of
a circular region at the center of region r; and a pixel inside region 𝑟 ∗ will be selected as the seed. Let I(p)
and 𝐼 (̅ 𝑝) be intensity and local mean intensity of pixel p, respectively, the growing criterion is defined by
1−𝑒

( )

≤ 𝑡 𝑎𝑛𝑑 1 −

|𝐼(𝑝) − 𝑚(𝑟 )|
≥ 𝑡 𝑜𝑟
𝑚(𝑟 )

( )

1−𝑒

≥ 𝑡 𝑎𝑛𝑑 1 −

| (̅ )

( )|
( )

≥𝑡

(32)

where m(r) is the average intensity of the current seed region, and t1, t2, and t3 are set as 0.5, 0.2 and 0.99,
respectively. The growing processing stops when no more pixel satisfies the above condition.
Kwak et al. [117] defined the cost of growing a region by modelling common contour smoothness and
region similarity (mean intensity and size):
𝐽(𝑟 , 𝑟) =

( )
∙

( )

( , )

∙

( )∙ ( )
,𝑟
( ) ( )

∈ 𝑁(𝑟 )

(33)

where 𝑚(∙) denotes the mean intensity of a region, 𝐴(∙) is the pixel number of the region, 𝐿𝐶(𝑟 , 𝑟) is the
length of the common contour between the seed region rs and region r, 𝑁(𝑟 ) is a set of regions adjacent to
rs, and 𝛼 and 𝛽 are two predefined constants. The region with the minimum value of J will be added to the
seed region. The growing repeats until ∑

∈ ( ) 𝐽(𝑟

, 𝑟) over the length of contour rs reaches the maximum.

6.3 Watershed
24 / 40

Watershed is a powerful image segmentation method, and usually produces more stable results than thresholding and region growing approaches. There are different definitions of watershed [119, 120]. The most popular definition is the watershed by flooding [119]. The most common implementation of watershed for image
segmentation can be found in [121]. The key issue in watershed segmentation is the marker selection. One
approach is to choose the local minimum gradient as the marker, which will usually result in over-segmentation
due to noise, and further step such as region merging should be involved. The other approaches choose makers
based on more complex predefined criteria that can utilize the task-related priors.
Table 5. Comparison of classical approaches
Ref.

Year

Category

[62,

2007

Global

111]

2008

thresholding

Candidate tumor

Iterative thresholding by finding the

Depended on post empirical rules to refine the

thresholding

region generation

local minima of histogram.

candidate regions; used fixed reference position.

ROI generation

Otsu’s algorithm [130]

Depended on image preprocessing.

2014

[55]

2003

Region grow

[117]

2005

Region grow

2010

Depended on image enhancement; could not

Global

[115]

[124]

Additional Comments

Fixed threshold

2008

2004

Threshold/Seed/Marker Generation

Pre-segmentation

[113]

[122]

Purpose

Global
thresholding

Watershed

Watershed

Pre-segmentation

Selected seed by formulating empirical rules.

Final segmenta-

User interaction to set an elliptical

tion

seed region

Final segmenta-

Selected marker by using intensity

tion

and connectivity

Pre-segmentation

[127]

2010

Watershed

Pre-segmentation

[128]

2014

Watershed

Pre-segmentation

adapt to variations of image quality.

Used fixed reference position (image center).
Depended on image enhancement; the growth
criteria were defined by formulating contour
roughness and region inhomogeneity.
Depended on image enhancement.

Decided the external and internal

Depended on image preprocessing; select 255

markers by computing the Beucher

groups of markers by thresholding image using

gradient [131] of the morphological

thresholds from 0 to 255; needed additional geo-

dilation and erosion of the binary

metrical measure [132, 133] to decide the final

image

tumor contour.

Used regions on the binary edge
map as markers
Local intensity minima

Used empirical rules to refine the results
Used empirical rules to refine the results

Huang et al. [122] applied the watershed to segment the preprocessed BUS images, and the markers were
selected based on grey level and connectivity. [109, 123] used watershed to segment ROI into small regions,
and used the predefined criteria (area, mean intensity, geodesic center, etc) to determine the final tumor region.
255 groups of markers were selected by thresholding (th = 1, 2, ⋯, 255) the image [124, 125]; the external
and the internal markers were defined by using the morphological dilation and erosion. Watershed method was
applied to generate 255 potential lesion boundaries by using the markers on different thresholds; the average
25 / 40

radial derivative (ARD) function [132, 133] was applied to determine the final tumor boundary. Zhang et al.
[126, 127] applied watershed to determine the boundaries of gray level images. The markers were set as the
connected dark regions. [128] applied watershed to generate meaningful regions, and refined the regions by
removing the top 50% hyper-echogenic (bright) regions and the regions connected to the image border to
generate candidate tumor regions; and the candidate regions were distinguished between tumors and non-tumors by using a logistic regression classifier [129] trained using region morphology, intensity and texture
features.
6.4 Summary
In this section, we present the theoretic background of three classical image segmentation approaches:
thresholding, region growing, and Watershed; and discuss their applications to BUS image segmentation. Table 5 gives a detailed comparison of 10 BUS image segmentation methods. The three approaches are quite
simple, fast, and efficient to conduct initial segmentation of BUS image, and facilitate further segmentation
procedures. To achieve good performance of BUS image segmentation, two additional steps are usually needed:
first, image preprocessing step is employed to improve image quality by denoising and enhancing contrast;
second, more delicate approaches are utilized to refine the segmentation results.
7. Other approaches
Beside the four main categories of BUS image segmentation approaches discussed in sections 2-5, there exist
some interesting approaches presented in few papers. We discuss them briefly in this section.
Cellular automata (CA): CA was introduced by von Neumann [134] and applied to interactive image
segmentation [135]. In image segmentation, a cell is usually associated with a pixel or superpixel. A CA is
defined as a triplet 𝐶𝐴 = (𝑆𝑡, 𝒩, 𝛿) where St is the state set, 𝒩 denotes the neighborhood system, and 𝛿 is
the transition function which defines the rule of updating the cell state based on the states of the neighborhood
cells in the previous step. Liu et al. [136] constructed the transition function by integrating the global information on the transition chain and local texture correlation. There are three main advantages of CA-based
approaches: (1) support multiple objects segmentation; (2) can generate precise object boundary and do not
have the “shrink” problem; and (3) support user input online. These approaches start with user interaction to
initialize seed cells, and then update the states of all other cells according to the evolution rule until reaching
the stable states or the fixed number of iterations. The computation cost is high; especially, when the image
size is large. For a fast CA-based segmentation approach, refer [137].

26 / 40

Cell competition: Chen et al. [138] proposed a cell-competition approach for BUS image segmentation.
The cells are small image regions generated by using a two-pass Watershed segmentation; and then adjacent
cells compete to generate new regions by splitting or merging. There are two types of competitions. In Type I
competition, two adjacent cells from different regions compete; a cell may split from a region and merge into
another region. In Type II competition, one cell splits from a multi-cell region and forms a single-cell region.
Cheng et al. [139] applied the approach to an initial slice selected by user, and used the results to partition the
cells of other slices into object or background regions. Chiang et al. [140] extended the approach to segment
3D BUS image and applied graph cuts for finding the final tumor boundary. No task-related knowledge is
integrated in the competition mechanism. It is simple and fast, but needs large amount of user interactions to
select ROI before the competition or to select tumor regions after the competition.
Radial gradient index (RGI): RGI [141] calculates around the boundary of each candidate partition, and
the partition with the largest RGI value was selected as the tumor region.
𝑅𝐺𝐼(ℳ ) = ∑

∈ℳ |∇ ( )|

∑

∈ℳ

⃑( )
)|

∇𝑓(𝑝) ∙ | ⃑(

(34)

In Eq. (34), ℳ is a set of contour points of the ith image partition; |∇𝑓(𝑝)| is the absolute value of the
intensity gradient at point p; and 𝑟⃑(𝑝) is the radial vector from the partition center to point p. The RGI value
measures the proportion of the intensity gradients of the boundary points along the radial direction. It takes
values in [-1, 1]; RGI value 1 indicates that all the gradients point outward along the radial vector; and -1
signifies that all the gradients point inward along the radial vector. For BUS tumor regions, the RGI values are
expected to close to 1. The application of RGI for BUS image segmentation can be found in [142 - 146]. The
RGI calculation is simple and easy to implement; however, it calculates a group of RGI values for each pixel,
and the computation cost is quite high; furthermore, it depends on image gradient, and cannot obtain accurate
tumor boundary of BUS image due to low image quality.
8. Conclusions and Future Directions
In this paper, we have reviewed the automatic BUS image segmentation approaches. A general comparison between the categories of BUS image segmentation approaches is listed in Table 6. The major future
directions of BUS image segmentation are summarized as follows:
Unconstrained BUS image segmentation techniques: currently, most BUS image segmentation approaches work well on BUS images collected in controlled settings such as high image contrast, less artifacts,
containing only one tumor per image, etc. However, their performance degrades greatly with BUS images
having large variations in image quality, degree and location of artifacts, and number of tumors per image.
27 / 40

Therefore, to promote the application of BUS CAD systems in clinical practice, it is crucial to develop unconstrained BUS segmentation techniques which are invariant to image settings. Potential directions are to learn
invariant and discriminative representations of tumors in BUS images, and to model human vision mechanism
[110, 154, 176].
Benchmark: A publicly accessible BUS image benchmark can be useful for comparing existing approaches, for discovering novel strategies that can contribute to better segmentation performance, for helping
researchers to develop better approaches, and for promoting the development and advance of breast cancer
research. Building of a publicly accessible BUS image dataset requires incredible effort (many years of hard
work, and large amount of resources); however, its impact will be significant and profound.
Table 6. General Comparison of the four main categories
Categories

Advantages

MRF-MAP

Organize BUS knowledge and image information in a

Only obtain local optimal solution;

approaches

unified framework; multiple-object segmentation

Sensitive to initial parameter estimation;
inefficient optimization algorithm

Graph-Based
Graph Cuts

Organize BUS knowledge and image information in a
unified framework; efficient optimization algorithm

PDM
DMs
GDM

Intuitive; fast
Adapt to multiple tumors in an BUS image

Unsupervised learnLearning-based

Disadvantages

Simple; fast

ing
Supervised

Integrate different levels of features and learn the

learning

knowledge between the inputs and target outputs

Classical approaches

Simple; fast

The “shrink” problem
Cannot adapt to segment multiple tumors;
sensitive to initialization
Sensitive to initialization; slow
Sensitive to initialization;
only applied in the BUS image preprocessing step

refinement is usually required
Utilized for initial BUS image segmentation;
Sensitive to image noise; refinement is required

Deep learning: in the last several years, deep learning has demonstrated impressive performance for many
tasks such as object recognition [158], image classification [159], semantic segmentation [160], facial expression recognition [163], speech recognition [164], medical applications [161, 170], etc. Deep learning models
have great potential to achieve good performance for BUS image segmentation because of their ability to learn
compact image representation using sufficiently large BUS image dataset.
High performance segmentation: segmentation performance is usually evaluated by memory cost, speed,
and accuracy. Currently, many BUS image segmentation approaches are computation and memory intensive,
which limits their widespread applications. For example, it is difficult to integrate resource-intensive algorithms into portable BUS devices for real time applications. In some resource-limited regions or countries,
28 / 40

many lives were lost because of unavailability of accurate and low-cost breast cancer detection techniques and
devices; high performance approaches consume much less resources than traditional approaches, and is vitally
important to provide an affordable means for early detection of breast cancer.
In addition, we have tried to collect codes or software for BUS image segmentation in the public domain;
however, we could not find any yet. It may be a future task for the research society.
References
[1] R.L. Siegel, K.D. Miller, A. Jemal, Cancer statistics, 2015, CA-Cancer J. Clin., 65 (2015) 5-29.
[2] L. Fan, K. Strasser-Weippl, J.-J. Li, J. St Louis, D.M. Finkelstein, K.-D. Yu, W.-Q. Chen, Z.-M. Shao, P.E.
Goss, Breast cancer in China, Lancet Oncol., 15 (2014) e279-e289.
[3] K. Drukker, M.L. Giger, C.J. Vyborny, E.B. Mendelson, Computerized detection and classification of cancer
on breast ultrasound, Acad. Radiol., 11 (2004) 526-535.
[4] H.D. Cheng, J. Shan, W. Ju, Y.H. Guo, L. Zhang, Automated breast cancer detection and classification using
ultrasound images: a survey, Pattern Recognit., 43 (2010) 299-317.
[5] C.M. Bishop, Pattern recognition and machine learning, Springer, New York, NY, 2006.
[6] J.M. Hammersley, P. Clifford, Markov field on finite graphs and lattices, (1971).
[7] E.A. Ashton, K.J. Parker, Multiple resolution Bayesian segmentation of ultrasound images, Ultrason. Imaging,
17 (1995) 291-304.
[8] T.N. Pappas, An adaptive clustering algorithm for image segmentation, IEEE TSP, 40 (1992) 901-914.
[9] D. Boukerroui, O. Basset, N. Guerin, A. Baskurt, Multiresolution texture based adaptive clustering algorithm
for breast lesion segmentation, EJU, 8 (1998) 135-144.
[10] D. Boukerroui, A. Baskurt, J.A. Noble, O. Basset, Segmentation of ultrasound images-multiresolution 2D and
3D algorithm based on global and local statistics, Pattern Recognit. Lett., 24 (2003) 779-790.
[11] G. Xiao, M. Brady, J.A. Noble, Y. Zhang, Segmentation of ultrasound B-mode images with intensity inhomogeneity correction, IEEE TMI, 21 (2002) 48-57.
[12] G. Pons, J. Martí, R. Martí, J.A. Noble, Simultaneous lesion segmentation and bias correction in breast ultrasound images, in: Pattern Recognition and Image Analysis, Springer, 2011, pp. 692-699.
[13] G. Pons, J. Martí, R. Martí, S. Ganau, J.A. Noble, Breast-lesion segmentation combining B-mode and elastography ultrasound, Ultrason. Imaging, 38 (2016) 209-224.
[14] S. Geman, D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE
TPAMI, (1984) 721-741.

29 / 40

[15] J. Besag, On the statistical analysis of dirty pictures, J. R. Stat. Soc., Series B (1986) 259-302.
[16] D.M. Greig, B.T. Porteous, A.H. Seheult, Exact maximum a posteriori estimation for binary images, J. R. Stat.
Soc., Series B (Methodol.) (1989) 271-279.
[17] S. Roy, I.J. Cox, A maximum-flow formulation of the n-camera stereo correspondence problem, in: IEEE
ICCV, Bombay, India, 1998, pp. 492-499.
[18] Y. Boykov, O. Veksler, R. Zabih, Fast approximate energy minimization via graph cuts, IEEE TPAMI, 23
(2001) 1222-1239.
[19] L.R. Ford, D.R. Fulkerson, Maximal flow through a network, Can. J. Math., 8 (1956) 399-404.
[20] V. Kolmogorov, R. Zabin, What energy functions can be minimized via graph cuts?, IEEE TPAMI, 26 (2004)
147-159.
[21] Y. Boykov, V. Kolmogorov, An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision, IEEE TPAMI, 26 (2004) 1124-1137.
[22] M. Xian, Y. Zhang, H.D. Cheng, Fully automatic segmentation of breast ultrasound images based on breast
characteristics in space and frequency domains, Pattern Recognit., 48 (2015) 485-497.
[23] M. Xian, J. Huang, Y. Zhang, X. Tang, Multiple-domain knowledge based MRF model for tumor segmentation in breast ultrasound images, in: IEEE ICIP, 2012, pp. 2021-2024.
[24] H.-H. Chiang, J.-Z. Cheng, P.-K. Hung, C.-Y. Liu, C.-H. Chung, C.-M. Chen, Cell-based graph cut for segmentation of 2D/3D sonographic breast images, in: IEEE ISBI, 2010, pp. 177-180.
[25] J. Zhang, S.K. Zhou, S. Brunke, C. Lowery, D. Comaniciu, Database-guided breast tumor detection and segmentation in 2d ultrasound images, in: SPIE MI, 2010, pp. 7624051-7624057.
[26] Z. Tu, Probabilistic boosting-tree: Learning discriminative models for classification, recognition, and clustering, in: IEEE ICCV, 2005, pp. 1589-1596.
[27] Z. Hao, Q. Wang, H. Ren, K. Xu, Y. K. Seong, J. Kim, Multiscale superpixel classification for tumor segmentation in breast ultrasound images, in: IEEE ICIP, 2012, pp. 2817-2820.
[28] Z. Hao, Q. Wang, X. Wang, J.B. Kim, Y. Hwang, B.H. Cho, P. Guo, W.K. Lee, Learning a structured graphical
model with boosted top-down features for ultrasound image segmentation, in: MICCAI, 2013, pp. 227-234.
[29] P.F. Felzenszwalb, R.B. Girshick, D. McAllester, D. Ramanan, Object detection with discriminatively trained
part-based models, IEEE TPAMI, 32 (2010) 1627-1645.
[30] I. Tsochantaridis, T. Hofmann, T. Joachims, Y. Altun, Support vector machine learning for interdependent
and structured output spaces, in: ACM ICML, Menlo Park, CA, 2004, pp. 1-8.

30 / 40

[31] J. Shi, J. Malik, Normalized cuts and image segmentation, IEEE TPAMI, 22 (2000) 888-905.
[32] L. Gao, W. Yang, Z. Liao, X. Liu, Q. Feng, W. Chen, Segmentation of ultrasonic breast tumors based on
homogeneous patch, Med. Phys., 39 (2012) 3299-3318.
[33] M. Alemán-Flores, L. Álvarez, V. Caselles, Texture-oriented anisotropic filtering and geodesic active contours
in breast tumor ultrasound segmentation, J. Math. Imaging Vis., 28 (2007) 81-97.
[34] X. Liu, Z. Huo, J. Zhang, Automated segmentation of breast lesions in ultrasound images, in: IEEE EMBS,
2005, pp. 7433-7435.
[35] R. Szeliski, R. Zabih, D. Scharstein, O. Veksler, V. Kolmogorov, A. Agarwala, M. Tappen, C. Rother, A
comparative study of energy minimization methods for Markov random fields, in: IEEE ECCV, 2006, pp. 1629.
[36] V. Koltun, Efficient inference in fully connected crfs with gaussian edge potentials, Adv. Neural Inf. Process.
Syst., 2 (2011) 4.
[37] D. Terzopoulos, On matching deformable models to images, in: Topical Meeting on Machine Vision Tech.
Digest Series, 1987, pp. 160-167.
[38] M. Kass, A. Witkin, D. Terzopoulos, Snakes: Active contour models, IJCV, 1 (1988) 321-331.
[39] L.D. Cohen, On active contour models and balloons, CVGIP: Image Underst., 53 (1991) 211-218.
[40] V. Caselles, F. Catté, T. Coll, F. Dibos, A geometric model for active contours in image processing, Numer.
Math., 66 (1993) 1-31.
[41] R. Malladi, J.A. Sethian, B.C. Vemuri, Shape modeling with front propagation: A level set approach, IEEE
TPAMI, 17 (1995) 158-175.
[42] A. Yezzi Jr, S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, A geometric snake model for segmentation of medical imagery, IEEE TMI, 16 (1997) 199-209.
[43] S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, A. Yezzi Jr, Conformal curvature flows: from phase
transitions to active vision, Arch. Ration. Mech. Anal., 134 (1996) 275-301.
[44] V. Caselles, R. Kimmel, G. Sapiro, Geodesic active contours, IJCV, 22 (1997) 61-79.
[45] J.A. Sethian, Level set methods and fast marching methods: evolving interfaces in computational geometry,
fluid mechanics, computer vision, and materials science, Cambridge university press, 1999.
[46] S. Osher, R. Fedkiw, Level set methods and dynamic implicit surfaces, Springer Science & Business Media,
2006.

31 / 40

[47] C. Li, C. Xu, C. Gui, M.D. Fox, Distance regularized level set evolution and its application to image segmentation, IEEE TIP, 19 (2010) 3243-3254.
[48] C. Li, C. Xu, C. Gui, M.D. Fox, Level set evolution without re-initialization: a new variational formulation,
in: IEEE CVPR, 2005, pp. 430-436 vol. 431.
[49] C. Li, C.-Y. Kao, J.C. Gore, Z. Ding, Minimization of region-scalable fitting energy for image segmentation,
IEEE TIP, 17 (2008) 1940-1949.
[50] Y. Chen, K.C. Keong, S.-B. Wee, Q. Zou, Adaptive expanding B-snake model for extracting ultrasound breast
lump boundary, in: IEEE ANZIIS, 2001, pp. 19-23.
[51] S. Menet, P. Saint-Marc, G. Medioni, Active contour models: Overview, implementation and applications, in:
IEEE SMC, 1990, pp. 194-199.
[52] C.-M. Chen, H.H.-S. Lu, Y.-S. Huang, Cell-based dual snake model: a new approach to extracting highly
winding boundaries in the ultrasound images, Ultrasound Med. Biol., 28 (2002) 1061-1073.
[53] S.R. Gunn, M.S. Nixon, A robust snake implementation: a dual active contour, IEEE TPAMI, 19 (1997) 6368.
[54] A. Madabhushi, D. Metaxas, Automatic boundary extraction of ultrasonic breast lesions, in: IEEE ISBI, 2002,
pp. 601-604.
[55] A. Madabhushi, D.N. Metaxas, Combining low-, high-level and empirical domain knowledge for automated
segmentation of ultrasonic breast lesions, IEEE TMI, 22 (2003) 155-169.
[56] B. Sahiner, A. Ramachandran, H.-P. Chan, M.A. Roubidoux, L.M. Hadjiiski, M.A. Helvie, N. Petrick, C. Zhou,
Three-dimensional active contour model for characterization of solid breast masses on three-dimensional ultrasound images, in: SPIE MI, 2003, pp. 405-413.
[57] B. Sahiner, H.-P. Chan, M.A. Roubidoux, M.A. Helvie, L.M. Hadjiiski, A. Ramachandran, C. Paramagul, G.L.
LeCarpentier, A. Nees, C. Blane, Computerized characterization of breast masses on three-dimensional ultrasound volumes, Med. Phys., 31 (2004) 744-754.
[58] R.-F. Chang, W.-J. Wu, W.K. Moon, W.-M. Chen, W. Lee, D.-R. Chen, Segmentation of breast tumor in
three-dimensional ultrasound images using three-dimensional discrete active contour model, Ultrasound Med.
Biol., 29 (2003) 1571-1581.
[59] D.-R. Chen, R.-F. Chang, W.-J. Wu, W.K. Moon, W.-L. Wu, 3-D breast ultrasound segmentation using active
contour model, Ultrasound Med. Biol., 29 (2003) 1017-1026.

32 / 40

[60] R.N. Czerwinski, D.L. Jones, W.D. O'Brien Jr, Detection of lines and boundaries in speckle images-application to medical ultrasound, IEEE TMI, 18 (1999) 126-136.
[61] Y.-L. Huang, D.-R. Chen, Automatic contouring for breast tumors in 2-D sonography, in: IEEE EMBS, 2006,
pp. 3225-3228.
[62] M. Yap, E.A. Edirisinghe, H.E. Bez, Fully automatic lesion boundary detection in ultrasound breast images,
in: SPIE MI, 2007, pp. 65123I1-65123I8.
[63] J. Deng, H.T. Tsui, A fast level set method for segmentation of low contrast noisy biomedical images, Pattern
Recognit. Lett., 23 (2002) 161-169.
[64] B. Liu, H.D. Cheng, J.H. Huang, J.W. Tian, J.F. Liu, X.L. Tang, Automated Segmentation of Ultrasonic Breast
Lesions Using Statistical Texture Classification and Active Contour Based on Probability Distance, Ultrasound
Med. Biol., 35 (2009) 1309-1324.
[65] W. Gómez, A. Infantosi, L. Leija, W. Pereira, Active Contours without Edges Applied to Breast Lesions on
Ultrasound, in: Springer MEDICON, 2010, pp. 292-295.
[66] T.F. Chan, L.A. Vese, Active contours without edges, IEEE TIP 10 (2001) 266-277.
[67] B. Liu, H. Cheng, J. Huang, J. Tian, X. Tang, J. Liu, Probability density difference-based active contour for
ultrasound image segmentation, Pattern Recognit., 43 (2010) 2028-2042.
[68] N. Paragios, R. Deriche, Geodesic active contours and level sets for the detection and tracking of moving
objects, IEEE TPAMI, 22 (3) (2000) 266–280.
[69] A. Rodtook, S.S. Makhanov, Continuous force field analysis for generalized gradient vector flow field, Pattern
Recognit., 43 (2010) 3522-3538.
[70] C. Xu, J.L. Prince, Generalized gradient vector flow external forces for active contours, Signal Process., 71
(1998) 131-139.
[71] M.I. Daoud, M.M. Baba, F. Awwad, M. Al-Najjar, E.S. Tarawneh, Accurate Segmentation of Breast Tumors
in Ultrasound Images Using a Custom-Made Active Contour Model and Signal-to-Noise Ratio Variations, in:
IEEE SITIS, 2012, pp. 137-141.
[72] S. Lobregt, M.A. Viergever, A discrete dynamic contour model, IEEE TMI, 14 (1995) 12-24.
[73] L. Gao, X. Liu, W. Chen, Phase-and gvf-based level set segmentation of ultrasonic breast tumors, J Appl.
Math., 2012 (2012) 1-22.
[74] P. Kovesi, Phase congruency: A low-level image invariant, Psychological Research, 64 (2000) 136-148.

33 / 40

[75] L. Cai, Y. Wang, A phase-based active contour model for segmentation of breast ultrasound images, in: IEEE
BMEI, 2013, pp. 91-95.
[76] Q. Lin, S. Liu, S.S. Parajuly, Y. Deng, L. Boroczky, S. Fu, Y. Wu, Y. Pen, Ultrasound lesion segmentation
using clinical knowledge-driven constrained level set, in: IEEE EMBC, 2013, pp. 6067-6070.
[77] S. Lankton, A. Tannenbaum, Localizing region-based active contours, IEEE TIP, 17 (2008) 2029-2039.
[78] Z. Liu, L. Zhang, H. Ren, J.-Y. Kim, A robust region-based active contour model with point classification for
ultrasound breast lesion segmentation, in: SPIE MI, 2013, pp. 86701P1-86701P8.
[79] B.H. Cho, Y.K. Seong, J. Kim, Z. Liu, Z. Hao, E.Y. Ko, K.-G. Woo, Ultrasound breast lesion segmentation
using adaptive parameters, in: SPIE MI, 2014, pp. 90351E1-90351E6.
[80] J. Yuan, Active contour driven by local divergence energies for ultrasound image segmentation, IET Image
Processing, 7 (2013).
[81] H.-C. Kuo, M.L. Giger, I. Reiser, K. Drukker, J.M. Boone, K.K. Lindfors, K. Yang, A. Edwards, C.A. Sennett,
Segmentation of breast masses on dedicated breast computed tomography and three-dimensional breast ultrasound images, JMI, 1 (2014) 0145011-01450112.
[82] H.-C. Kuo, M.L. Giger, I. Reiser, J.M. Boone, K.K. Lindfors, K. Yang, A. Edwards, Level set segmentation
of breast masses in contrast-enhanced dedicated breast CT and evaluation of stopping criteria, J. Digit. Imaging,
27 (2014) 237-247.
[83] M. Kupinski, M.L. Giger, Automated seeded lesion segmentation on digital mammograms, IEEE TMI, 17
(1998) 510-517.
[84] Y. Yuan, M.L. Giger, H. Li, K. Suzuki, C. Sennett, A dual-stage method for lesion segmentation on digital
mammograms, Med. Phys., 34 (2007) 4180-4193.
[85] J.C. Dunn, A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters,
Journal of Cybernetics, 3 (1973) 32-57.
[86] C.B. James, Pattern recognition with fuzzy objective function algorithms, Kluwer Academic Publishers, Norwell, MA, USA, 1981.
[87] Y. Xu, A modified spatial fuzzy clustering method based on texture analysis for ultrasound image segmentation, in: IEEE ISIE, 2009, pp. 746-751.
[88] K.-S. Chuang, H.-L. Tzeng, S. Chen, J. Wu, T.-J. Chen, Fuzzy c-means clustering with spatial information for
image segmentation, Comput. Med. Imag. Grap., 30 (2006) 9-15.

34 / 40

[89] C. Lo, Y.-W. Shen, C.-S. Huang, R.-F. Chang, Computer-aided multiview tumor detection for automated
whole breast ultrasound, Ultrason. Imaging, 36 (2014) 3-17.
[90] D. W. Hosmer Jr, and S. Lemeshow, Applied logistic regression: John Wiley & Sons, 2004.
[91] W.K. Moon, C.-M. Lo, R.-T. Chen, Y.-W. Shen, J.M. Chang, C.-S. Huang, J.-H. Chen, W.-W. Hsu, R.-F.
Chang, Tumor detection in automated breast ultrasound images using quantitative tissue clustering, Med. Phys.,
41 (2014) 042901.
[92] Y.Z. Cheng, Mean Shift, Mode Seeking, and Clustering, IEEE TPAMI, 17 (1995) 790-799.
[93] American College of Radiology, Breast imaging reporting and data system atlas (BI-RADS atlas), Reston, VA:
American College of Radiology, vol. 98, 2003.
[94] J. Shan, A fully automatic segmentation method for breast ultrasound images, Dissertation, USU, 2011.
[95] J. Shan, H. Cheng, Y. Wang, A novel segmentation method for breast ultrasound images based on neutrosophic
l-means clustering, Med. Phys., 39 (2012) 5669-5682.
[96] B.E. Boser, I.M. Guyon, V.N. Vapnik, A training algorithm for optimal margin classifiers, in: ACM Computational learning theory, 1992, pp. 144-152.
[97] C. Cortes, V. Vapnik, Support-vector networks, Machine Learning, 20 (1995) 273-297.
[98] B. Liu, H.D. Cheng, J.H. Huang, J.W. Tian, X.L. Tang, J.F. Liu, Fully automatic and segmentation-robust
classification of breast tumors based on local texture analysis of ultrasound images, Pattern Recognit., 43 (2010)
280-298.
[99] V. Vapnik, Statistical Learning Theory, Wiley-Interscience, New York, 1998.
[100] P. Jiang, J. Peng, G. Zhang, E. Cheng, V. Megalooikonomou, H. Ling, Learning-based automatic breast
tumor detection and segmentation in ultrasound images, in: IEEE ISBI, 2012, pp. 1587-1590.
[101] Y. Freund, R.E. Schapire, A decision-theoretic generalization of on-line learning and an application to boosting, J. Comput. Syst. Sci., 55 (1997) 119-139.
[102] P. Viola, M.J. Jones, Robust real-time face detection, IJCV, 57 (2004) 137-154.
[103] S.-F. Huang, Y.-C. Chen, W.K. Moon, Neural network analysis applied to tumor segmentation on 3D breast
ultrasound images, in: IEEE ISBI, 2008, pp. 1303-1306.
[104] A.A. Othman, H.R. Tizhoosh, Segmentation of Breast Ultrasound Images Using Neural Networks, in:
Springer EANN, 2011, pp. 260-269.
[105] J. Shan, Y. Wang, H.-D. Cheng, Completely automatic segmentation for breast ultrasound using multipledomain features, in: IEEE ICIP, 2010, pp. 1713-1716.

35 / 40

[106] J. Shan, H.D. Cheng, Y.X. Wang, Completely Automated Segmentation Approach for Breast Ultrasound
Images Using Multiple-Domain Features, Ultrasound Med. Biol., 38 (2012) 262-275.
[107] M.-C. Yang, C.-S. Huang, J.-H. Chen, R.-F. Chang, Whole breast lesion detection using naive Bayes classifier for portable ultrasound, Ultrasound Med. Biol., 38 (2012) 1870-1880.
[108] E. Bribiesca, An easy measure of compactness for 2D and 3D shapes, Pattern Recognit., 41 (2008) 543-554.
[109] Y. Ikedo, D. Fukuoka, T. Hara, H. Fujita, E. Takada, T. Endo, T. Morita, Development of a fully automatic
scheme for detection of masses in whole breast ultrasound images, Med. Phys., 34 (2007) 4378-4388.
[110] F. Xu, M. Xian, H. Cheng, J. Ding, Y. Zhang, Unsupervised saliency estimation based on robust hypotheses,
in: IEEE WACV, 2016, pp. 1-6.
[111] M.H. Yap, A novel algorithm for initial lesion detection in ultrasound breast images, J. Appl. Clin. Med.
Phys, 9 (2008).
[112] S. Joo, Y.S. Yang, W.K. Moon, H.C. Kim, Computer-aided diagnosis of solid breast nodules: use of an
artificial neural network based on multiple sonographic features, IEEE TMI, 23 (2004) 1292-1300.
[113] J. Shan, H.D. Cheng, Y.X. Wang, A novel automatic seed point selection algorithm for breast ultrasound
images, in: ICPR, 2008, pp. 3990-3993.
[114] R.-F. Chang, W.-J. Wu, W.K. Moon, D.-R. Chen, Automatic ultrasound segmentation and morphology based
diagnosis of solid breast tumors, Breast cancer research and treatment, 89 (2005) 179-185.78
[115] M. Xian, H.D. Cheng, Y. Zhang, A Fully Automatic Breast Ultrasound Image Segmentation Approach Based
on Neutro-Connectedness, in: ICPR, 2014, pp. 2495-2500.
[116] J.I. Kwak, M.N. Jung, S.H. Kim, N.C. Kim, 3D segmentation of breast tumor in ultrasound images, in: SPIE,
MI, 2003, pp. 193-200.
[117] J.I. Kwak, S.H. Kim, N.C. Kim, RD-based seeded region growing for extraction of breast tumor in an ultrasound volume, in: Computational Intelligence and Security, Springer, 2005, pp. 799-808.
[118] J. Massich, F. Meriaudeau, E. Pérez, R. Martí, A. Oliver, J. Martí, Lesion segmentation in breast sonography,
in: Digital Mammography, Springer, 2010, pp. 39-45.
[119] S. Beucher, C. Lantuéjoul, Use of watersheds in contour detection, in: International workshop on image
processing: real-time edge and motion detection/estimation, Rennes, France, 1979.
[120] J. Cousty, G. Bertrand, L. Najman, M. Couprie, Watershed cuts: Minimum spanning forests and the drop of
water principle, IEEE TPAMI, 31 (2009) 1362-1374.

36 / 40

[121] S. Beucher, F. Meyer, The morphological approach to segmentation: the watershed transformation, Optical
Engineering-New York-Marcel Dekker Incorporated, 34 (1992) 433-433.
[122] Y.-L. Huang, D.-R. Chen, Watershed segmentation for breast tumor in 2-D sonography, Ultrasound Med.
Biol., 30 (2004) 625-632.
[123] Y. Ikedo, D. Fukuoka, T. Hara, H. Fujita, E. Takada, T. Endo, T. Morita, Computer-aided detection system
of breast masses on ultrasound images, in: SPIE MI, 2006, pp. 61445L1-61445L8.
[124] W. Gómez, L. Leija, A. Alvarenga, A. Infantosi, W. Pereira, Computerized lesion segmentation of breast
ultrasound based on marker-controlled watershed transformation, Med. Phys., 37 (2010) 82-95.
[125] W. Gómez, L. Leija, W.C.A. Pereira, A.F.C. Infantosi, Segmentation of Breast Nodules on Ultrasonographic
Images Based on Marke d-Controlled Watershed Transform, Computación y Sistemas, 14 (2010) 165-174.
[126] M. Zhang, Novel approaches to image segmentation based on neutrosophic logic, PhD thesis, USU, 2010.
[127] M. Zhang, L. Zhang, H.-D. Cheng, Segmentation of ultrasound breast images based on a neutrosophic
method, Opt. Eng., 49 (2010) 117001-117012.
[128] C.M. Lo, R.T. Chen, Y.C. Chang, Y.W. Yang, M.J. Hung, C.S. Huang, R.F. Chang, Multi-Dimensional
Tumor Detection in Automated Whole Breast Ultrasound Using Topographic Watershed, IEEE TMI, 33 (2014)
1503-1511.
[129] D. W. Hosmer, and S. Lemeshow, Applied logistic regression: Wiley-Interscience, 2000.
[130] N. Otsu, A threshold selection method from gray-level histograms, Automatica, 11 (1975) 23-27.
[131] J.-F. Rivest, P. Soille, S. Beucher, Morphological gradients, in: SPIE/IS&T Symposium on Electronic Imaging: Science and Technology, 1992, pp. 139-150.
[132] K. Horsch, M.L. Giger, L.A. Venta, C.J. Vyborny, Automatic segmentation of breast lesions on ultrasound,
Med. Phys, 28 (2001) 1652-1659.
[133] K. Horsch, M.L. Giger, L.A. Venta, C.J. Vyborny, Computerized diagnosis of breast lesions on ultrasound,
Med. Phys, 29 (2002) 157-164.
[134] J. V. Neumann, Theory of Self-Reproducing Automata: University of Illinois Press, 1966.
[135] V. Vezhnevets, V. Konouchine, GrowCut: Interactive multi-label ND image segmentation by cellular automata, in: proc. of Graphicon, Citeseer, 2005, pp. 150-156.
[136] Y. Liu, H. Cheng, J. Huang, Y. Zhang, X. Tang, An effective approach of lesion segmentation within the
breast ultrasound image based on the cellular automata principle, JDI, 25 (2012) 580-590.

37 / 40

[137] L. Zhu, I. Kolesov, Y. Gao, R. Kikinis, A. Tannenbaum, An effective interactive medical image segmentation
method using fast growcut, in: MICCAI Workshop on Interactive Medical Image Computing, 2014.
[138] C.-M. Chen, Y.-H. Chou, C.S. Chen, J.-Z. Cheng, Y.-F. Ou, F.-C. Yeh, K.-W. Chen, Cell-competition algorithm: A new segmentation algorithm for multiple objects with irregular boundaries in ultrasound images, Ultrasound Med. Biol., 31 (2005) 1647-1664.
[139] J.-Z. Cheng, C.-M. Chen, Y.-H. Chou, C.S. Chen, C.-M. Tiu, K.-W. Chen, Cell-based two-region competition
algorithm with a map framework for boundary delineation of a series of 2D ultrasound images, Ultrasound Med.
Biol., 33 (2007) 1640-1650.
[140] H.-H. Chiang, J.-Z. Cheng, P.-K. Hung, C.-Y. Liu, C.-H. Chung, C.-M. Chen, Cell-based graph cut for segmentation of 2D/3D sonographic breast images, in: IEEE ISBI, 2010, pp. 177-180.
[141] M. Kupinski, M.L. Giger, Automated seeded lesion segmentation on digital mammograms, IEEE TMI, 17
(1998) 510-517.
[142] K. Drukker, M.L. Giger, K. Horsch, M.A. Kupinski, C.J. Vyborny, E.B. Mendelson, Computerized lesion
detection on breast ultrasound, Med. Phys, 29 (2002) 1438-1446.
[143] K. Drukker, M.L. Giger, K. Horsch, C.J. Vyborny, Computerized analysis of sonograms for the detection of
breast lesions, in: SPIE MI, 2002, pp. 1320-1324.
[144] K. Drukker, M.L. Giger, C.J. Vyborny, R.A. Schmidt, E.B. Mendelson, M. Stern, Computerized detection
and classification of lesions on breast ultrasound, in: SPIE MI, 2003, pp. 106-110.
[145] H.-C. Kuo, M.L. Giger, I. Reiser, K. Drukker, A. Edwards, C.A. Sennett, Automatic 3D lesion segmentation
on breast ultrasound images, in: SPIE MI, 2013, pp. 8670251-8670256.
[146] L.D. Cohen, I. Cohen, Finite-element methods for active contour models and balloons for 2-D and 3-D images, IEEE TPAMI, 15 (1993) 1131-1147.
[147] J.M. Dias, J.M. Leitao, Wall position and thickness estimation from sequences of echocardiographic images,
IEEE TMI, 15 (1996) 25-38.
[148] Y. Yu, S.T. Acton, Speckle reducing anisotropic diffusion, IEEE TIP, 11 (2002) 1260-1270.
[149] K.Z. Abd-Elmoniem, A.-B. Youssef, Y.M. Kadah, Real-time speckle reduction and coherence enhancement
in ultrasound imaging via nonlinear anisotropic diffusion, IEEE TBE, 49 (2002) 997-1014.
[150] C. Tomasi, R. Manduchi, Bilateral filtering for gray and color images, in: IEEE ICCV, 1998, pp. 839-846.
[151] M. Elad, On the origin of the bilateral filter and ways to improve it, IEEE TIP, 11 (2002) 1141-1151.
[152] M. Xian, Y. Zhang, H.D. Cheng, F. Xu, J. Ding, Neutro-connectedness cut, IEEE TIP, 25 (2016)4691-4703.

38 / 40

[153] M. Xian, F. Xu, H. D. Cheng, EISeg: Effective Interactive Segmentation, in: ICPR, 2016, pp. 1982-1987.
[154] H. Shao, Y. Zhang, M. Xian, H.D. Cheng, F. Xu, J. Ding, A saliency model for automated tumor detection
in breast ultrasound images, in: IEEE ICIP, 2015, pp. 1424-1428.
[155] J.A. Jensen, Field: A program for simulating ultrasound systems, in: Medical & Biological Engineering &
Computing, Citeseer, 1996, pp. 351-353.
[156] J.A. Jensen, N.B. Svendsen, Calculation of pressure fields from arbitrarily shaped, apodized, and excited
ultrasound transducers, IEEE TUFFC, 39 (1992) 262-267.
[157] Y. Zhang, H.D. Cheng, J. Tian, J. Huang, X. Tang, Fractional subpixel diffusion and fuzzy logic approach
for ultrasound speckle reduction, Pattern Recognit., 43 (2010) 2962-2970.
[158] D. Cireşan, U. Meier, J. Masci, J. Schmidhuber, Multi-column deep neural network for traffic sign classification, Neural Networks, 32 (2012) 333-338.
[159] D. Ciregan, U. Meier, J. Schmidhuber, Multi-column deep neural networks for image classification, in: IEEE
CVPR, 2012, pp. 3642-3649.
[160] J. Long, E. Shelhamer, T. Darrell, Fully convolutional networks for semantic segmentation, in: IEEE CVPR,
2015, pp. 3431-3440.
[161] J.-Z. Cheng, D. Ni, Y.-H. Chou, J. Qin, C.-M. Tiu, Y.-C. Chang, C.-S. Huang, D. Shen, C.-M. Chen, Computer-Aided diagnosis with deep learning architecture: applications to breast lesions in US images and pulmonary nodules in CT scans, Scientific Reports, 6 (2016).
[162] L. Deng, D. Yu, Deep learning: methods and applications, Foundations and Trends in Signal Processing, 7
(2014) 197-387.
[163] P.O. Glauner, Deep convolutional neural networks for smile recognition, arXiv:1508.06535, (2015).
[164] L. Deng, G. Hinton, B. Kingsbury, New types of deep neural network learning for speech recognition and
related applications: An overview, in: IEEE ICASSP, 2013, pp. 8599-8603.
[165] Q.-H. Huang, S.-Y. Lee, L.-Z. Liu, M.-H. Lu, L.-W. Jin, A.-H. Li, A robust graph-based segmentation
method for breast tumors in ultrasound images, Ultrasonics, 52 (2012) 266-275.
[166] Q. Huang, X. Bai, Y. Li, L. Jin, X. Li, Optimized graph-based segmentation for ultrasound images, Neurocomputing, 129 (2014) 216-224.
[167] P. Coupé, P. Hellier, C. Kervrann, C. Barillot, Nonlocal means-based speckle filtering for ultrasound images,
IEEE TIP, 18 (2009) 2221-2229.

39 / 40

[168] P. Milanfar, A tour of modern image filtering: New insights and methods, both practical and theoretical,
IEEE Signal Process. Mag., 30 (2013) 106-128.
[169] A. T. Stavros, Breast ultrasound: Lippincott Williams & Wilkins, 2004.
[170] T. Kooi, G. Litjens, B. van Ginneken, A. Gubern-Mérida, C.I. Sánchez, R. Mann, A. den Heeten, N. Karssemeijer, Large scale deep learning for computer aided detection of mammographic lesions, Med. Image Anal.,
35 (2017) 303-312.
[171] D. Shen, G. Wu, H.-I. Suk, Deep Learning in Medical Image Analysis, Annu. Rev. Biomed. Eng., (2017).
[172] A.K. Sinop, L. Grady, A Seeded Image Segmentation Framework Unifying Graph Cuts and Random Walker
Which Yields A New Algorithm, in IEEE ICCV, 2007, pp. 1-8.
[173] L. Grady, Random walks for image segmentation, IEEE TPAMI, 28 (2006) 1768-1783.
[174] C. Shi, Y. Cheng, F. Liu, Y. Wang, J. Bai, S. Tamura, A hierarchical local region-based sparse shape composition for liver segmentation in CT scans, Pattern Recogn, 50 (2016) 88-106.
[175] Q. Huang, Y. Luo, Q. Zhang, Breast ultrasound image segmentation: a survey, International journal of computer assisted radiology and surgery, (2017) 1-15.
[176] Y. Xie, K. Chen, J. Lin, An Automatic Localization Algorithm for Ultrasound Breast Tumors Based on Human Visual Mechanism, Sensors-Basel, 17 (2017) 1101.
[177] A. Levinshtein, A. Stere, K.N. Kutulakos, D.J. Fleet, S.J. Dickinson, K. Siddiqi, Turbopixels: Fast superpixels using geometric flows, IEEE TPAMI, 31 (2009) 2290-2297.
[178] S. Xiang, C. Pan, F. Nie, C. Zhang, Turbopixel segmentation using eigen-images, IEEE TIP, 19 (2010) 30243034.
[179] R. Achanta, A. Shaji, K. Smith, A. Lucchi, P. Fua, S. Süsstrunk, SLIC superpixels compared to state-of-theart superpixel methods, IEEE TPAMI, 34 (2012) 2274-2282.
[180] C. Shi, Y. Cheng, J. Wang, Y. Wang, K. Mori, S. Tamura, Low-rank and sparse decomposition based shape
model and probabilistic atlas for automatic pathological organ segmentation, Medical Image Analysis, 38 (2017)
30-49.

40 / 40

