- Research
- Open Access
Robust MRI abnormality detection using background noise removal with polyfit surface evolution
- Changjiang Liu†^{1, 2, 3}Email author,
- Irene Cheng^{3},
- Anup Basu†^{3} and
- Jun Ye^{1, 2, 4}
https://doi.org/10.1186/s13640-017-0209-y
© The Author(s) 2017
- Received: 30 June 2017
- Accepted: 22 August 2017
- Published: 31 August 2017
Abstract
Image segmentation plays a vital role in MRI abnormality detection. This paper presents a robust MRI segmentation method to outline potential abnormality blobs. Thresholding and boundary tracing strategies are employed to remove background noises, and hence, the ROIs in the whole process are set. Subsequently, a polyfit surface evolution is proposed to approximately estimate bias field, which makes segmentation robust to image noises. Simultaneously, customized initial level set functions are devised so as to detect subtle bright and dark blobs which are highly potential abnormality regions. The proposed method improves bias field estimation and level set method to acquire fine segmentation with low computational complexities. Analysis of experimental results and comparisons with existing algorithms demonstrates that the proposed method can segment weak-edged, low-resolution MR brain images, and its performance prevails in accuracy and effectiveness.
Keywords
- Magnetic resonance (MR)
- Segmentation
- Abnormality detection
- Polyfit
- Bias field estimation
- Level set method
1 Introduction
With the exploration of magnetic resonance imaging (MRI) technology, dramatic changes have been made in visualization of anatomical structures [1, 2]. MRI is a powerful imaging modality driven by its flexibility and sensitivity to a broad range of tissue properties [3]. However, a CT scan is best suited for viewing bone injuries, diagnosing lung and chest problems, and detecting cancers [4, 5]. MRI is used to find other problems, such as tumors, bleeding, injury, blood vessel diseases, and infections. For example, researchers strive to detect brain abnormalities in MR images [6, 7]. In this paper, our goal is to segment MR brain images to assist doctors’ diagnosis.
Intensity inhomogeneity or bias field in MR image, which arises from the imperfections of the image acquisition process and manifests itself as slow intensity variation over the image domain [8]. This inherent artifact is difficult for a human to perceive. However, many segmentation methods are very sensitive to spurious intensity variations. In 1986, Haselgrove and Prammer [9] first discussed MRI intensity inhomogeneity correction. However, Haselgrove and Prammer assumed that the position and orientation of the surface coil were known, as obstructed its practical application. In the past two decades, many bias field correction algorithms have been presented. The authors in [8] noted that two main approaches, namely prospective [10–14] and retrospective approaches [15–21], had been applied to minimize the intensity inhomogeneity in MR images. Among these abovementioned methods, Andersen et al. [15] incorporated radio frequency inhomogeneity correction into probabilistic classification model to partition an MR image. In addition, Li et al. [22] proposed a new approach for bias field estimation and tissue segmentation in an energy minimization framework. They mathematically justified that the proposed energy is convex in each of its variables. Quantitative evaluations and comparisons verified its robustness and accuracy. The bias field estimation proposed by Li et al. needs no previous knowledge of noise distribution, which makes it more applicable. However, it is a region-based segmentation method and cannot extract small homogeneous regions as level set methods do.
Image segmentation is a fundamental process in many medical imaging applications [23]. Segmentation methods can be roughly divided into eight categories [24–26]: (a) thesholding approaches, (b) region growing approaches, (c) classifiers, (d) clustering approaches, (e) Markov random field models, (f) artificial neural networks, (g) deformable models, and (h) atlas-guided approaches. The level set method, as one of the deformable models, was first introduced to delineate region boundaries by using closed parametric curves [27]. It is able to acquire closed contours of regions from an image, which helps partition of a medical image accurately. The authors in [28–30] considered a two-phase level set formulation, in which only one level set function was used to construct two membership functions to segment the image domain into two disjoint regions. The two-phase level set method can only partition images into two parts, making it unsuitable for multi-class segmentation in some medical applications. Recently, researchers have developed multi-phase level set methods [31, 32], using two or more level set functions to define more than two membership functions, which makes it more practical in medical applications. Li et al. [31] have combined bias field estimation with multi-phase level set method. In this framework proposed by Li’s, the formation of initial level set functions was not mentioned yet. Experimental results show initial level set functions influence final segmentation to some extent, especially in certain small regions. At the same time, bias field estimation in [31] lacks denoising capability as well.
- (1)
A coarse to fine segmentation method is proposed. Otsu’s method is employed not only to remove background noise but also to set the ROI for the level set method.
- (2)
A multi-phase level set method with bias field polyfit estimation is proposed. This method can partly depress image noise latent in tissues.
- (3)
Customized initial level set functions are formulated. The initial level set functions are widely applicable to detect small tissues in MR images.
This remainder of this paper is organized as follows. We first review MRI bias field estimation and multi-phase level set method in Section 2. Section 3 presents a robust MRI abnormality detection method, including background removal or ROI setting, multi-phase level set method with bias field polyfit estimation, and customized initial level set functions. Experimental results and comparison with existing methods are outlined in Section 4. Finally, concluding remarks are given in Section 5.
2 Literature review on MRI bias field estimation and multi-phase level set method
where b(x) is bias field that accounts for the intensity inhomogeneity in the observed image I(x), n(x) is the additive Gaussian noise with zero mean, J(x) is the true image without bias field and noise, and x is a tuple like (x,y) representing image coordinates.
- (1)Image domain Ω can be partitioned into disjoint parts as described below:in which J is approximately constant c _{ i } for the ith region Ω _{ i }. Furthermore, c _{ i } is regarded as class center of fuzzy c-means algorithm [33].$$\Omega = \sum \limits_{i=1}^{N} \Omega_{i},~\Omega_{i} \bigcap \Omega_{j} = \Phi~(i \neq j), $$
- (2)The bias field b varies slightly in a small neighborhood region of any point y on the ith region Ω _{ i }, and leads to the approximate relation in Eq. (2):where \(\mathcal {O}_{\mathbf {y}} \triangleq \{ \mathbf {x}:|\mathbf {x} - \mathbf {y}| \leq \rho \} \).$$b(\mathbf{x}) J(\mathbf{x}) \approx b(\mathbf{y}) c_{i},~\mathbf{x} \in \mathcal{O}_{\mathbf{y}} \bigcap \Omega_{i} $$
where Φ=(ϕ _{1},…,ϕ _{ k }) is a vector valued function.
where \(e_{i}(\mathbf {x}) = \int K(\mathbf {y}-\mathbf {x}) |I(\mathbf {x}) - b(\mathbf {y}) c_{i}|^{2} d\mathbf {y}\).
where ∇ is the vector differential operator, namely gradient operator, H is the heaviside function.
- (1)Optimization of ϕ _{ j }:$$ \left\{ \begin{array}{l} \frac{\partial \phi_{j}}{\partial t} = - \sum \limits_{i = 1}^{N} \frac{\partial M_{i}(\boldsymbol{\Phi})}{\partial \phi_{j}} e_{i} + \nu \delta(\phi_{j}) \text{div} \left(\frac{\nabla \phi_{j}}{| \nabla \phi_{j} |} \right)\\ + \mu \left[ \Delta \phi_{j} - \text{div} \left(\frac{\nabla \phi_{j}}{|\nabla \phi_{j}|}\right) \right]\\ e_{i}(\mathbf{x}) = I^{2} \cdot (\mathbf{1} \ast K) - 2c_{i} I \cdot (b \ast K) + c_{i}^{2} (b^{2} \ast K) \\ (j = 1,2,\ldots,k) \end{array} \right. $$(12)
where · calculates the per-element product of two matrices, ∗ is the convolution operator, 1 is a matrix of ones with the same size as I, δ(·) is the derivative of the heaviside function and div(·) is the divergence.
- (2)Optimization of c:$$ c_{i} = \frac{\int (b \ast K) I M_{i}(\boldsymbol{\Phi} (\mathbf{y})) d \mathbf{y}}{\int (b^{2} \ast K) M_{i}(\boldsymbol{\Phi}(\mathbf{y})) d \mathbf{y}} ~(i = 1,\ldots,N) $$(13)
- (3)Optimization of b:$$ b = \frac{IJ^{(1)} \ast K}{J^{(2)} \ast K} $$(14)where$$\left\{ \begin{array}{ll} J^{(1)} = \sum \limits_{i=1}^{N}c_{i} M_{i}(\boldsymbol{\Phi}(\mathbf{y}))\\ J^{(2)} = \sum \limits_{i=1}^{N}{c_{i}}^{2} M_{i}(\boldsymbol{\Phi}(\mathbf{y})) \end{array} \right.. $$
3 Methods
Repeated trials expose imperfections of Li et al.’s method [22, 31] in detecting abnormalities from MR images: (a) background noise gives rise to redundant contours, (b) unsmooth bias field estimation exists, and (c) some possible abnormalities are omitted. We propose a robust MRI abnormality detection method to fix these problems based on a multi-phase level set method in combination with bias field estimation.
3.1 Background removal (ROI setting)
- 1.
Compute the optimal threshold value using Otsu’s algorithm and denote it by T.
- 2.Apply a fixed-level threshold to each array element of image f and obtain the binary image g:$$ g(i,j) = \left\{ \begin{array}{rl} 255, & f(i,j) \ge \eta T\\ 0, & \text{otherwise} \end{array} \right. $$(15)
where constant 0<η≤1 can guarantee that the regions of foreground with lower gray values are not ignored. Based on empirical observations, this constant commonly takes values in the interval [0.7,0.9].
- 3.Trace only the outer contours of image g. For the ith contour, if the area is greater than A, fill the area bounded by the contour with the gray value 255 and denote the corresponding mask image by B _{ i }. The constant A can skip small regions incurred by noise. Actually, A can be easily defined by professionals’ prior knowledge about the area of the target region. The union set of such B _{ i }, denoted by \(B~=~\bigcup B_{i}\), is the final ROI image, with the notation R in which the value 1 represents the points to be further processed:$$ R(i,j) = \left\{ \begin{array}{rl} 1, & B(i,j) = 255\\ 0, & \text{otherwise} \end{array} \right. $$(16)
Background noise is likely to bring out spurious contours by Li et al.’s method, shown in Fig. 1 a. After the R is calculated, background noise is removed with the values of background pixels assigned to zero. However, it is apparent that there are still some faulty contours with open contours, see Fig. 1 b. For this reason, it is wise to neglect the background region which causes abnormalities. Furthermore, only the pixels in these locations whose corresponding values are 1 in the ROI R are considered in our proposed method, not only to obtain accurate final contours (see Fig. 1 c) but also to speed up calculation.
3.2 Multi-phase level set method with bias field polyfit estimation
Naturally, we introduce bias field polyfit estimation to the multi-phase level set method. Experiments in Section 4 on detecting abnormalities from MR images demonstrate that this can significantly improve segmentation results.
The relationship of the degrees and terms for basis function
Degrees | 3 | 4 | 5 | 6 | 7 | … | p |
---|---|---|---|---|---|---|---|
Terms L | 10 | 15 | 21 | 28 | 36 | … | \(\frac {(p+1)(p+2)}{2}\) |
where \(\mathcal {E}_{\mathbf {x}} = \sum \limits _{i=1}^{N} \int K(\mathbf {y} - \mathbf {x}) |I(\mathbf {x}) - \mathbf {w}^{\mathrm {T}} G(\mathbf {y}) |^{2} M_{i}(\boldsymbol {\Phi }(x)) d \mathbf {y}\).
3.3 Customized initial level set functions to detect abnormalities
One of the disadvantages of traditional level set methods is that it requires manual placement of a closed curve near the desired boundary. Recently, researchers have employed random initial level set functions. Normally, once level set functions are stable, the process of evolution stops. Nevertheless, it is a challenge to jump out of a local extremum in (9). Moreover, some abnormalities occur as negligible patches, therefore no suitable initial level set functions can result in such abnormalities being detected. As a result, we introduce level set functions which intersect the target region in MRIs as much as possible. When level set functions during adjacent iterations are invariant, corresponding contours are the exact boundaries of target regions including abnormalities. These initial level set functions help us find out the abnormalities automatically, especially the negligible patches.
Definition of \(\phi _{1}^{0}(x,y), \phi _{2}^{0}(x,y)\)
Function InitialLevelSetFunction(H, W, ρ) |
---|
//Initialization |
for y←0 to H−1 do |
for x←0 to W−1 do |
\(\phi _{1}^{0}(x,y) = \rho \), \(\phi _{2}^{0}(x,y) = \rho \) |
repeat |
x←x+1 |
endfor |
repeat |
y←y+1 |
endfor |
//Evaluation 1 |
for y←y _{min} to y _{max} do |
for x←x _{min} to x _{max} do |
\(\phi _{1}^{0}(x,y) = - \rho \), \(\phi _{2}^{0}(x+1,y) = - \rho \) |
repeat |
x←x+2 |
endfor |
repeat |
y←y+2 |
endfor |
//Evaluation 2 |
for y←y _{min}+1 to y _{max} do |
for x←x _{min} to x _{max} do |
\(\phi _{1}^{0}(x,y) = - \rho \), \(\phi _{2}^{0}(x+1,y) = - \rho \) |
repeat |
x←x+2 |
endfor |
repeat |
y←y+2 |
endfor |
//ROI clipped |
ϕ _{1}=ϕ _{1}·R |
ϕ _{2}=ϕ _{2}·R |
It is worth pointing out that the member functions mentioned meet 0≤M _{ i }(x)≤1 and \(\sum \limits _{i = 1}^{3} M_{i}(\mathbf {x}) = 1\).
3.4 ROI-based numerical implementation
In order to remove the influence of noise in the background and reduce computational cost, we propose an ROI-based implementation for the aforementioned algorithm.
- 1.
ROI mask. I=I·R.
- 2.
Initialization. Set the following parameters: N, η, p, σ, ν, μ, ε and τ. Initialize b and ϕ _{1},…,ϕ _{ k }. Due to their invariability during iterative procedures, we prepare G, G G ^{T}, 1∗K _{ σ }, (1∗K _{ σ })·I ^{2}, (G∗K _{ σ })·I and G G ^{T}∗K _{ σ }.
- 3.
Iterative procedure. For the ith iteration, first update c via (13). Second, update Φ via (25), (12), and (26). Finally, update b via (21), (22), and (23).
- 4.
ROI mask. ϕ _{ j }=ϕ _{ j }·R for next iteration.
- 5.
Redo step (iii) until i exceeds the predefined maximal iteration.
4 Results and discussion
Parameters for MRI in this paper
Width | 96 | Modality | MR |
Height | 192 | Repetition time | 36 s |
Bit depth | 12 | Echo time | 9.2 s |
Slice thickness | 1 mm | Imaging frequency | 63.6250 |
Pixel spacing | (1.0417mm, 1.0417mm) | Protocol name | COR 3D PreSc Norm OFF 1’ S’ |
Parameters related to experiments
N | η | p | σ | ν | μ | ε | τ |
---|---|---|---|---|---|---|---|
3 | 0.7 | 4 | 4.0 | 4.0 | 1.0 | 1.0 | 0.1 |
4.1 Segmentation results
4.2 Segmentation assessment
For objective evaluation of our method, we consider manual contours drawn by specialists as the ground truth. We introduce two metrics to segmentation assessment. One metric m _{1} is defined to estimate the difference between the ground truth and the contours extracted by our method. For one specific ground truth contour, we first select its nearest contour edge in contours from our proposed method, then we calculate the distance between the contour pair. The other metric m _{2} is to account for how many accurate possible abnormal blobs are detected.
Assuming ground truth contours are denoted by \(C_{g}~=~\left \{ C_{g}^{1}, C_{g}^{2}, \ldots, C_{g}^{n_{g}} \right \}\), and contours from the proposed method are denoted by \(C_{p} = \left \{ C_{p}^{1}, C_{p}^{2}, \ldots, C_{p}^{n_{p}} \right \}\).
where \(\left |C_{p}^{k_{i}}\right |\) is the number of elements in \(C_{p}^{k_{i}}\).
4.3 Comparisons with existing methods
4.4 Discussion
In this paper, we introduced Otsu algorithm to remove background noise from original image. It is simple but effective in coarse segmentation. Such course segmentation helps to improve accuracy in final segmentation. Additionally, bias field polyfit estimation gives a more continuous bias field map, see Fig. 2 b. Furthermore, customized initial level set functions proposed in this paper helps to segment weak-edged, low-resolution MR brain images. In a sense, we incorporate bias field estimation into multi-phase level set method to acquire fine segmentation with low computational complexity. The proposed method can outline possible abnormalities. However, lesion recognition is to be determined in future work.
5 Conclusions
In this paper, we proposed a robust MRI abnormality detection method, which utilized background noise removal and polyfit level set method. Note that we improve the work in [22, 31], with our method being able to segment subtle bright or dark blobs automatically. Background removal helped us to exclude background noise, which also provided ROI to speed up successive processing. Polyfit level set method with customized initial level set functions in this paper does segment MRIs into individual parts, including tiny tissues. Experimental results demonstrate that our method has good performance in extracting all the blobs in MRIs, in which, there are potential lesions. But, as for each divided part, whether it is abnormal is yet to be determined. In future work, we will apply our technique on brain injury detection, such as for white matter injury detection.
Declarations
Acknowledgements
The authors would like to thank NSERC, Canada, for their financial support of this research.
Funding
The work was supported in part by the Open Project of the Artificial Intelligence Key Laboratory of Sichuan Province under grant nos. 2014RZY02 and 2017RZJ03, the Open Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing under grant no. 2014QZY01, Natural Science Foundation of Sichuan University of Science and Engineering (SUSE) under grant nos. 2015RC08 and 2017RCL23, and Educational reform project of SUSE under grant no. JG-1707. The work was also supported in part by the Training Programs of Innovation and Entrepreneurship of Sichuan Province for Undergraduates under grant no. 201710622088. The work was also supported in part by Guangxi Key Laboratory of Cryptography and Information Security under grant no. GCIS201607.
Availability of data and materials
Not applicable.
Authors’ contributions
CL and AB designed the algorithm, and CL wrote the paper and also performed the experiments. IC and AB reviewed and edited the manuscript. JY gave a critical suggestion on experimental section. All authors read and approved the manuscript.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
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