Human visual system based optimized mathematical morphology approach for enhancement of brain MR images

Abstract

Brain tumor is a life-threatening disease with fast growth rate, which makes its detection a critical task. However, low contrast and noise content in brain magnetic resonance images (MRI) hampers the screening of brain tumor. Therefore, contrast enhancement of these images are necessary to obtain a more definitive imaging for tumor detection. This paper presents an optimized enhancement model for processing Brain MRI by employing morphological filters in coherence with human visual system (HVS) system. The HVS coherence in response of filtering process is incorporated by combination of top-hat and bottom-hat morphological operators using logarithmic image processing model. Application of morphological filter requires selection of structuring element of requisite shape and size to ensure precision in brain tumor detection. This process is challenging as brain tumors (in MRI) may vary rigorously in size and morphology with each case or stages of tumor. Herein, this constraint has been resolved by using a disk-shaped structuring element whose order (size) is optimized using particle swarm optimization algorithm. The enhancement results are quantitatively evaluated using image quality measurement parameters like contrast improvement index, average signal to noise ratio, peak signal to noise ratio and measure of enhancement.

Introduction

Background

Brain imaging analysis has become very important part of biomedical research due to increasing number of brain abnormalities; amongst which brain tumor has been the most ominous and intractable disease which can cause death. Based on their growth, tumors can be classified into Benign or Malignant tumor (Gudigar et al. 2019; Alankrita et al. 2011; Bahadure et al. 2018). Due to structural complexity and varied impact on different individuals, tumor screening has become a difficult task; magnetic resonance imaging (MRI) is therefore one of the most adaptive and preferred technique. It consists of various imaging modalities such as MR-T1/MR-T2, each highlighting its own contrast characteristics (Rajinikanth and Satapathy 2018). Further, the entire process of tumor detection and classification is a laborious task and associated with challenges such as poor contrast, background noise and unclear boundaries (Akram and Usman 2011). To overcome these challenges, in the initial stages of detection, brain MR images are subjected to contrast and edge enhancement algorithms as a mandatory pre-processing operation. This is necessary to simplify the process of computer-aided detection of brain tumor.

Review of related works

Previous studies on brain tumor detection employing computer assisted techniques mainly focused on algorithms/approaches like histogram equalization, multi-resolution and morphological filters. Enhancement approaches based on histogram equalization are very common with their adaptive modifications (Stark 2000). These methods had a limitation of noise amplification; this very attribute was improved when a combination of contrast limited adaptive histogram equalization (CLAHE) and discrete wavelet transform (DWT) was deployed by Lidong et al. (2015). In the former technique, noise was suppressed by amplifying only low frequency components but had the limitation of changing the brightness of image and saturating it. Therefore, mathematical morphology was deployed by Kharrat et al. (2009) and Hassanpour et al. (2015). Later, Benson and Lajish (2014) proposed a method for MRI contrast enhancement using morphological filters. The algorithm was simple and could be applied in various applications such as tumor detection, volume analysis and classification as reported. In comparison to other approaches, morphological filters therefore possesses the requisite potential to enhance the poor-quality MRI with simplicity and less processing time along with noise suppression capability. However, the performance of these filters is constrained due to the enlisted factors:

• Improper shape and size of structuring element can distort image features and poses difficulty in detection of tumor at subsequent stages.

• Inappropriate choice of operators can distort diagnostic structures in MRI.

• Non-adaptive filtering and manual selection of structuring element hinders the generalization of approach for variants of MRI.

• Filtering operation should retain the diagnostic features in MRI without amplifying noise.

• Morphological filter responses do not correlate with HVS when applied to medical images.

The rest of the paper is organized in the following sections: Sect. 2 discusses the problem formulation; Sect. 3 provides the general overview of morphological filtering, HVS model along with discussion of proposed enhancement methodology. Section 4 presents image quality assessment (IQA) metrics deployed for the quantitative evaluation of enhanced MRI. Section 5 narrates the results and discusses the outcomes of the work presented whereas conclusions are drawn in Sect. 6.

Problem formulation

Morphological filtering is an effective technique for contrast and edge enhancement; but requires careful selection of shape and size of structuring element in context to processing medical images. To improve upon the existent challenges of morphological filtering (as discussed in Sect. 1.2); an improved enhancement model has been formulated in this paper. The proposed morphological operators using disk shaped structuring element as shown in Fig. 1. To accommodate the enhancement response of the filter in coherence with HVS characteristics; conventional arithmetic combination of morphological operators has been replaced with LIP model. LIP is a mathematical model that has a set of algebraic operations which can be applied on intensity images (Trivedi et al. 2013). Morphological operators (Verma et al. 2013; Tiwari et al. 2018) used are largely dependent on the structuring element. The proper selection of shape and size (Raj et al. 2011) of the structuring element is very important because the appropriate visualization of tumor details upon reconstruction is largely dependent upon this factor. This issue has been trivial because manual selection of structuring element could not generalize the approach for variety of tumor sizes. Selection of structuring element of requisite size is a time taking process and is therefore the obtained results are not very satisfactory or have less precision (Hassanpour et al. 2015). Also, manually checking the performance by using different structuring element sizes until the satisfactory results are obtained is practically impossible and a cumbersome process. This constraint has been resolved by deploying optimization techniques that could help in optimal size selection of the structuring element for a particular MRI. Various bio-inspired algorithms are available which are either based on evolutionary intelligence such as bacterial foraging optimization (BFO) or swarm intelligence such as particle swarm optimization (PSO) (Poli et al. 2007). PSO is a popular optimization algorithm that simulates the behavior of birds flocking (Ayoobkhan et al. 2018). In PSO every bird is considered as a particle and a fitness value which is the value to be optimized is assigned to them. For every fitness value, a fitness function is evaluated based on which optimization process is iteratively carried out. Hence, PSO algorithm has been deployed in this paper to optimize the size of structuring element for improvement of enhancement response of HVS based morphological filter.

Fig. 1 [Images not available. See PDF.]

Disk shape structuring element of size 4

Proposed enhancement methodology

Morphological filtering

Morphological filtering (Verma et al. 2013; Tiwari et al. 2018) is a set of non-linear filtering techniques that are based on the structural properties of the objects. They are implemented through a combination of morphological operators which are related to the shape of entities in the image. These operators are applied on two inputs which are the input image and the structuring element. Structuring element is a template that designates the pixel neighborhood and the choice of its shape and size depends upon the application and information being fetched (Raj et al. 2011). The common morphological operators are Erosion, Dilation, Opening and Closing (Raj et al. 2011) which can further be used in several combinations for a variety of filtering operations. Morphological filtering finds a wide range of application in medical imaging including thermographic, MR and ultrasound images (Arya et al. 2019). In MRI, noise reduction and contrast enhancement are the primary requisites in any of its application for medical diagnosis (Bhateja et al. 2013a, b).

Logarithmic image processing (LIP) model

LIP model is based on mathematical theory that provide new operations for image processing. The main significance of LIP is that this model has proven to be consistent with the laws of HVS, e.g. brightness scale, saturation properties, contrast characteristics and Weber and Fechner Laws (Trivedi et al. 2013). In LIP algebra, absorption function of gray scale values is referred to as a gray tone function. The gray scale of image is the amount of light that passes through the light filter. Each point of the tone function is called gray tone. The gray scale (x) of pixel is related to gray tone (X) as

1

$$x=M-X$$where M is intensity of the light source.

LIP addition is represented as:

2

$$k_1\tilde{\oplus }{k}_2=k_1+k_2-\frac{k_1{k}_2}{m}$$where $\tilde{\oplus }$ is operator for LIP addition, k₁ and k₂ denote gray scale function and m is the maximum value of pixel in the image.

Proposed morphological filter for contrast enhancement

This paper proposes an improved approach for brain MRI enhancement using LIP combination of morphological top-hat and bottom-hat operators. As shown in Fig. 2, the input image after pre-processing is forwarded to enhancement stage. In this stage PSO algorithm is deployed for selecting the optimal size of structuring element which is used further in the enhancement algorithm. The enhanced image is then assessed based on the image quality metrics.

Fig. 2 [Images not available. See PDF.]

Block diagram of proposed enhancement methodology

Top-hat transform (Hassanpour et al. 2015) act as a high pass filter and highlights the bright objects on a dark background. This transform leads to a distinct visibility of tumor region which originally was merged with the background. The most important utility of Top-Hat transform is to correct the non-uniformity in intensity which is a pervasive problem in MR images. Bottom-hat transform (Hassanpour et al. 2015) is just the converse of top-hat transform and is used to highlight the darker regions of the image. These operations are stated in Eqs. (3) and (4) respectively. Top-hat and bottom-hat operators are added using LIP algebra considering its significance in image enhancement from HVS concept. It is desirable to minimize the background features that are not relevant for diagnostic purposes; hence after a series of steps further, bottom-hat transform is subtracted from top-hat in the final step. This particular step helps in segregation of the tumor region with respect to the background tissues.

3

$$T_{\mathit{hat}}(f)=f-(f\circ se)$$

4

$$B_{\mathit{hat}}(f)=(f\bullet se)-f$$where se is the structuring element and operator ◦ and • represent opening and closing respectively.

The procedural steps for the proposed enhancement approach using morphological filters are summarized under Algorithm I. Herein firstly the input MR image (I₁) is read and converted from RGB to an image in Grayscale profile (I₂). Secondly, the mathematical morphology operations are performed over grayscale image (I₂) to yield outcomes of top-hat (I₃) followed by bottom-hat (I₄) operations (Hassanpour et al. 2015). Then using LIP operators of Eq. (2), the top-hat image (I₃) is added to bottom-hat (I₄) to generate (I₅). This is followed by arithmetic subtraction of bottom-hat (I₄) from resultant (I₅) to yield resulting image (I₆). This image (I₆) is then complemented to yield (I₇) and bottom-hat (I₄) is again subtracted from (I₇) to produce finally (I₈). The size of structuring element chosen must be enough to trap tumor region without blurring the images. The performance of this filtering approach is improved further by optimizing the size of structuring element using particle swarm optimization (PSO) (Poli et al. 2007) algorithm as shown in Algorithm II.

Adaptive and optimized selection of structuring element using PSO

As already discussed, the optimal selection of structuring element for morphological filters has been made using PSO algorithm. PSO algorithm in this work use measure of enhancement (EME, refer Sect. 4.3) as the fitness function which means that the optimum size of the structuring element is chosen based on the EME value of the enhanced image when the morphological operations are performed using this size. This optimization algorithm (Algorithm-II) operates via four modules. In the first module, PSO parameters such as the number of particles (nPop), iterations (It), range of initial position (varMax/varMin) are initialized. In the second module, the aforesaid particles are created and are initialized. Each particle has its initial best position i.e. fitness value stored in pBest and its corresponding EME values i.e. the fitness function stored in pBest_Cost.Global Best contain the overall best position and their corresponding EME values are stored in gBest (initially 0) and gBest_Cost (initially EME_o-denotes EME of the original MRI) respectively. The main iterative loop of PSO begins in the third module. This module consists of a nested loop with outer loop defining the number of iterations till which the entire PSO function will be iteratively executed. In the inner loop, particle velocity p_vel is computed according to Eq. (5) and this value is used to update particle position p_pos according to Eq. (6). This is followed by the computation of EME_f which is the value of EME computed at updated value of p_pos. The pBest and pBest_Cost are updated, if the test condition is true. At the end of all the iterations, pBest will contain the best position of each particle; this is the last module of this algorithm. Amongst these, the pBest that has the best EME value (greater than gBest_Cost) is chosen as the gBest. The final output of the algorithm is gBest that yields the optimized size of the structuring element. This optimal value of size/order of the structuring element is then utilized for the filter function of morphological operators in Algorithm-I (step-3).

5

$$\begin{array}{cc}\hfill \text{p}\_\text{vel}\left[\text{i}\right]\left[\text{d}\right]& =\text{p}\_\text{vel}\left[\text{i}\right]\left[\text{d}\right]+\text{c1}\ast \text{rand}()\ast \left(\text{pBest}\left[\text{i}\right]\left[\text{d}\right]-\text{p}\_\text{pos}\left[\text{i}\right]\left[\text{d}\right]\right)\hfill \\ \hfill & +\text{c2}\ast \text{rand}()\ast \left(\text{gBest}\left[\text{i}\right]\left[\text{d}\right]-\text{p}\_\text{pos}\left[\text{i}\right]\left[\text{d}\right]\right)\hfill \\ \hfill \end{array}$$

6

$$\text{p}\_\text{pos}\left[\text{i}\right]\left[\text{d}\right]=\text{p}\_\text{pos}\left[\text{i}\right]\left[\text{d}\right]+\text{p}\_\text{vel}\left[\text{i}\right]\left[\text{d}\right]$$where [i] is the particle number and [d] is the dimensionality of the algorithm which has been set to 1 in our algorithm.

c1 and c2 are acceleration factors and rand() is a function that generates random values between 0 and 1.

Image quality assessment (IQA) metrics for enhancement

IQA metrics for MRI enhancement deployed in this work include: contrast improvement index (CII), peak signal to noise ratio (PSNR), average signal to noise ratio (ASNR) (Srivastava et al. 2011; Bhateja et al. 2013a, b; Jain et al. 2013) and measure of enhancement (EME) (Wharton et al. 2008). It is known, that enhancement refers to the adjustment of image contrast by modifying the gray-level values of pixels. However, it is also evident that enhancement may result in amplification of noise level also due to under- or over-enhancements. Therefore, CII may not be considered solely as quality assessment parameter for the enhanced MRI. Therefore, PSNR and ASNR are also computed in parallel to ensure that the enhancement operation is not accompanied with enhancement of background noise. Additionally, a non-reference assessment of contrast has also been evaluated using EME. This metric has played a dominant role as it is utilized for determining the terminating condition of PSO algorithm.

Contrast improvement index (CII)

Contrast (C) parameter used in computation of CII uses a region of interest (ROI-region containing tumor, also called as foreground) and its immediate surrounding neighborhood as background. C is the contrast of the ROI which is given by:

7

$$C=\frac{m_f-m_b}{m_f+m_b}$$where $m_f$ and $m_b$ are the mean of foreground and background regions in and about ROI respectively.

Ratio of contrast of enhanced image to the contrast of original image is called CII.

8

$$CII=\frac{C_E}{C_O}$$where $C_E$ and $C_O$ are contrast of enhanced and original images respectively.

Equation (8) denotes that CII is a relative quantity which means that higher the value of CII more is the improvement in contrast of the enhanced MRI.

Peak signal to noise ratio (PSNR) and average signal to noise ratio (ASNR)

PSNR and ASNR are absolute quantities used for measuring the noise level in an image. Higher value of PSNR and ASNR denotes better quality of enhanced MRI. They are defined as:

9

$$PSNR=\frac{m_f^m-m_b}{\sigma }$$

10

$$ASNR=\frac{m_f^{}-m_b}{\sigma }$$where $m_f^m$ denotes maximum gray level value of foreground, $m_f$ and $m_b$ are the mean of foreground and background respectively and $\sigma$ is the standard deviation denoting the level of noise in background.

Measure of enhancement (EME)

It is used for the absolute measurement of contrast enhancement observed in an image. In this paper, EME (Huang and Nguyen 2019; Bhateja et al. 2018), being a non-reference IQAmetric for contrast; is used as a fitness function in the PSO algorithm. Let (m, n) be the size of an image which is split into r × c blocks, where each block is represented as $B_{k,l}\left(i,j\right)$. $I_{max;k,l}$ and $I_{min;k,l}$ be the maximum and minimum intensities in an image block $B_{k,l}\left(i,j\right)$. Using, the aforesaid variables, the EME may be mathematically expressed as in Eq. (11).

11

$$EME=\frac{1}{r\times c}\sum _{i=0}^r\sum _{k=0}^c\left[20ln\left(\frac{I_{max;k,l}}{I_{min;k,l}}\right)\right]$$

Results and discussions

This section presents the results obtained from the proposed enhancement approach in combination with optimization using PSO algorithm. The MR images that have been used herein for simulations are taken from the database: whole brain atlas (WBA) (WBA 2019) and internet brain segmentation repository (IBSR) (IBSR 2019). WBA is a neuro-imaging database containing axial, sagittal and coronal cross section of MRI and CT with over 100 brain structures and IBSR provides manually guided expert segmentation result along with MRI database. Morphological filter combination is applied on pre-processed MRI using the disk-shaped structuring element (using Algorithm I). PSO algorithm iteratively generates the optimal value of order or the size of this element (for application of morphological filters) wherein the best possible EME values are obtained for the enhanced MRI (using Algorithm II). Table 1 show different values of sizes of the structuring element obtained at 10, 15 and 50 iterations of the PSO. The difference in results at different iterations is due to randomization of PSO parameters. Initially, the results obtained for 10 iterations are assumed to be a temporary value. However, later on it can be observed that the size as well as the obtained EME values do not differ much when number of iterations is increased from 10 to be 15 and 50 respectively.

Table 1. Optimal size of structuring element obtained at various iterations of PSO

Input images	Number of iterations (It)
	It = 10		It = 15		It = 50
	Size	EME	Size	EME	Size	EME
MRI#1	52	3.2480	101	5.0787	96	5.0133
MRI#2	72	4.5258	78	6.6149	84	6.2561
MRI#3	71	3.2417	69	4.0020	68	3.9156
MRI#4	31	4.1526	31	4.1836	38	4.0257
MRI#5	73	4.1210	82	5.8731	89	5.5861

Using the obtained values of optimized structuring element size for a given MRI; Fig. 3 shows the enhanced response obtained after performing the proposed enhancement approach for different samples of MRI. The quality assessment of the enhanced MRI is carried out in terms of EME, CII, PSNR and ASNR as already mentioned in Sect. 4 and summarized in Table 2. It shows a comparison of these quality metrics for enhanced MRI obtained without and with PSO algorithm with morphological filters. The size of structuring element is taken 30 for the test samples of MRI (#1–#5) without PSO while the optimized size is different for different MRI as provided in Table 1. On optimization, there is slight decrement in ASNR/PSNR (in few cases only) but a significant increment in the values of CII and EME. The higher values of these IQA metrics indicate a significant contrast improvement and effective noise removal when compared with original MRI.

Fig. 3 [Images not available. See PDF.]

Results of proposed enhancement methodology. a Input MR image, b enhanced MR image

Table 2. Comparison of IQA metrics for proposed enhancement approach

	Without PSO					With PSO
	SIZE	ASNR	EME	PSNR	CII	SIZE	ASNR	EME	PSNR	CII
MRI#1	30	1.2087	4.2276	9.4963	1.6541	65	1.0872	5.0787	8.3141	2.6273
MRI#2	30	1.0414	4.8103	5.5717	1.7769	81	2.4126	6.6149	4.7624	2.2273
MRI#3	30	0.6853	3.3882	4.9496	1.4901	68	1.8985	4.0020	4.3706	2.0058
MRI#4	30	0.5576	4.1738	5.0797	2.0299	32	2.0259	4.1836	5.0420	2.4366
MRI#5	30	1.2260	5.0958	7.9085	1.5095	88	1.4099	5.8731	5.5461	2.0489

From Fig. 4, a clear distinction can be made between the images obtained in the two cases i.e. without PSO and with PSO algorithm using proposed morphological filters. It may be observed that original MRI contains high intensity homogenous patches which might be the ROI (i.e. tumor region). The visible results of the enhancement (with PSO) are much better and informative than the results without optimization. For enhanced MRI (with PSO) the background noise is well suppressed, and insignificant features are omitted to a great extent. The preserved features are of same intensity as that in the original MRI and there is no alteration in the image brightness. However, the images without optimization have poor visibility of the remaining features due to their poor contrast; also, there is a slight change in the size of the features in images without optimization. This alteration in the intensity values of the pixels lead to a significant loss of information which is of importance in later stages of processing. The superiority of the optimization results is also verified by the higher values of EME.

Fig. 4 [Images not available. See PDF.]

MR images obtained with proposed enhancement approach. a Input MRI. b Enhanced MRI without PSO. c Enhanced MRI with PSO

Conclusion

Computer-assisted analysis of brain MR images is necessary for effective detection and diagnosis of brain tumor. In this paper, an improved approach for HVS based contrast enhancement of MRI is proposed deploying morphological filtering. Further, to attain generalization in approach for variety of cases in MRI and make the filter adaptive for tumor segregation; a disk-shaped structuring element is used whose size is optimized using PSO algorithm. The structuring element therefore adaptively varies with the image yielding improved detection outcomes. The enhancement results on MRI shows a considerable improvement in contrast and effective filtering of noise as indicated by the incrementing values of CII, EME, ASNR and PSNR respectively. Enhancement of MRI with PSO algorithm shows a more promising response supported with a considerate increase in value of CII and EME than those obtained without PSO algorithm. The obtained enhancement results are expected to further simplify the challenges encountered during subsequent phases involving segmentation and classification of brain tumor at later stages.

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