A novel brightness preserving gradient based joint histogram equalization technique for mammogram image contrast enhancement

Abstract

Mammogram image analysis is a crucial domain in the image-based diagnosis process. It is a trusted modality of non-invasive imaging for detecting tumour regions in the breast mass. However, poor contrast in the mammogram images is a key challenging issue. To address the issue, a brightness preserving gradient based joint histogram equalization (BPGJHE) method is suggested for enhancing the image quality while restoring the actual brightness and the structural information. The key contributions of the proposed method are (1) preserve the actual brightness of the mammogram images, (2) preserve the multi-scale structural details using an improved gradient filtering approach, (3) enrich the performance of the histogram equalization approach by incorporating the spatial information in the histogram. The suggested method is assessed using a series of mammogram images from standard datasets. The performance of the suggested method is validated in competence to the cutting-edge schemes. The quantitative assessment is performed using extensive validation metrics. The results indicate the efficacy of the suggested method.

Keywords

Mammogram image analysis histogram equalization gradient based filtering

1. Introduction

Based on the report of World Health Organization, breast cancer is found to be an alarming disease in the women [1]. Early detection plays a vital role in assisting the treatment planning and reducing the mortality rate. Image based diagnosis is an effective alternative in detecting and analysing the cancerous cells in the breast mass. Mammogram imaging is useful and potentially life-saving tool in the disease diagnosis and treatment planning process [2, 3, 4]. However, discriminating the normal and malignant tissues in a poor contrast environment is a major challenging factor in the image-based diagnosis process. Poor contrast may occur due to low dose of X-ray on the breast mass, which is applied for keeping the patient safe from radiation hazard. Enhancement of the mammogram image using a suitable retrospective technique is helpful for extracting more significant features and improving the malignant detection accuracy. It may also help in predicting the developmental stage of the cancerous cells in the breast mass and aiding the radiologists in the diagnosis process [5, 6, 7]. Therefore, the enhancement of contrast in the mammogram images is an important concern.

In the literature, many histogram equalization (HE) based techniques are reported for addressing the problem at hand. The improvements to the HE technique, such as: adaptive HE (AHE), Contrast Limited AHE (CLAHE), etc., are also reported. A common problem with the HE based approaches is over enhancement. They don’t preserve the actual brightness of the images. In addition to this, preserving the structural details is a key concern for the image based diagnosis. In this work, a brightness preserving gradient based joint histogram equalization (BPGJHE) method is suggested for enhancing the mammogram image quality, restoring the actual brightness and the multi-scale structural details. The input mammogram image is reformed into two sub-images before the enhancement process. It helps in preserving the actual brightness. An improved Gaussian pyramid based gradient filter is designed for retaining the multi-scale edge details of the image. Finally, the sub-images are enhanced using a modified joint histogram equalization (JHE) technique [8, 9]. The suggested technique is experimented with the use of several mammogram images from prevailing datasets. The performance comparison is carried-out with cutting-edge schemes. It appears to be a straightforward and operative formulation for enhancing mammogram images while restoring the structural information.

The upcoming sections are arranged as follows: a synopsis of the related studies is presented in Section 2. In Section 3, the formulation of the proposed method is briefly described. The simulation results with discussion are presented in Section 4. Lastly, the proposed work is concluded with the future direction in Section 5.

2. Related studies

In the last decade, a numeral method has been reported for addressing the problem at hand. Histogram equalization (HE) is reported as an initial solution for the enhancement of mammogram images. Adaptive HE (AHE) and contrast limited AHE (CLAHE) are the common progresses reported in the literature [10]. In addition to this, many advanced image processing tools such as machine learning, neural networks, fuzzy rules, etc., are integrated with the HE for solving the problem. Heinlein et al. [11] proposed an integrated wavelet transform with HE (IW-HE) for enhancing the microcalcification in mammogram images. They employed a model based method for improving the general contrast enhancement approaches. Christopher and Simon [12] proposed a nonlinear unsharp masking and L0 gradient minimization for mammogram enhancement. Their technique enhances the fine details in mammograms by subtracting a smoothed image using L0 gradient minimization from the original image. This helps in improving contrast and visibility of hidden masses in mammograms.

Sundaram et al. [13] reported an optimization technique based two stage process for contrast enhancement. They used HE and local contrast enhancement (HE-LCE) mechanism for addressing the problem. In [14], Burhan et al. presented a study that aims to enhance mammogram images by utilizing denoising filtering techniques. Their work demonstrated the effectiveness of various filters such as the median filter, CLAHE, and Wiener filter for reducing noise, enhancing contrast, and improving image quality. Dabass et al. [15] reported a CLAHE based method for contrast enhancement in mammogram images. They used intuitionistic fuzzy model for anticipating the entropy based features. Suradi et al. [16] reported a fuzzy anisotropic diffusion HE (FADHE) method for enhancing of mammogram images while restoring the actual brightness. They used fuzzy inference system for clipping the intensity levels in the enhancement process. Jenifer et al. [17] proposed a fuzzy clipped CLAHE method for enhancing the poor contrast while preserving the structural details. However, it does not address the poor contrast in the mammogram images with lesion regions. Chaira calculated the degree of hesitation in [18] in order to generate an interval type 2 fuzzy set for enhancing mammogram images. Zadeh’s fuzzy t-conorm is used to combine the membership functions to form a new one. Using intuitionistic fuzzy divergence and the restricted equivalence function, the thresholding value is calculated. An improved fuzzy hyperbolization process is performed using the computed thresholding value and a limited fuzzifier value for the problem at hand. Mohan et al. [19] integrated the fuzzy C-means (FCM) algorithm with CLAHE for enhancing contrast. The morphological gradient is employed for enhancement and accomplish segmentation at different scales, highlighting different features in the image. However, the above methods involve computational complexity and are parameter dependent.

Duan et al. [20] suggested a multiscale contrast enhancement technique using unsharp masking (UME) in Laplacian pyramid. They used the Laplacian pyramid for preserving the structural details in each scale. In [21], the authors suggested a mammogram image enhancement in the Dyadic wavelet transform domain. However, the approach is limited to analyze micro-calcification in the infant mammogram images. In [22], the authors proposed a s-curve transformation approach for contrast enhancement in mammograms. They showed the effect of sigmoidal function on genetic algorithm for enhancing the lesion regions. Their method aimed to abate the effect of poor contrast on the insight of the abnormalities. In [23, 24], the authors employed CLAHE and morphological operators for improvising the identification of microcalcifications, which are crucial markings of breast cancer. In [25, 26], the authors proposed metaheuristic approaches for medical image segmentation. They stochastically employed the metaheuristic (PSO, DE, ABC) on each sub-population, providing flexibility and adaptability in the optimization process. In [27, 28], the authors employed the CLAHE approach for enhancing the contrast in the mammogram images in the wavelet domain. They employed seam carving for removing the unnecessary pixels and preserving important information requiring manual intervention in the automated process.

Pawar and Talbar [29] proposed a strategy by fusing the discrete wavelet transform coefficients of original and enhanced images through CLAHE. The detail coefficients are combined using a maximum entropy based fusion rule. Their process aims to retain the maximum information pixels for enhanced contrast. In [30, 31], the authors applied Laplacian filtering for denoising or enhancing the mammogram images. Their methods extracted many statistical texture features such as contrast, correlation, etc. Tripathy and Swarnkar [32] proposed a CLAHE based mammogram enhancement technique based on statistical features. They employed a contrast improvement index (CII) to percept artifacts in the mammogram images. Thresholding values are utilized to identify the boundaries of breast masses, facilitating the identification of abnormalities such as calcifications.

In [33, 34], the authors proposed contrast enhancement methods that suppresses normal breast parenchyma and focusing on areas that deviate from the typical tissue density. They help in isolating suspicious regions for further analysis. Kumar et al. [35] combined the contrast adaptive gamma correction (CAGC) and support vector machine (SVM) for mammogram image enhancement. The CAGC balances the overall luminosity of poor-quality mammogram images affected by uneven illumination and low lighting conditions. The SVM in wavelet domain dynamically estimates the intensity transform function based on mammograms statistical features and enhances the contrast. Alshamrani et al. [36] proposed a histogram intensity windowing (HEIW) technique for contrast enhancement in the mammograms. It improves the detection and classification of breast abnormalities, potentially aiding in early diagnosis and treatment planning. Ghosh et al. [37] proposed a CNN based intuitionistic fuzzy special set for mammogram enhancement. Their method particularly focused on improving the visibility of abnormalities such as lesions, lumps, and tumors in low-dose mammogram images. In [38, 39], the authors proposed non-parametric methods for the classification of clinical images. The training data in the feature space is associated with pre-defined classes, and each element is classified based on its K-nearest neighbors. However, the method may be sensitive to noise present in the mammogram, which can affect the accuracy. In [40], we proposed an improved gradient based JHE approach, in which an improved gradient filter is developed using the Gaussian pyramidal filters.

Table 1
Summary of different mammogram enhancement methods

References	Databases	Merits	Demerits
[11, 12]	Mini MIAS	These methods improve the visibility of masses and calcifications within dense X-ray mammograms, aiding in the identification of cancerous abnormalities.	Improper parameter selection could potentially impact the quality of image enhancement and the overall effectiveness of these methods.
[13]	MIAS	Their approach provides optimal contrast enhancement while restoring local spatial data of the mammogram image.	The method involves multiple stages of processing, which may increase the computational complexity of the enhancement process.
[14]	DDSM, MIAS, INbreast, CBIS-DDSM	The method enhances the quality of mammogram images by reducing noise and improving contrast, making it easier to identify and diagnose breast cancer accurately.	Implementing multiple filtering stages may increase the computational complexity of the image enhancement process, potentially leading to longer processing times.
[17]	MIAS	The algorithm maintains an optimum value mean brightness, ensuring better preservation of brightness in the enhanced mammogram images.	There may still be some loss of information due to the clipping process.
[18]	DDSM, MIAS, INbreast, CBIS-DDSM	With the use of intuitionistic fuzzy set theory, the reported scheme can efficiently enhance the visual quality and contrast of the images.	The efficiency of the suggested approach may be sensitive to the selection of parameters such as fuzzifier values.
[22]	Mini MIAS	By optimizing the local transformation function parameters, the method achieves a simultaneous increment in Image Quality Assessment.	The efficacy of the suggested approach relies on finding the optimal parameters for the local transformation function.
[27, 28]	MIAS, CBIS-DDSM	By combining wavelet decomposition, seam carving, and CNN architecture optimization, the method enhances the detection of discriminative features in digital mammograms.	In some cases, wavelet transformations can introduce artifacts or distortions in the processed images.
[33, 34]	DDSM, MIAS, INbreast	These methods are effectively enhancing the contrast of mammographic images, making subtle features and focal densities more visible.	The method’s effectiveness could vary depending on the characteristics of the focal densities or masses being analysed.
[35]	Mini MIAS	The use of the CAGC approach for luminosity control allows for dynamic calculation of intensity transformation functions based on statistical parameters.	The method’s performance in the presence of noise, artifacts, or distortions in mammogram images is not explicitly discussed in the document.
[36]	DDSM, Mini MIAS	The method helps in enhancing mammogram images containing benign, malignant masses, micro calcifications, and healthy tissue.	Noise in mammographic images can interfere with the enhancement process and affect the performance of the neural network in detecting abnormalities.
[37]	DDSM, Mini MIAS, MedPix	The method enhances the visibility of mammography lesions, lumps, and abnormal cells, making it easier for radiologists to interpret and identify potential abnormalities.	The method needs a larger annotated training data to effectively learn the features and patterns in mammogram images.

A brief summary in terms of databases used, merits and demerits of the above discussed methods is tabulated in Table 1.

The above discussion depicts the following marks, (1) Over enhancement is a fundamental issue with the use of HE based approaches in mammogram images. (2) Parameter initialization and updating are major issues while using clustering based techniques. (3) The learning based methods need a larger amount of annotated training data for effective performance. To address these issues, the BPGJHE technique is proposed for effective enhancement of poor contrast in the mammogram images, while preserving the actual brightness and structural details.

3. Suggested methodology

Figure 1.

An architectural representation of the suggested BPGJHE method.

The suggested method is implemented in three-steps. In step-1, the mean intensity value of the mammogram image is calculated. Using this mean intensity value, the image is reformed into two sub-images. In step-2, the gradient images are generated using an improved gradient filter. In step-3, image enhancement is accomplished using a modified joint histogram equalization technique. An architectural representation of the suggested BPGJHE method for mammogram contrast enhancement is shown in Fig. 1.

Let $I=\{i(m,n)|1\leqslant m\leqslant M$ and $1\leqslant n\leqslant N\}$ is the mammogram image to be enhanced. Here, $i(m,n)$ are the pixel values, ( $m$ , $n)$ are the coordinates of the pixels. The intensity values in the image is in the range [0,…, $L-1$ ], considering $L$ number of intensity values.

3.1 Formation of sub-images

In this stage, the mean intensity value ( $I_{\mu})$ of the mammogram image ( $I)$ is calculated. Based on this mean intensity, two sub-images ( $I_{L}$ and $I_{U})$ are formed, such that:

\displaystyle I_{L}\in\left\{{\left.{i(m,n)}\right|i(m,n)\leqslant I_{\mu},% \quad\forall i(m,n)\in I}\right\}

(1)

and

\displaystyle I_{U}\in\left\{{\left.{i(m,n)}\right|i(m,n)>I_{\mu},\quad\forall i% (m,n)\in I}\right\}

(2)

Now, the sub-image $I_{L}$ is having the gray levels in the range {0, …, $I_{\mu}$ } and sub-image $I_{U}$ is having the gray levels in the range ( $I_{\mu}+1$ , …, $L-1$ ).

3.2 Extraction of the gradient image

In this stage, the gradient information of the mammogram image is extracted for incorporating the multiscale features. It is calculated in two steps. In the first step, an adaptive dark pass filter is employed on the mammogram image to abstract multiscale features. The multiscale images are obtained using an improved Gaussian pyramid. In the second step, in each succeeding stages, the Gaussian pyramid decomposes the low contrast image by down sampling. The first-level decomposition results in the bottom-level image of the multiscale pyramid. Initially, a Gaussian kernel size of 5 $\times$ 5 is used. The kernel size reduces for lower mean square error value images. The coefficients of the Gaussian kernel $w(i,j)$ , here ( $i,j)$ shows the dimension of the kernel, are designed with the given limiting conditions.

\displaystyle\mbox{Normalizing:}~{}\sum\limits_{i=-1}^{1}{\sum\limits_{j=-1}^{% 1}{w(i,j)=1}}

(3)

\displaystyle\mbox{Symmetric:}~{}w(-j)=w(j)

(4)

\displaystyle\mbox{Unimodal:}~{}w(j_{1})\geqslant w(j_{2})\mbox{ for }j_{1}% \leqslant j_{2}

(5)

\displaystyle\mbox{Influance:}~{}\sum\limits_{i=-1}^{1}{\sum\limits_{j=-1}^{1}% {w(i+2j)=\frac{1}{2}}}

(6)

By satisfying these limiting conditions, the kernel coefficients are computed as:

\displaystyle w(0,0)=a;w(0,1)=w(0,-1)=w(1,0)\,=\,w(-1,0)=0.25

(7)

\displaystyle w(1,1)=w(1,-1)=w(-1,1)=w(-1,-1)=0.25-0.5a;

(8)

\displaystyle w(i,j)=\left[{{\begin{array}[]{ccc}{0.25-0.5a}&\quad{0.25}&\quad% {0.25-0.5a}\\ {0.25}&\quad{a}&\quad{0.25}\\ {0.25-0.5a}&\quad{0.25}&\quad{0.25-0.5a}\end{array}}}\right]

(9)

Here, $a$ indicates the shape information of the kernel. For a suitable value of $a$ , the kernel gives Gaussian distribution effect. Here for $a=$ 0.3750, the kernel satisfies all the limiting conditions stated above. The normalized Gaussian kernel is applied on the bottom-level image $\left({I_{l}(m+i,n+j)}\right)$ and decimated by 2. It is expressed as

\displaystyle I_{l-1}(m,n)=\sum\limits_{i=-1}^{1}{\sum\limits_{j=-1}^{1}{w(i,j% ).I_{l}(m+i,n+j)}}

(10)

Therefore, the dark pass filter $(D_{l-1}(i,j))$ is expressed as:

\displaystyle D_{l-1}(i,j)=-\sum\limits_{N(i,j)}{\min\left({\frac{I_{l-i}(i-1,% j-1)-I_{l-i}(i+1,j+1)}{L-1},0}\right)}

(11)

Here, $N(i,j)$ defines the 4-neighboring data points of the center pixel ( $i,j)$ and $L-1$ is the highest possible intensity level in the image. The resulting multiscale image is interpolated using a bi-cubic filter. It gives the geometric mean values $(u_{l-k})$ .

\displaystyle u_{l-k}=U\left({D_{l-k},2^{k}}\right)

(12)

where, $U(\cdot)$ is the interpolation process with the factor of 2^k. Here, $k$ is an integer value. The gradient image $({I}^{\prime})$ is computed by:

\displaystyle I^{\prime}(m,n)=\left({\prod\limits_{i=0}^{l-1}{\max(u_{l-1}(m,n% ),\delta)^{\frac{1}{l}}}}\right).

(13)

Here, $\delta$ is a small positive value. It is used for restricting the negative intensities in the gradient image. For experimentation purpose, we used ( $\delta=$ 0.001 and $l=$ 4).

3.3 Contrast enhancement using joint histogram

The JHE approach incorporates the neighboring intensity values of a data point in the equalization process. A weighted Gaussian filter is used for generating an approximated image from the gradient image. The pixel value and its neighboring data points are considered for estimating the intensity pair counts. As in Fig. 1, $I_{L}^{\prime}=\{i(m,n)|1\leqslant m\leqslant M,1\leqslant n\leqslant N\}$ is the gradient image obtained from the sub-image ( $I_{L})$ of size $M\times N$ . Similarly, $I_{U}^{\prime}=\{i(m,n)|1\leqslant m\leqslant M,1\leqslant n\leqslant N\}$ is the gradient image obtained from the sub-image ( $I_{U})$ of same size. Here, $I_{L}^{\prime}$ and $I_{U}^{\prime}$ are the approximated images comprising of the structural as well as the spatial information. The size of images $I_{L}\mbox{ and }I_{L}^{\prime}$ are same, i.e., $M\times N$ with pixel values in the range {0, …, $I_{\mu}$ }. Similarly, the size of images $I_{U}$ and $I_{U}^{\prime}$ are same, i.e., $M\times N$ with pixel values in the range { $I_{\mu}+$ 1, …, $L-1$ }. Let the data point $f_{L}(m,n)=p$ and its spatially approximated data point $g_{L}(m,n)=q$ be taken from the input sub-image $(I_{L})$ and its approximated image $(I_{L}^{\prime})$ . The joint histogram $(H_{L})$ for the sub-image $(I_{L})$ is defined as:

\displaystyle H_{L}=\left\{{h_{L}(p,q)|0\leqslant(p,q)\leqslant I_{\mu}}\right\}

(14)

Here, $h_{L}(p,q)$ is the intensity pair count at the location $(m,n)$ . The intensity pair $f_{L}(m,n)$ and $g_{L}(m,n)$ are located in both $I_{L}$ and $I_{L}^{\prime}$ images, respectively.

Similarly, the data point $f_{U}(m,n)=p$ and its spatial approximated data point $g_{U}(m,n)=q$ be taken from the input sub-image $(I_{U})$ and its approximated image $(I_{U}^{\prime})$ . The joint histogram $(H_{U})$ for the image $(I_{U})$ is defined as:

\displaystyle H_{U}=\left\{{h_{U}(p,q)|I_{\mu}+1\leqslant(p,q)\leqslant L-1}\right\}

(15)

Here, $h_{U}(p,q)$ is the intensity pair count at the location $(m,n)$ . The intensity pair $f_{U}(m,n)$ and $g_{U}(m,n)$ are located in both $I_{U}$ and $I_{U}^{\prime}$ images, respectively.

The 2D cumulative distribution functions (CDF) for the two sub-images are calculated from the pixel pair population, as:

\displaystyle\textit{CDF}_{L}(p,q)=\sum\limits_{m=1}^{p}{\sum\limits_{n=1}^{q}% {h_{L}(m,n)}}

(16)

and

\displaystyle\textit{CDF}_{U}(p,q)=\sum\limits_{m=1}^{p}{\sum\limits_{n=1}^{q}% {h_{U}(m,n)}}

(17)

Table 2

Evaluation indices used for validating the contrast enhancement techniques

Formula	Description
$\textit{MSE}=\frac{1}{M\times N}\sum\limits_{i=0}^{M-1}{\sum\limits_{j=0}^{N-1% }{\left[{Y_{R}(i,j)-Y_{S}(i,j)}\right]^{2}}}$	The parameter is used to estimate the average of square of errors. The values approximating to zero are better [45].
$\textit{DE}_{N}=\frac{1}{1+\frac{\log(256)-\textit{DE}(Y_{O})}{\log(256)-% \textit{DE}(Y_{R})}}$	The parameter is estimating the dispersion in intensity distribution in the image. The range of DE_N value is [0, 1] [46].
$\textit{AMBE}=\frac{1}{1+\left\|{E(Y_{R})-E(Y_{O})}\right\|}$	The metric is estimating the actual brightness of the image. It is estimated from the average values of input and output images. A lower value approximating to 0 defines better brightness. The range of AMBE value is [0, 1] [47].
$\textit{EBCM}=\sum\limits_{i=1}^{M}{\sum\limits_{j=1}^{N}{\frac{con(i,j)}{M% \times N}}}$	It is used for estimating the pixel values of edges in smaller spatial kernel. The range of EBCM value is [0, 1] [48].
$\textit{RCM}=\sum\limits_{\forall i}{\sum\limits_{\forall j}{G(i,j)w(i,j)}}$	The index states the relative contrast change. The value approaching to “1” is for large scale contrast improvement. The range of RCM value is [ $-$ 1 1] [49].

Here, the calculation of 2D CDF does not depend on the image size. They are utilized for estimating the contrast enhanced intensity values. The enhanced intensities at location $(m,n)$ are as follows:

\displaystyle h_{L_{\textit{eq}}}(p,q)=\textit{round}\left({\frac{I_{\mu}}{% \textit{MN}-1}\left({\textit{CDF}_{L}(p,q)-(\textit{CDF}_{L}(p,q))_{\min}}% \right)}\right)

(18)

and

\displaystyle h_{U_{\textit{eq}}}(p,q)=\textit{round}\left({\frac{L-1}{\textit% {MN}-1}\left({\textit{CDF}_{U}(p,q)-(\textit{CDF}_{U}(p,q))_{\min}}\right)}\right)

(19)

where $(\textit{CDF}_{L}(p,q))_{\min}$ and $\textit{CDF}_{U}(p,q))_{\min}$ are the least non-zero CDF values of the pixel pairs. The equalized joint histograms $(H_{L_{\textit{eq}}},H_{U_{\textit{eq}}})$ for the pixel pairs are calculated as follows:

\displaystyle H_{L_{\textit{eq}}}=\left\{{h_{L_{\textit{eq}}}(p,q)|0\leqslant p% \leqslant I_{\mu},0\leqslant q\leqslant I_{\mu}}\right\}

(20)

and

\displaystyle H_{U_{\textit{eq}}}=\left\{{h_{U_{\textit{eq}}}(p,q)|I_{\mu}+1% \leqslant p\leqslant L-1,I_{\mu}+1\leqslant q\leqslant L-1}\right\}

(21)

This process increases the dynamic range of the input image, thereby preserving the structural details. Now the mammogram image intensity values $f_{L}(m,n)$ are replaced by $h_{L_{\textit{eq}}}(p,q)$ for all the instances of $m$ with $n$ only in $I_{L}$ . In a similar context, the gray scales $f_{U}(m,n)$ are substituted by $h_{U_{\textit{eq}}}(p,q)$ for all the cases of $m$ with $n$ only in $I_{U}$ . The enhanced image (Î ) is re-constructed by mapping the equalized gray levels of the sub-images. This is achieved as follows:

\displaystyle\hat{I}=I_{L}\cup I_{U}

(22)

The suggested method enhances both the sub-images uniquely as per the gradient based joint histograms. Here, the intensity values of the sub-image $(I_{L})$ is equalized in the range $[0,\ldots,I_{\mu}]$ , while the sub-image $(I_{U})$ is mapped in the range $[I_{\mu}+1,\ldots,L-1]$ . In this way, the dynamic range of the mammogram image is equalized in the range $[0,\ldots,L-1]$ . This approach not only enhances the poor contrast but also restores the multi-scale structural information as well as the actual brightness of the mammogram images.

4. Results and discussion

In this section, the experimental outcomes and a brief note on them is reported. The suggested BPGJHE technique is simulated in a standard computer with MATLAB. For validating the efficacy of the proposed approach, a comprehensive quantitative assessment is carried out. The state-of-the-art schemes, such as: CLAHE [10], IW-HE [11], HE-LCE [13], FADHE [16], FCM-CLAHE [19], UME [20], ASFO-CLAHE [24], RICE [33], CAGC [35], WEIW [36] and IGJHE [40] are taken for comparison. The mammogram images from the standard datasets, such as: DDSM [41], INbreast [42], MIAS [43] and CBIS-DDSM [44]are used. For quantitative analysis, validation indices (“mean square error (MSE) [45], normalised discrete entropy (DE ${}_{N})$ [46], absolute mean brightness error (AMBE) [47], edge based contrast measure (EBCM) [48], and relative contrast measure (RCM) [49]”) are used. The formulation detail for the validation indices is provided in Table 2. The symbols used carry the same meaning as described in the corresponding references.

Figure 2.

Simulation results with the use of DDSM dataset.

Figure 3.

Simulation results with the use of INbreast dataset.

Figure 4.

Simulation results with the use of MIAS dataset.

Figure 5.

Simulation results with the use of CBIS-DDSM dataset.

The subjective assessment of the proposed method is presented in Fig. 2 to Fig. 5. In Fig. 2, the experimental results of mammograms (benign and malignant) from the DDSM dataset are shown. In this figure, the simulation outcomes for the input images D1_A_1413_1. LEFT_CC (4) (benign) and D1_A_1169_1. LEFT_CC (malignant) are presented. Row 1 of the figure shows the mammogram image and its contrast improved image using the suggested technique. In the second row, the 2D histogram of each image is shown. In the contrast enhanced benign class of mammogram images, the fatty region is observed as a nested bright structure, whereas in the malignant class, the lesion region is observed as a deep white mass. The 2D histograms show the equalization of the intensity pixels, which is relatively better. Similarly, Figs 3, 4, and 5 present the simulation results for the mammogram images from the INbreast, MIAS, CBIS-DDSM databases, respectively. The simulation results of the input images 20586934 (4) (benign) and 20586908 (60) (malignant) from the INbreast dataset are presented. From the MIAS dataset, the input images mdb005 (35) (benign) and mdb023 (3) (malignant) are used. Similarly, the input images P_00038_RIGHT_CC_1(13) (benign) and P_00062_LEFT_CC_1 (3) (malignant) are shown from the CBIS-DDSM database.

Table 3

Quantitative assessment with the use of DDSM dataset

	Method	MSE	DE_N	AMBE	EBCM	RCM
Benign	CLAHE [10]	165.23	0.7856	0.2310	0.8759	0.7859
	IW-HE [11]	135.34	0.8234	0.1952	0.8684	0.8256
	HE-LCE [13]	132.69	0.8462	0.1835	0.8965	0.8268
	FADHE [16]	93.75	0.8127	0.1346	0.9123	0.8028
	FCM-CLAHE [19]	100.23	0.8346	0.1236	0.8962	0.8236
	UME [20]	120.85	0.7952	0.1875	0.9235	0.8759
	ASFO-CLAHE [24]	98.65	0.8659	0.1856	0.9324	0.8349
	RICE [33]	108.34	0.8924	0.1653	0.9119	0.8247
	CAGC [35]	99.38	0.9023	0.1472	0.9234	0.8568
	WEIW [36]	89.36	0.9168	0.1362	0.9124	0.8724
	IGJHE [40]	79.83	0.9134	0.1008	0.9348	0.9023
	Proposed	72.35	0.9256	0.1023	0.9502	0.9251
Malignant	CLAHE	178.25	0.9096	0.1718	0.8571	0.8726
	IW-HE	140.25	0.8679	0.1862	0.8793	0.7632
	HE-LCE	138.26	0.8958	0.1729	0.8762	0.7956
	FADHE	128.27	0.8564	0.1426	0.8138	0.8324
	FCM-CLAHE	112.34	0.8759	0.1523	0.8567	0.8469
	UME	140.26	0.9012	0.1637	0.8647	0.7384
	ASFO-CLAHE	103.45	0.8657	0.1234	0.8695	0.8574
	RICE	99.56	0.9039	0.1214	0.8746	0.8759
	CAGC	106.35	0.9234	0.1189	0.9024	0.8691
	WEIW	100.24	0.9356	0.1345	0.9129	0.9035
	IGJHE	98.35	0.9238	0.1020	0.9234	0.8867
	Proposed	92.34	0.9526	0.0987	0.9456	0.9243

Table 4

Quantitative assessment with the use of INbreast dataset

	Method	MSE	DE_N	AMBE	EBCM	RCM
Benign	CLAHE	135.26	0.8754	0.1235	0.8457	0.8072
	IW-HE	129.52	0.8659	0.1152	0.8675	0.8091
	HE-LCE	111.37	0.8759	0.1238	0.8841	0.8125
	FADHE	84.36	0.9148	0.0967	0.8765	0.8289
	FCM-CLAHE	93.25	0.8932	0.1011	0.9024	0.8426
	UME	102.45	0.8685	0.1018	0.8965	0.8277
	ASFO-CLAHE	93.27	0.8856	0.1235	0.9123	0.8247
	RICE	102.34	0.9034	0.1367	0.8859	0.8024
	CAGC	96.35	0.9125	0.1425	0.8752	0.8468
	WEIW	90.71	0.8835	0.0938	0.9036	0.8236
	IGJHE	80.26	0.9001	0.0823	0.9021	0.8493
	Proposed	77.51	0.9356	0.0749	0.9238	0.8897
Malignant	CLAHE	142.23	0.8785	0.1754	0.8268	0.8425
	IW-HE	134.52	0.9021	0.1652	0.8574	0.8732
	HE-LCE	124.18	0.9024	0.1246	0.8365	0.8759
	FADHE	89.38	0.8867	0.1241	0.8467	0.8567
	FCM-CLAHE	92.36	0.9034	0.1352	0.8567	0.8629
	UME	105.24	0.8975	0.1124	0.8428	0.8895
	ASFO-CLAHE	93.65	0.8956	0.1126	0.8686	0.8762
	RICE	100.23	0.9231	0.1238	0.8795	0.8991
	CAGC	87.34	0.9025	0.1295	0.8991	0.9123
	WEIW	98.61	0.8863	0.1012	0.9135	0.9189
	IGJHE	92.85	0.9230	0.1029	0.8958	0.9024
	Proposed	89.67	0.9435	0.0962	0.9345	0.9238

Table 5

Quantitative assessment with the use of MIAS dataset

	Method	MSE	DE_N	AMBE	EBCM	RCM
Benign	CLAHE	128.56	0.7854	0.1207	0.8657	0.7892
	IW-HE	140.85	0.8246	0.1137	0.7968	0.8246
	HE-LCE	120.63	0.8642	0.1296	0.8024	0.8439
	FADHE	89.53	0.9025	0.0935	0.8329	0.8467
	FCM-CLAHE	92.35	0.8925	0.1231	0.8567	0.8694
	UME	107.52	0.8765	0.1024	0.8436	0.8756
	ASFO-CLAHE	102.53	0.9231	0.1124	0.8569	0.8749
	RICE	89.36	0.9360	0.1210	0.8794	0.8896
	CAGC	83.26	0.9023	0.1102	0.8897	0.9029
	WEIW	94.81	0.8989	0.1008	0.9195	0.9125
	IGJHE	91.47	0.9234	0.1010	0.9054	0.8989
	Proposed	91.23	0.9435	0.0831	0.9345	0.9348
Malignant	CLAHE	130.52	0.8791	0.1426	0.8754	0.8754
	IW-HE	142.85	0.8452	0.1527	0.8968	0.8869
	HE-LCE	134.29	0.8735	0.1342	0.8859	0.8759
	FADHE	103.20	0.8347	0.1247	0.9235	0.9124
	FCM-CLAHE	98.56	0.8695	0.1356	0.8936	0.9235
	UME	121.08	0.8661	0.1019	0.9123	0.9027
	ASFO-CLAHE	92.38	0.8749	0.1212	0.9124	0.8965
	RICE	89.35	0.8969	0.1385	0.9238	0.8862
	CAGC	100.35	0.9002	0.1426	0.8934	0.8679
	WEIW	98.37	0.8956	0.1123	0.9239	0.9039
	IGHJE	90.25	0.9127	0.0903	0.9480	0.9362
	Proposed	85.24	0.9356	0.0725	0.9238	0.9536

Table 6

Quantitative assessment with the use of CBIS-DDSM dataset

	Method	MSE	DE_N	AMBE	EBCM	RCM
Benign	CLAHE	147.36	0.8759	0.1223	0.8425	0.8759
	IW-HE	139.36	0.8356	0.1258	0.8029	0.8562
	HE-LCE	111.28	0.8596	0.1396	0.8248	0.8629
	FADHE	98.36	0.9120	0.0993	0.8536	0.8682
	FCM-CLAHE	110.25	0.8989	0.1025	0.8695	0.8952
	UME	123.51	0.8856	0.1120	0.8629	0.8956
	ASFO-CLAHE	113.78	0.9235	0.1148	0.8751	0.9024
	RICE	90.36	0.9136	0.1263	0.8963	0.9126
	CAGC	85.69	0.8935	0.1102	0.9092	0.9368
	WEIW	93.65	0.9008	0.1230	0.9125	0.9156
	IGJHE	92.36	0.9233	0.1010	0.9154	0.9180
	Proposed	88.52	0.9536	0.0729	0.9435	0.9396
Malignant	CLAHE	142.36	0.8986	0.2215	0.8968	0.8859
	IW-HE	138.25	0.8769	0.1852	0.9035	0.9036
	HE-LCE	140.29	0.9002	0.1712	0.8952	0.8991
	FADHE	111.92	0.8628	0.1621	0.9128	0.9028
	FCM-CLAHE	106.34	0.8729	0.1592	0.9235	0.9131
	UME	126.35	0.8963	0.1634	0.9231	0.9127
	ASFO-CLAHE	99.35	0.9002	0.1472	0.8956	0.9238
	RICE	100.31	0.9170	0.1125	0.8874	0.9148
	CAGC	95.63	0.8963	0.1358	0.9026	0.9028
	WEIW	97.61	0.9024	0.1028	0.9307	0.9247
	IGJHE	90.25	0.9127	0.0903	0.9480	0.9348
	Proposed	85.63	0.9369	0.0714	0.9568	0.9562

The quantitative assessment of the suggested method is presented in Table 3to Table 6 using the mammogram images from DDSM, INbreast, MIAS and CBIS-DDSM databases, respectively. The values in the tables present an average of 50 randomly selected benign and malignant class mammogram images. These tables show the comparison in terms of MSE, DE_N, AMBE, EBCM and RCM. From the outcomes, it is observed that the suggested method is clearly the best in terms of most of the evaluation indices. However, in few cases, the suggested method is the second contestant.

Figure 6.

Performance comparison of different approaches using (a) MSE, (b) DE_N, (c) AMBE, (d) EBCM, (e) RCM.

A graphical analysis is also presented in Fig. 6. Figure 6(a) presents the comparison of the methods using the MSE. From the graph, it is reported that the suggested approach shows least values for both benign and malignant mammogram images, which ensures minimum error in the enhanced image. Figure 6(b) presents a comparison of the discussed techniques in terms of DE_N. The maximum value of this parameter ensures better preservation of structural details in the enhanced images. Figure 6(c) presents the comparison of the enhancement assessment using AMBE. The lower value of AMBE with the use of the suggested approach ensures better restoration of the actual brightness in the mammogram images. Finally, Fig. 6(d) and 6(e) show the assessment of different approaches using EBCM and RCM, respectively. The maximum value in these indices also ensure better contrast enhancement as compared to the cutting-edge approaches.

5. Conclusion

In this work, a brightness preserving gradient based joint histogram equalization method is suggested for enhancement of the contrast in mammogram images. The approach shows a higher relative contrast measure in the quantitative assessment. It may be due to the process of sub-image HE, which restores the actual brightness of the images. The improved gradient pyramid based dark pass filter is employed for incorporating the spatial and multi-scale features in the contrast enhancement process, which increases its performance. The representation of 2D histograms show the equalization of intensity values more appropriately. The performance of the suggested method is depicted in contrast to many cutting-edge approaches. The comparison is done based on a set of standard evaluation metrics and tested over multiple mammogram images from standard datasets. From the qualitative and quantitative assessments, the superiority of the suggested method is claimed. The outcomes obtained will enhance the research in mammogram image analysis in future.

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A novel brightness preserving gradient based joint histogram equalization technique for mammogram image contrast enhancement

Abstract

Keywords

1. Introduction

2. Related studies

Table 1 Summary of different mammogram enhancement methods

References

Table 1
Summary of different mammogram enhancement methods