An Improved Medical Image Fusion Approach Using ... - IEEE Xplore

2014 International Conference on Medical Imaging, m-Health and Emerging Communication Systems (MedCom)

An Improved Medical Image Fusion Approach Using PCA and Complex Wavelets Himanshi

Vikrant Bhateja, Member IEEE

Abhinav Krishn

Akanksha Sahu

Deptt. of Electronics and Comm. Engg., SRMGPC, Lucknow (U.P.), India. [email protected]

Deptt. of Electronics and Comm. Engg., SRMGPC, Lucknow (U.P.), India. [email protected]

Deptt. of Electronics and Comm. Engg., SRMGPC, Lucknow (U.P.), India. [email protected] m

Deptt. of Electronics and Comm. Engg., SRMGPC, Lucknow (U.P.), India. akankshasahu1708@gmail .com

tissue contrast allows better visualization of tumors. This highlights the need towards the development of multimodality medical imaging sensors for extracting clinical information to explore the possibility of data reduction along with better visual representation [24]-[26]. In the past decades, several fusion algorithms varying from the traditional fusion algorithms like simple averaging and weighted averaging, maximum and minimum selection rule [27] have been proposed. With the advancement of research in this field, algorithms such as Intensity–Hue–Saturation (IHS) [28] and Brovey transform (BT) [29] have been used to fuse medical images. In the recent years multi-resolution approaches using Mallat [30], the à trous [31] transforms, contourlet [32]-[33] have been proposed for image fusion. Fusion approaches employing wavelets analysis include transforms such as SWT [34], LWT [35], MWT [35], RDWT [36], and complex wavelet [27]. Y. Luo et al. [37] used a combination of PCA with à trous wavelet transform which focused on the spatial and spectral resolutions. But, the technique did not laid emphasis on edge or shape detection, which are fundamental structures in natural images and particularly relevant from a visual point of view. Y. Yang et al. [38] proposed a fusion method based on window selection and the discrete wavelet transform. The technique emphasized on the treatment of the low and high frequency bands with different selection rule separately. The method proposed performed better than pixel averaging and conventional DWT with maximum selection rule, but has a limitation of reduced contrast in the fused image. D. A. Godse in their work [39] selected maximum pixel intensity approach along with wavelet to perform fusion. The said combination produced a focused image but the image suffered with blurring. On the other hand, work of R. Singh and A. Khare [40] conferred a method integrating Daubechies complex wavelet transform and weighted average rule for fusion but resulting in a highly blurred image. As, both the relevant and irrelevant information from the source images are included in the fused one. S. K. Sadhasivam in their work [41] applied PCA along with the selection of maximum pixel intensity to perform fusion. The method yielded an image with less structural similarity with the source images along with low contrast and luminescence. The above discussion incurred the desire to improve the quality of the fused image by removing the redundant information from the images. The

Abstract— Medical image fusion facilitates the retrieval of complementary information from medical images for diagnostic purposes. This paper presents a combination of Principal Component Analysis (PCA) and Dual Tree Complex Wavelet (DTCWT) as an improved fusion approach for MR and CT-scan images. Unlike real valued discrete wavelet transforms, DTCWT provides shift invariance and improved directionality along with preservation of spectral content. The decomposed images are then processed using PCA a based fusion rule to improve upon the resolution and reduce the redundancy. Simulation results demonstrate an improvement in visual quality of the fused image supported by higher values of fusion metrics; this further justifies the effectiveness of the proposed approach in comparison to other approaches. Index Terms—CT-Scan, DTCWT, Entropy, MRI, PCA.

I. INTRODUCTION Computer Aided Diagnosis (CAD) is an emerging and evolutionary research domain in diagnostic radiology. Medical imaging technique helps to create visual representations of the internal structure of human body for clinical analysis [1]-[7]. These CAD approaches serve as a ‘second opinion’ tool for the radiologists in decision making of life threatening diseases like breast cancer [8]-[14], brain tumors [15]-[16] and lungs cancer [17]. The complementary nature of medical imaging sensors of different modalities, (X-ray, Magnetic Resonance Imaging (MRI), Computed Tomography (CT)) has brought a great need of image fusion for the retrieval of relevant information from medical images. ‘Medical Image Fusion’ is the process of combining and merging complementary information into a single image from two or more source images to maximize the information content of images and minimize the distortion and artifacts in the resulting image [18]-[20]. The significance of fusion process is important for multimodal images as single modal medical images provides only specific information; thus it is not feasible to get all the requisite information from image generated by single modality [21]-[23]. To elaborate further, CT helps in accessing the extent of disease; yet it is limited in soft-tissue contrast, needed for differentiating tumors from scar tissues. On the other hand, MRI scores over CT in terms of soft tissue discrimination. This is necessary because the soft

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reason behind choosing the complex wavelet based approach in comparison to other approaches is that they are localized in time and frequency and can be defined with specific time span. Hence, the complex wavelets preserve time and frequency information as well as provides shift invariance and better directionality, thereby yielding a suitable approach for medical image fusion. The proposed work therefore presents a combination of DTCWT and PCA as an improvement to the aforementioned limitations. The obtained results have been evaluated using entropy (E), fusion factor (FF) as fusion metrics; yielding satisfactory performance. The rest of the paper is organized as follows: The proposed fusion approach is discussed in section II. Section III presents experimental results and finally the paper is concluded in section IV.

B. Proposed Fusion Algorithm The first step in the proposed fusion approach involves the pre-processing of the MRI and CT-scan images, i.e. the conversion of image from RGB scale to Gray scale (RGB components of the image are converted into Gray scale components).The next step is to decompose the source images using DTCWT [45]. The complex wavelet decomposes the image into frequency bands namely a lower-frequency band and other higher-frequency bands. The DTCWT is shift invariant and has high directional selectivity in comparison to real valued wavelet transforms. The improvement in directional selectivity not only reflects directional features but also represent the information across boundaries of the image properly. In addition to it, DTCWT provides phase information which makes fusion process better by merging the wavelet coefficients. Once the source images are decomposed using DTCWT, the approximation and detailed coefficients are obtained; PCA is applied as a fusion rule to selectively combine the appropriate complex wavelet coefficients of input images [46],[47]. PCA serves to transform/project the features from the original domain to a new domain (PCA domain) where they are arranged in order of their variance. Fusion in PCA domain is achieved by only retaining those features that hold a pregnant amount of information. This can be achieved by retaining only those components which have a larger variance. Thus the redundant information which is present there in DTCWT is removed by using PCA. The steps involved in the proposed PCA algorithm are outlined in fig. 2. The next step involves, the reconstruction of the processed coefficients (after PCA fusion rule) using inverse DTCWT transform to generate the fused image.

II. PROPOSED FUSION APPROACH Modalities like CT and MRI generally contain solitary information i.e. either demonstration of disease extent or the details of soft tissues. Thus, this section discusses the application of PCA fusion rule in complex wavelet domain as an approach to combine the complementary information from both the images into a single one for precise diagnosis [42][43]. A. Motivation Digital Images are generally described via orthogonal, nonredundant transforms like wavelet or discrete cosine transform for the purpose of multi scale analysis. Inspite of being easy to implement, the wavelet transform also renders more emphasis on point singularities in the images. The complex wavelets preserves time and frequency content of the images to be fused. Since, a long time many other transforms like Fourier transform were used to obtain good spatial and spectral information. While, the basic advantage of complex wavelet transform over the other transforms is that it contains the temporal information of the images; i.e. it captures both the location and frequency that makes it suitable for the fusion purposes. Moreover, by using complex wavelet transform we can easily detect the local features involved in the signal process. Complex wavelets are oscillatory function with finite duration having zero average value. The irregularity and good localization are the properties that provide a good platform for the analysis of signal with discontinuities [44]. The general block diagram of the proposed approach is outlined in fig. 1.

BEGIN Step 1

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Step 2

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Step 8

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Step10 Step11

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Input: Wavelet coefficients (of both MRI & CT). Compute: Column vectors from complex wavelet coefficients. Compute: Covariance matrix using these vectors. Process: Diagonal elements of the covariance vector. Compute: Eigen vectors and Eigen values of covariance matrix. Process: Column vector corresponding to large Eigen value (by dividing each element with the mean of Eigen vector). Compute: Multiplication of normalized Eigen vector values by each term of complex wavelet coefficient matrix. Process: Repeat the above steps for all the approximation and detailed coefficients Compute: Inverse complex wavelet transform of scaled matrices calculated in Step 8. Process: Sum of the images calculated in Step 9. Output: Fused image.

END Fig. 2: PCA Algorithm in Complex Wavelet Domain.

C. Objective Evaluation of Proposed Fusion Approach Once the fusion process is completed; the final step requires the objective evaluation of the proposed approach using the

Fig. 1: Block Diagram of Procedure Involved in Proposed Fusion Algorithm.

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appropriate Image Quality Assessment (IQA) approaches [48]-[58]. In the present work, the performance evaluation is carried out using Entropy (E) and Fusion Factor (FF) as fusion metrics [27].[58]-[59].

Set-1

Set-2

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1) Entropy Entropy of an image is the measure of the information content in the fused image. Higher values of entropy indicate that the fused image contains more information than the other fused images having lower value of entropy. Entropy is given by Eq. (1). L −1

E = −¦ Pl log 2 Pl

(1)

L =0

where: L represents no. of gray level,

Pl is the ratio between

the no. of pixels with gray values l and total no. of pixels. 2) Fusion Factor For two input images A, B and the fused image F, fusion factor is given by Eq. (2). FF = IAF + IBF

(2)

where: IAF and IBF are mutual information between source images and the fused image. Higher values of fusion factor indicate better fusion results.

Fig. 3: Image Fusion Results for Different Sets of MRI and CT Images with the Proposed Approach. (a1) & (a2) Input CT image, (b1) Input MR-T1, (b2) Input MR-T2, (c1) & (c2) Fused images.

III. EXPERIMENTAL RESULTS AND DISCUSSIONS Simulations in the present work have been performed on images of two different modalities (CT and MRI). This section deals with the qualitative and quantitative analysis of the fused image obtained from the proposed approach. The results of fused images obtained using the proposed approach are given in Fig. 3; while, the quantitative analysis of the same has been shown in table I. Fusion results in Fig. 3 for Set 1 & Set 2 show that the fused image has a better visual characteristic from the diagnostic point of view. CT-scan images give information about the shape of the tumor which is helpful in determining the extent of disease; whereas MRI image gives soft tissue details. It can be clearly seen that fused image contains complementary information of both the images; i.e. soft tissue details as well as the shape of the tumor. This is further supported by high values of fusion metrics (FF and E). High values of entropy depicts the increased information content and a good quality of fused image; demonstrating the effectiveness of the proposed fusion approach.

Table I: Quantitative Analysis of Proposed Fusion Approach. Set No.

E

FF

1. 2.

5.1869 5.2026

5.7812 3.0776

A. Comparison with Other Fusion Approaches The present approach has been compared with the DTCWT based fusion approach in work of R. Singh et al. [60] and sparse representation approaches like Simultaneous Orthogonal Matching Pursuit (SOMP) and Orthogonal Matching Pursuit (OMP) [61] for Medical image fusion. The obtained result shows the effectiveness of the proposed approach in visual representation as compared to DTCWT, SOMP and OMP approaches [60]-[61]. The fused image obtained from the proposed approach represents that the information from the source images are preserved as compared to images obtained from other approaches; which can be clearly seen in Fig. 4. Moreover, the higher values of the fusion metric shown in table II validate, that the proposed fusion approach has better diagnostic utility than the other approaches.

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(a)

metrics, have been obtained from the proposed fusion approach. Comparison results show a significant improvement in restoration of information and quality features in the obtained fused image; as depicted by high value of fusion factor, in comparison to other fused images. Hence, the proposed fusion approach is more precise and can be used more effectively for medical diagnosis than the other methods of fusion.

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Fig. 4: Qualitative Comparison of Fused Images. (a) Input CT image, (b) Input MRI image, (c) Fused by Proposed Approach, (d) Fused by SOMP, (e) Fused by OMP, (f) Fused by DWT-Max, (g) Fused by DWT Avg-Max, (h) DTCWT Avg-Max.

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Table II: Performance Comparison of Fused Images. Fusion Approach DWT Avg – Max DTCWT Avg – Max DWT Max OMP SOMP Proposed Approach

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FF 1.6390 1.6582 2.2713 2.2964 2.2965 4.3942

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IV. CONCLUSION This paper presents an approach for medical image fusion employing PCA in complex wavelet domain. The shift invariance and high directionality property of DTCWT and feature enhancement property of PCA makes this approach more suitable for medical image fusion. The fused image of the proposed fusion approach is more refined in representing spectral and spatial information, as well as the soft tissue details of tumor. Thus, it is providing the details of two different modalities in one single image, justifying the purpose of medical image fusion. Significant results relevant from a visual point of view, as well as high values of the fusion

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