Complex Ensemble Empirical Mode Decomposition and Alpha-Rooting for Image Contrast Enhancement

Complex Ensemble Empirical Mode Decomposition and Alpha-Rooting for Image Contrast Enhancement

Somayeh Bakhtiari, Sos S. Agaian and Mo Jamshidi

Department of Electrical and Computer Engineering

University of Texas at San Antonio

San Antonio, TX 78249

[email protected]

ABSTRACT

This paper presents a new image contrast enhancement method based on the complex Ensemble Empirical Mode Decomposition (EEMD) and alpha-rooting approaches. The new scheme also takes advantage of Fourier transform properties and complex Intrinsic Mode Functions (IMFs). The experimental results show that the images obtained by this combination are more appealing than the best results yielded by classical alpha-rooting technique. This algorithm is tested on the medical images, hazy aerial images and other low contrast images. Keywords: Image Contrast Enhancement, Ensemble Empirical Mode Decomposition, Alpha Rooting.

1. INTRODUCTION

To improve the visual appearance of the low contrast images, the digital image enhancement is an inevitable step. The degradation in some medical images is so severe that they cannot be directly used for diagnosis purposes. Hazy aerial images are the other examples that do not expose the necessary details and thus, need to be enhanced. The purpose of image enhancement is to reveal the critical features of the image that are invisible or hardly visible in the original image. Image enhancement methods can be classified into two general categories: spatial domain and frequency domain methods. The methods in the first group manipulate pixels and include region-based and rational morphology based methods. The second category operates on image transforms, such as the Fourier, wavelet, and cosine transforms. The main advantages of transform based enhancement methods are 1) low computational cost and 2) the essential role of the orthogonal transforms in digital signal/image processing, where they are used in different processing steps such as filtering, coding, recognition, and restoration analysis. Decomposing the image into spectral coefficients, transforms present the spectral information. These coefficients can be adjusted for enhancement and visualization. Working in transform domain facilitates viewing and manipulating the frequency composition of the image, without direct reliance on spatial information [1]. Alpha-rooting (AR) is a well-known technique for image enhancement which exponentially reduces the magnitudes of the transform coefficients [2]. It has been used with some orthogonal transforms such as DFT or DCT in order to improve the image quality in term of de-noising or visual enhancement. This method was later extended to log alpha-rooting, modified unsharp masking and filtering, and adapted on wavelet transforms [2] In order to emphasize the fine details and edges in an image, a promising approach is to decompose the signal into frequency oscillatory modes and give weight to each of them and ultimately recombine them. In 1998, Huang et al. [3] proposed a new technique called Empirical Mode Decomposition (EMD) to extract the frequency components of a signal. In this method, the signal is split into various frequency oscillatory modes called intrinsic mode functions (IMFs). Enhanced signal can be produced by combining the weighted components. Since, the higher frequencies contain the fine structures of the image, if they receive higher weights, the resulting image will expose more details compared with the original image.

Mobile Multimedia/Image Processing, Security, and Applications 2011, edited by Sos S. Agaian, Sabah A. Jassim, Yingzi Du, Proc. of SPIE Vol. 8063, 806313 · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.887424

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The goal of this paper is to gain a better image quality by merging the advantages of alpha rooting, EEMD and orthogonal transforms which cannot be achieved by implementing them independently.

2. BACKGROUND

In this section, we review the Alpha rooting and Ensemble Empirical Mode Decomposition algorithms. These methods will be later coupled to modify the image contrast. Alpha-Rooting Alpha-rooting is a transform based method used for image enhancement [4]. It performs an orthogonal transform, such as the Fourier Transform and modifies the coefficients while keeping the phase unchanged. In the end, it performs the inverse transform. The coefficients, C(n,m), are modified as follows [2]: , , | , | where, O(p,s) is the 2-D Fourier Transform of the output image, X(p,s) is the 2-D Fourier transform of the input image, and ranges in 0 ≤ α ≤ 1. Empirical Mode Decomposition (EMD) and Ensemble EMD (EEMD) Empirical Mode Decomposition (EMD) is a signal decomposition technique, first introduced by Huang [3]. It has been widely used for analysis of nonlinear and non-stationary processes. EMD is an adaptive local decomposition method that works based on localization of signal maxima and minima. This technique carries out a sifting process to decompose the signal into a set of components called Intrinsic Mode Functions (IMFs) and a residue. The IMFs are specified by having the same number of zero crossings and extrema and, having envelopes symmetric with respect to the local mean. A basic advantage of EMD is that the basis functions are derived from the signal itself [5]. By adding the IMFs and the residue we can reconstruct the original signal without any loss. The sifting procedure is as follows [6][7]: • find all the local minima and all the local maxima in the image, • interpolate the local maxima to form the upper surface, S t , • interpolate the local minima to construct the lower surface, S t , • calculate the mean of the upper and the lower surfaces: m x, y 12 S x, y S x, y •Assign , with the difference of original image, , and , : h x, y I x, y m x, y Repeat this process times until , is an IMF. First IMF, , is estimated as: h h x, y m x, y imf x, y h x, y Subtract , from the original image R x, y I x, y imf x, y Treat R x, y as a new signal and repeat the above procedure n times. The iteration is expressed as: R x, y R x, y imf x, y



The original image can be constructed by summing all the IMFs and the residue without any loss. I x, y imf x, y R x, y

Where , is the original image, , is the ith Intrinsic Mode Function, and , is the residue. The first IMF contains highest level of the details in the signal and the residue is the ultimate large scale trend. Despite all the advantages EMD has, it suffers from Mode Mixing problem. To mitigate this problem, Ensemble EMD (EEMD) was introduced [8]. EEMD iteratively decomposes the signal into IMFs using the EMD technique. White noise with finite amplitude is added to the original signal in each iteration. Then, ensemble IMFs with in same level produced in each trial will be averaged and considered as EEMD IMFs. EEMDimf 1IterNum imfI N

Where, EEMDimf is the ith IMF of EEMD, is the ith IMF in jth iteration and IterNum is number of iterations.

3. PROPOSED METHOD The proposed algorithm integrates the traditional alpha-rooting method with Ensemble Empirical Mode Decomposition. First, the image is decomposed into its IMFs using EEMD. The complex IMFs, then, will be constructed by combining each IMF with its subsequent IMF. For example, the combination of IMF1 and IMF2 will produce the complex form of IMF1+jIMF2. This procedure is illustrated in Fig. 1 and the following equation: , 1: 1 where, CIMFi is the ith complex IMF.

Figure 1. Image decomposition using EEMD and forming the complex IMFs As shown in Fig. 2, alpha-rooting will be performed on the complex IMFs in the Fourier domain. By performing inverse Fourier transform the enhanced complex IMFs will be obtained. Fig. 3 illustrates that the enhanced complex IMFs are converted to the real modified IMFs and weighted to form the final enhanced image. This procedure is as follows:

2 … 1

where, ECIMFi is the ith enhanced complex IMF and EIMFi is the ith enhanced real IMF. Real and Imag are used to separate the real and imaginary parts of the signal, respectively.

Original Image EEMD

j

IMFi

IMFi+1

CIMFi



where, EI is the final enhanced image and Wi is the weight for the ith IMF.

Figure 2. Enhancing the complex IMFs

Figure 3. Constructing the final enhanced image by transforming the enhanced complex IMFs to real, weighting and then summing them up.

4. EXPERIMENTAL RESULTS

In computer simulations, the proposed method is compared with the traditional alpha-rooting technique. The results demonstrate that the combination of EEMD and alpha-rooting can increase performance of the classical alpha-rooting algorithm in term of EME.

To evaluate the new method, first, we find the best enhanced image by conventional -rooting. To find the best , EME is plotted versus . The right most local maximum determines the best . For example, for the first hazy image used in this paper, the graph is depicted in Fig. 4. For this type of image the values ranging between 0.5 and 0.9 are evaluated. According to the graph, equals 0.79 produces the highest EME for this specific image. The values applied to each IMF will be chosen around the best for the classical -rooting.

Wn

Wi+1

W1

Imag

Imag

Re

Re

ECIMFn

ECIMF1 EIMF1

EIMFn

ECIMFi

ECIMFi+1

Avg EIMFi+1 Enhanced Image

CIMFi FFT Rooting IFFT ECIMFi



Figure 4. EME versus α.

Fig. 5 shows how a complex IMF is constructed using two consecutive IMFs. Fig. 6 presents different enhanced images using traditional alpha rooting and the proposed approach. It is visually obvious that contrast of the results by the new algorithm is much higher than the alpha rooting outputs. The zoomed views of these images are also shown in Fig. 7 which demonstrates more details and structures revealed by the proposed algorithm. Table 1 compares the EME achieved by each method.

(a) (b) (c) Figure 5. Forming a complex IMF (a) IMF1 (b) IMF2 (c) Magnitude of the complex IMF, IMF1+ j IMF2

Aer

ial 1

A

eria

l 2



Plan

e M

edic

al 1

M

edic

al 2

B

reas

t

Figure 6. Results comparison, left column: original image, middle column: enhanced by alpha-rooting, right column:

enhanced by EEMD and alpha-rooting



Figure 7. Zoomed views of the images in Fig. 6; left column: original image; middle column: enhanced by alpha-rooting; right column: enhanced by EEMD and alpha-rooting

Table 1. Comparison of enhancement by classical alpha rooting and the proposed method Image Best in alpha

rooting EME by alpha-

rooting on Original image

EME by alpha-rooting on IMFs

Hazy image 1 0.79 14.4781 30.8547 Hazy image 2 0.8 8.1489 22.1998 Medical image1 0.8 48.1308 50.4508 Medical image2 0.96 40.4924 48.1308 Plane 0.9 36.7988 48.1502 Breast image 0.93 46.1489 48.1308 Girl 0.93 25.7444 31.2674 Truck 0.86 36.4161 46.6633 Tank 0.85 36.3231 47.4568 Chemical Plant 0.88 34.7751 44.9658

5. CONCLUSIONS

In this article, a new enhancement model was presented based on the complex EEMD and alpha-rooting. The successive IMFs were combined to form the complex IMFs. Then, the alpha-rooting was applied on each complex IMF. This method demonstrated a great ability to expose the hidden structures in the medical, hazy images and other types of image. The comparison between enhanced images was made based on the EME measure. We illustrated that using the proposed algorithm we could achieve an EME higher than the best EME that could be obtained using classical alpha rooting technique.

REFERENCES

[1] S. Agaian, K. Panetta, and A. M. Grigoryan, “Transform-Based Image Enhancement Algorithms with Performance Measure”, IEEE Transactions on Image Processing, v 10, n 3, p 367-82, March 2001 [2] K. Panetta, E. Wharton, and S. Agaian, “Parameterization of logarithmic image processing models,” IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, Jan. 2007



[3] N.E. Huang,” The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis”, Proc Roy Soc London A., 454(4): 903 – 995, 1998. [4] R. Kogana, S. Agaian, K. Panetta, “Visualization Using Rational Morphology and Zonal Magnitude-Reduction”, Proceedings of the SPIE - The International Society for Optical Engineering, v 3387, p 301-12, 1998 [5] A.O. Boudraa, J.C. Cexus and Z. Saidi, “EMD-based signal noise reduction”, International Journal of Signal Process., vol. 1, no. 1, pp. 33-37, ISSN: 1304-4494, 2004. [6] X. Qin, S. Liu, W. Zhengqiang, J. Han, "Medical Image Enhancement Method Based on 2D Empirical Mode Decomposition", Bioinformatics and Biomedical Engineering, 2008. ICBBE 2008. The 2nd International Conference on Volume, Issue, 16-18 May 2008 Page(s):2533-2536. [7] A. Ogier, T. Dorval, A. Genovesio, "Biased image correction based on empirical mode decomposition" , Proceedings 2007 IEEE International Conference on Image Processing, ICIP 2007, pp. 533-6, 2007 [8] Z. Wu, N.E. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method, Advances in Adaptive Data Analysis” 1 (2009) 1–41.



Complex Ensemble Empirical Mode Decomposition and Alpha-Rooting for Image Contrast Enhancement

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