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Procedía Engineering 15 (2011) 3754 - 3758

Procedía Engineering

www.elsevier.com/Iocate/procedia

Advanced in Control Engineering and Information Science

The Fuzzy Nonlinear Enhancement Algorithm of Infrared Image Based on Curvelet Transform

Jingchao ZHAO, Shiru QU *

_School of Automation Northwestern Polytechnical University Xi 'an China_

Abstract

Considering the low contrast and strong noise and without obvious distinction between target and background of infrared images, an enhancement algorithm is proposed. Firstly, Curvelet transform is performed on the original infrared image, and nonlinear gain function is applied to enhance the image's global contrast in the low frequency sub-band, set different thresholds using fuzzy nonlinear operator to adjust high-frequency coefficients, which extracts multi-scale detail features of the image; finally, reconstruct the image through the inverse Curvelet transform. Compared with other several infrared image enhancement algorithms, experimental results demonstrate that the algorithm reduce the noise of original image and enhance target content information effectively, and can preserve more contour features of the image.

Keywords: Infrared Image Enhancement, Curvelet transform, Nonlinear gain, Fuzzy logic ;

1. Introduction

The so called infrared imaging guidance is the main direction of development for the precision guided weapons, the role of infrared imaging equipment is in long distance, good nature for hiding, and it also has a strong environmental adaptability. When compared with the visible light, in addition to the image features such as a little interference and the simple information, the infrared images can also reflect heat radiation characteristics of the objects, which are widely used in military and civilian fields. [1] However, the overall brightness of infrared images generally have lots of the shortness like dim, noisy, target and background in low contrast, the edge is not clear enough, the image gray distribution is more concentrated and it is not easy to observe the details of the goals. Therefore, regarding to the detection and recognition of the target, it is necessary for enhancement process of infrared image, the main purpose of it is to remove noise and improve the contrast for target and background.

The currently often used methods mainly include infrared enhancement equalization of the histogram [2], wavelet algorithm and so on. However, the histogram equalization has only considered the global

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This work was supported by aviation science fund (Grant Number: 20090153002).

1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.703

information, ignoring the local information, when it is enhancing the contrast, it also has magnified the noise while the visual effects image after processing is stiff, not soft enough, and sometimes it even will cause the deterioration of image quality. Wavelet transform method can not well represent the direction of information in the image, lack of detail enhancements, and it is prone to have the "ringing" effect. The propose and development of the theory of geometric analysis (MGA) [3] is to make up for this shortcoming of wavelet transform, Curvelet transform [4] has a strong multi-scale as well as multi-direction, and the characteristics of precise expression for the direction of the image and detailed information.

Because of the complexity and relevance for the actual image information itself, making it with uncertainty and imprecision appears during the process of dealing with the image, the so called fuzzy theory [5] have a good description of capacity towards the uncertainty of the images, and it also the noise has robustness, so the fuzzy theory is applied to the enhancement of the image. In order to improve the overall image contrast, so it is important to retain more detailed information while reducing noise levels, this paper presents a fuzzy nonlinear enhancement algorithm for the infrared image based on Curvelet transform, in the Curvelet there's non-linear processing respectively towards the low frequency coefficients domain sub-band and the direction of the band-pass sub-band coefficients, and the image is enhanced through the inverse transform. The results show that this method can effectively enhance the low contrast infrared image, when regarding to the visual effect, it is better than the rest of several traditional methods.

2. The Description of Enhancement Algorithm

2.1. The processing of the low frequency coefficients

The low-frequency sub-band coefficients after the image is decomposed by Curvelet, which reflects the basic information and key energy of the image, this part is related to the overall image contrast but with less noise. For the low-contrast infrared image, the coefficient of the decomposed low-frequency sub-band is usually in small difference, to achieve enhanced results, it is necessary to stretch the gray value, and therefore, the treatment of low-frequency coefficients is a critical step in particular. The introduction of the mapping function to handling the low-frequency coefficients so as to enhance the overall contrast, in this paper, the author has made the use of a simple and low computational complexity gain function to improve the contrast of the image when making the choice of non-linear gain function, it just need to adjust a parameter, increasing the adaptability.

E - tanh(a® - b) + tanh(b) ^

n tanh(a - b) + tanh(b)

In the formula, b-jfXNy),a — k1C

After the transform of the Curvelet low frequency coefficients® £ [0,1], C is the normalized for the standard deviation of the image noise, k1 is the correction factor and M x N is for the image size of the low-frequency sub-band, of which the gain factor a is used to control the curve of the critical point, b and a have decided to enlarge the range of intervals, the following Fig.1(a) is its projected curve.

2.2. The adjustment of high frequency coefficients

The image after the Curvelet decomposition, the scale for the high frequency sub-band coefficients of the

various directions has reflected the detailed information of the image, different from the low frequency coefficients, the numerical value of the high frequency coefficient is small, and it also contains the noise. According to the different point of view as well as the sub-scales coefficient, with the use of fuzzy linear of the enhancement operator, to adjust the control the increase rate of the coefficient, and then to enhance the image contrast together with the detailed information, and highlight the target information in the image.

Fig. 1. (a)Low-frequency Coefficient Projected Curve (b)Nonlinear Enhancement Curves of High Frequency Coefficients

As the performance of the edge components is signal of the high frequency, the image noise in components of high-frequency account for a large component, and it is difficult to give a specific definition of the division, thus introduced the fuzzy theory to this. Fuzzy theory does not do positive and negative towards the simple things, but with a certain degree of membership to reflect the things that belong to a category level. [5]

Fuzzy enhancement approach is to convert the signal to the domain of the fuzzy spatial, that is, to turn the high frequency sub-band images into the same size of the coefficient matrix of the fuzzy membership matrix, and to achieve the processing of distinction purposes between different sub-bands by stretching the transformation towards the membership. Membership function that can take many forms, a large number of experiments show that the expression of different little effect is on the operation, in view of a linear function of operating speed on the advantages, the paper has selected the linear function as follow:

u(X) = (x - Xmin )/(Xmax - Xmin ) (2)

Then to obtain a gain function in accordance with the Curvelet of the degree membership coefficient [6]:

Wu \u\ < Ts

a{sigma[c(u - b)] - sigma[-c(u - b)]} u > Ts

Of which, a = {sigma[c(1 - b)] - sigma[-c(1 - b)]}-1, sigma(x) = 1/(1 + e~x), 0 < b < 1, b and C is in the control of enhanced range and increased intensity separately, normally the value of c ranges from 20 to 50, let's take b=0.25, c=40 as an example, non-linear gain function f (u) is shown in Fig. 1(b), through the adjustment of various coefficients can get more styles of enhanced curve. While in the enhanced image it can suppress the noise of the image, by adjusting the parameter Ts of each sub-band to adjust detailed enhancement and noise suppression, through changing the value of W you can adjust the level of the noise reduction.

Then to arrange the inverse-transformation towards (2), that is:

X = (Xmax - Xmin ) • f (u) + Xmax (4)

f (u) = \

Lastly, we obtain the high-frequency coefficients through (4).

2.3. The Determination of Thresh/id

As for the images, noise variance c is unknown, the traditional wavelet of the sub-band coefficients in the first layer of high frequency is estimated as c , while most of the noise is at the highest sub-band in Curvelet transform coefficients, the experiments show that, the estimate at the highest sub-band is more accurate, and therefore we use the classical formula [7] method can get the c through the estimation of the middle value: c = median(abs(C))/0.675 ,of which C is the coefficient after the transform by Curvelet, the threshold value Ts is set asTs = kjC , the coefficient kj is the gain coefficient of the scale j , to adjust its value according to the noise level of different sub-band.

2.4. Steps of image enhancement

The Fuzzy Nonlinear Enhancement Algorithm of Infrared Image Based on Curvelet Transform process as follows:

Stepl: Curvelet transform is performed on the original infrared image, obtaining the Coarse scale coefficients and a series of high-frequency coefficients in scale of j and in direction ofl , estimate c at the highest sub-band. Step2: The gain function expressed as (1) act on the normalized low-frequency subband coefficients. Step3: Setting different noise threshold ts on each sub-band, firstly, the high frequency sub-band coefficient via(2) for fuzzy, and then adjust the fuzzy Variable by the nonlinear gain function (3), at last each sub-band coefficients after adjustment were obtained through defuzzification. Step4: The image is enhanced through the inverse Curvelet transform for all sub-bands coefficients.

3. Experimental Results and Analysis

The experiment two sites have chosen two infrared pictures that are with less contrast for enhancing processing, the corresponding pixel for the gray value of the infrared image in the background area is low and relatively slow, but it is the image with high gray value in the target area. Fig.2 (a) and Fig.3 (a) are the two original images, in the picture, there is a seated person, the plan clearly reflects the unique infrared images with the features of the high background as well as the low-contrast, the contrast between target and background is very poor target edge is very vague and it is very inadequate within the texture information , if its goal is in direct detection, test results are certainly not ideal.

Fig.2. Experimentl (a)Original Image (b)Histogram Equalization(c) Dual-histogram Equalization(d)Un-sharp Masking (e)Wavelet

Enhancement(f)Our Method

Even though, both of the histogram equalization and dual-histogram equalization have adjusted the contrast between the target and the background, due to most the target area is in the dark zone, after the enhancement the background information has also been proved to some extent, it enlarges the background clutter or background suppression that is not very good And the target image of the details within the texture is almost submerged, making the result that the target edge and contrast is not improved

accordingly.

Fig.3. Experiment2 (a)Original Image (b)Histogram Equalization(c) Dual-histogram Equalization(d)Un-sharp Masking (e)Wavelet

Enhancement(f)Our Method

Although the enhancement for un-sharp masking method and wavelet method have remained a part of the detailed information of the image, the overall image contrast after the enhancement is poor, the target information is not clear enough.

Through the comparison, it is more obvious of the enhanced image in contrast with the proposed algorithm targets of the background to enhance the overall outline, in addition, the detailed information of the internal texture especially the target person in the second experiment is relatively abundant, it enables verification of the ability to capture the details of Curvelet, and make the inhibition of the background noise with force, so as to enhance the contrast degree of the image, improve the image clarity.

4. Conclusion

The proposed fuzzy nonlinear enhancement algorithm on the basis of the Curvelet transform not only take both of the global information contrast into account, but also parts of the detailed information, the algorithm uses multi-resolution tool to extract multi-scale features of the images with Curvelet transform, and through the fuzzy nonlinear operator to enhance the differences for the characteristics of the subband images to enhance the intensity, infrared images to enhance the contrast and detail information but also reduces the level of the background noise. Experimental results show that the algorithm not only been in good enhancement for overall contrast, the texture information of local area has also been increased accordingly, but there are more parameters involved in the text, more intelligent adaptive method remains to be elucidated.

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