UW-Madison ECE 533 - Image Enhancement Using Logarithmic Image Processning (Lip) Technique

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Table of ContentsSection 1: AbstractIMAGE ENHANCEMENT USING LOGARITHMICIMAGE PROCESSNING (LIP) TECHNIQUEByBenjamin J. Weisenbeck AndOiki WongDepartment of Electrical and Computer EngineeringECE 533: Digital Image ProcessingDec 14, 20040Table of Contents1. Abstract…….……………………………………….………………………………..12. Introduction .…………………………………………………………………………13. Theory.……………………………………………………………………………….24. Implementation………………….…………………………………………………...45. Simulations And ResultI.  and …...………………………………………………………………...6II. Window Sizing……………………...………………………………..…..10III. LIP vs. Histogram Equalization ………………………………………….11IV. Noise…………………………………………...…………………………146. Conclusion……………………………………………………………………….......18Appendix I …………………………………………………………………………........IAppendix II…………………………………….………………………………………..IIAppendix III 1. GUI Files………………………………………..…………………….........III2. User Defined Functions……………………………………………………IXAppendix IV – References…………………………………………………………...XIII1Appendix V – Individual Responsibility Chart………………………………………XIVSection 1: AbstractThis project implements an image enhancement algorithm that is based on a logarithmic imageprocessing model proposed by Deng [2]. This algorithm is a new implementation of Lee’s imageenhancement algorithm and is based on a mathematical structure for logarithmic imageprocessing developed by Jourlin and Pinoli [5]. This technique is capable of simultaneouslyenhancing both the overall contrast and the sharpness of the image. We will investigate theeffects of each parameter on the enhanced image and compare the results obtained by thismethod with the traditional histogram processing method for both clean and noisy images. Section 2: IntroductionTraditionally, an over- (under-) exposed image is processed by the method of histogramequalization. This method works by performing a transformation that spreads out the histogramof the original image so that the levels of the equalized image will span a fuller range [3].However, this method is not always the best method for image enhancement [Gonzalez &Woods, pp 100-102], especially for color images where equalizing all three components, R, G,and B, may create color distortion. Therefore, linear or non-linear contrast and dynamic rangestretching is used. Deng [2] has proposed a logarithmic based image-processing algorithm:))],(log()),([log()),(log()),(log( jiajifjiajif (2.1)where ),( jif and),( jif are the normalized enhanced and the normalized original images.),( jia is the arithmetic mean of an (n x n) window of the original image.  and  areparameters that govern the dynamic ranges and contrast. This image-processing algorithm can effectively enhance details in the very dark or very brightareas of an image, which can be useful for enhancing an underexposed or overexposed image.This algorithm can also be used to adjust the sharpness of an image. The organization of this report is as follows: Section 3 will describe the theory behind Deng’salgorithm. Section 4 briefly describes our implementation of the algorithm and the user interfaceof our program. Finally, we will simulate the algorithm in section 5-I, investigate window sizingin 5-II, compare between histogram equalization in 5-III and finally, look at noise effect in 5-IV. 2Section 3: TheoryThe logarithmic image processing technique proposed by Deng [2] is a new implementation ofLee’s image enhancement algorithm. Lee's original algorithm [1] is as follows:)],(),([),( jiAjiFjiAF  (3.2)where ),( jiFand ),( jiFare the enhanced and original images and A(i,j) is the arithmeticmean of an (n x n) window of the original image. We define the following 3 operations: f + g =Mfggf  (3.3) f - g = gMgfM (3.4)  x f = MfMM 1 (3.5)where f =M-F, the complement transform of pixel brightness, F. M is the glare limit of the grayscale range. Appendix II contains the proof which shows that with equations (3-3) through (3-5),Lee’s equation can be re-written as equation (2.1). To see the effects of  and , start with (2.1) written as:)),(log()),(log()()),(log( jifjiajif (3.6)If  = 0, the enhancement is simply a power function of the (n x n) window-averaged image, andthe result is dynamic range stretching. If  > 1, the range of the bright areas is stretched. If  <1, it stretches the range of the dark area. When  < 0, it produces a negative transformation.On the other hand, if  = 0, the result is a linear function of the difference of the log of theoriginal image with its (n x n) window-averaged image. ))],(log()),([log()),(log( jiajifjif  (3.7)Therefore the logarithmic difference is linearly amplified. Equation (3.7) looks similar to high-boost filtering where a blurred version of the image is subtracted from its own and multiplied bya constant to produce a sharpened image in the logarithmic space. However, the inverse-log isnot linear, therefore this enlarges the difference between an individual pixel and its neighbors,and the result is crisped edges. The contrast between neighborhood pixels can be measured with the following equation:3c(f,g)=Max(f,g) - Min(f,g) (3.8)Appendix I will show that (3.8) is equivalent to the following:c(f,g)=P(f - g), (3.9)where P(f)=f if f 0, P(f) = 0 - f if f 0;The enhancement of contrast can be analyzed by means of average contrast C(i,j) between apixel at f(i,j) and its 8 neighbor (for a 3 x 3 window). Given the definition of contrast above [1],we can define C(i,j):


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