Enhancement of Medical Images Using a Fuzzy Model for Segment Dependent Local Equalization

Ioannis Stephanakis1, George Anastassopoulos2, Anastasios Karayiannakis3

and Constantinos Simopoulos3

1 HellenicTelecom. Organization (OTE), 151 24, Athens, Greece stephan@ote.gr

2 Medical Informatics Lab, Democritus University of Thrace, GR-68100 Alexandroupolis, Greece anasta@med.duth.gr

3 Second Dept. of Surgery, Democritus University of Thrace, GR-68100, Alexandroupolis, Greece akarayan@usa.net csimop@med.duth.gr

Abstract

A novel model for fuzzy equalization of medical

images is proposed. The method requires a preprocessing step which accomplishes a fuzzy segmentation of the image into N segments with overlapping fuzzy boundaries. Histogram equalization is performed according to individual equalization functions derived from each segment of the image. A fuzzy membership function is associated with each segment. Enhancement results compare well against histogram equalization techniques that derive the equalization transform function from the global histogram of the image. 1. Introduction

Fuzzy methods have found wide application in image processing and analysis during the last years [1,2]. A variety of algorithms based upon fuzzy rules and fuzzy filtering has been developed (see for example [3,4] for fuzzy methods applied to noise reduction and image restoration). These methods apply theories developed in the context of several disciplines in the realm of signal processing and computer science (like the rough set segmentation algorithm presented in [5] which exploits data mining techniques). These methods allow for efficient adaptive processing of regions of the image with different statistical characteristics, enhance conventional techniques in terms of flexibility and compare well against them. 2. A fuzzy model for segment dependent equalization 2.1. Fuzzy equalization

Histogram equalization techniques may be used to enhance a digital medical image [6] and distribute its pixel values uniformly throughout its dynamic range. The transform, which accomplishes histogram equalization, is a non-linear operation. It results in an enhanced image with a linear cumulative histogram.

The following relation holds true for the equalized mage denoted as H(I(m,n)), i

constant))1(),((Pr( =∆+<≤∆ xknmIHxk (1) where k∆x and (k+1)∆x belong to the enhanced dynamic range of the image.

Nevertheless histogram equalization is a non-adaptive technique that operates upon pixels of an image without encompassing any local information about regions of the image having different statistical characteristics. Thus the method performs poorly in cases where enhancing the local contrast of images is important. Medical images, which incorporate highly illuminated regions due to capturing techniques as well as dark regions, are such an example [7,8].

The proposed model tackles this issue by assuming

that the image is segmented in N regions Ri, i=1 … N, during a preprocessing step. Each region is characterized by its own histogram which yields a separate equalizing function for each region, Hi(.). A fuzzy membership function – denoted as µi(.) – is associated with each region so that,

)( 1)),((1∑=

∀=N

ii m,nnmIµ (2)

The overall equalized image is found as a fuzzy superposition of the equalized segments of the image,

[ ] )),(( )),(()),((1

nmInmIHcLnmIH i

N

iiii µ∑

=

∆+=

(3)

The lower limit – denoted as Li – and the higher limit – denoted as Li+∆ci – of the pixel value of region Ri of the enhanced image are chosen in such a way that the continuity of the overall histogram is preserved. 2.2. Outline of the enhancement algorithm

The block diagram of the proposed segment dependent fuzzy equalization is presented in Fig. 1. It

Fuzzy segmentation of the image Determination of the segments of the imageN

Fuzzification of segment histograms Definition of membership functions Determination of the equalization functions for each segment of the image

µi

STEP 1

STEP 2

STEP 3

STEP 4

Selection of the lower and the upper pixel values [L, U] for each segment

i i

Fuzzification of the output of equalization functions Application of equalization functions according to membership functions

Figure 1: Block diagram of the proposed algorithm

consists of four distinctive steps. The preprocessing step (Step 1) segments the image into N segments using a rough set segmentation algorithm like the one presented in [5] or fuzzy clustering algorithms for image segmentation [2]. Alternatively, the valleys of the global histogram of the image may be used to determine the N segments along the lines of [9] or via minimization of a fuzzy index [10]. The boundaries of the segments of the image, i.e. the pixels with values at the valleys of the global histogram, are not crisp. Each pixel at the boundaries is assigned to a segment according to a fuzzy membership function. The fuzzified histogram of a segment i of the image, is found by taking into account the values of the pixels at the boundaries according to the following relationship,

)),(())1(),(())1(),(

∑∆+<≤∆

=∆+<≤∆xknmIxk

iii nmIxknmIxkhist µ

(4)

where the summation runs over the pixels of the image whose values lie within the desired interval. This is referred to as Step 2 of the algorithm. The histogram equalization functions per segment of the image are determined during this step. Mapping the fuzzified dynamic range of each segment to an output fuzzified dynamic range is critical since continuity of the overall histogram has to be preserved. Segments that contain significant perceptual information for a physician are allocated a wider dynamic range while others are suppressed. This is done in Step 3. Finally the equalized

image is found according to Eq. 3 as a weighted superposition of the segment dependent equalization functions (Step 4). 3. Acquisition techniques of the medical images used in the experiments

The medical imagery data are imported from a medical database that has been developed in the Second Department of Surgery of the University Hospital of Alexandroupolis, Greece. The following platform (connected to a 100 Mbps Fast Hub Ethernet LAN) is employed:

a PC (Pentium 4 – 1.8 Ghz, 512 Mbytes RAM, 40 Gbyte hard disk), containing the entire database,

a Heidelberg Lynotype CPS Saphir/Opal Scanner, and

a PC (Pentium 4 – 1.5 GHz, 256 Mbyte RAM, 40 Gbyte hard disk) with a 32 Mbyte graphics card and a 21’’ display.

Intra-operative cholongiography images are used to apply the proposed enhancement methodology. Intra-operative cholongiography is often used to investigate the anatomy of the biliary tree and to detect stones or other pathology within the Common Bile Duct (CBD). The images are acquired during surgery by mobile X-ray equipment. However, the technique has several technical limitations, resulting in poor and non-informative X-ray images, most often because the exposure conditions are not well calculated as the patient is under anaesthesia and the capabilities of the mobile X-ray equipment are limited. In most cases, the result is overexposed images containing information that is difficult to interpret due to the limited range of the histogram of the image. In our study, after acquisition of the intra-operative images, the X-ray films are scanned with a Heidelberg Lynotype CPS Saphir/Opal scanner in multiple resolutions, in order to achieve the best image according to the directions of the surgeons. 4. Experimental results

One of the original images that are examined is presented in Fig. 2. It shows a case of CBD injury (transection) with contrast injected in the proximal end of CBD. The intra-operative cholongiography shows the anatomy of the extra and intrahepatic biliary tree with abrupt cessation of contrast material into the duodenum. There is an overexposed region of the image due to capturing techniques. Valuable information for a medical diagnosis is contained within this region. Enhancement results using a unique equalization function derived from the histogram of the image are presented in Fig. 3. The contrast of the region of interest is slightly enhanced but part of the image is still overexposed. Much better enhancement

Figure 2: Original image

Figure 3: Equalized image using global histogram

equalization

Figure 4: Equalized image using local histogram

equalization for each segment results are obtained should the proposed enhancement algorithm be used. The image is segmented into two (N=2) regions [9], one of them being the region of interest. Local mean - derived from a window of 7x7 pixels - and local contrast - derived as the difference between the pixel value and the local mean - are enhanced using two separate equalization functions for each segment of the image. This ensures the integrity of the histogram of the whole image. Fuzzy equalization is performed along the lines of Eq. 3 for both the local mean and the local contrast. Enhancement results are presented in Fig. 4. There is a distinct improvement compared to the original image and the enhanced image using the conventional technique.

The histogram of the original image is presented in

Fig. 5. The segmentation of the original image is based upon information obtained from this histogram. The two peaks of the histogram are assigned to the two different regions. Pixels with a value below 185 are assigned to Region 1 whereas pixels with a value above 225 are assigned to Region 2. Pixels with values in between are considered to belong to the boundary of the two regions. The two segments of the image obtained in Step 1 (preprocessing) are depicted in Fig. 6 and Fig. 8. The corresponding fuzzified histograms of the two regions are presented in Fig. 7 and Fig. 9 respectively (Step 2). They are obtained by the application of Eq. 4 to both regions.

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pixel value

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els

Figure 5: Global histogram for the original image

Figure 6: Region 1 of the original image

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Figure 7: Local histogram of Region 1 of the original

image

The equalization functions are obtained for each segment of the image from the fuzzified histograms in such a way that the cumulative histograms of the enhanced segments are linear (Eq. 1). This is carried out during Step 2 of the proposed algorithm. The local mean and the local contrast within each segment are equalized separately since this yields a better blend of the two regions at the boundaries. The equalization function corresponding to the local contrast of the region of interest (Region 2) enhances to a greater degree its dynamic range as compared to Region 1. This is explained by the fact that the dynamical range of Region 2 before enhancement is more restricted compared to that of Region 1.

Figure 8: Region 2 of the original image

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Figure 9: Local histogram of Region 2 of the original

image

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Figure 10: Fuzzification of the equalization function

for each segment of the image (Region 1&2)

Fuzzification of the enhanced dynamic ranges of the segments allows for overlapping boundaries in the enhanced image (Step 3). Values U1 and L2 do not coincide. This is presented in Fig. 10 that illustrates the mapping of the input dynamic ranges to the enhanced dynamic ranges. The output dynamic range (0 to 255) is split into two equal parts with pixel values between 110 and 140 corresponding to the boundary region (region between the dashed lines). A segmentation of the original image into more than two segments with a slightly different mapping is possible, nevertheless no significant improvement of the original image is observed after enhancement.

The equalization functions for the local mean and the local contrast, which correspond to the two segments of the image, are presented in Fig. 11 and Fig. 12. The overall equalization function for the local mean, which results from the application of the proposed algorithm, is compared with the equalization function obtained from the global histogram of the image. The suppression of the dynamic range of Region 1 and the simultaneous expansion of the dynamic range of Region 2 are noticeable. This holds true as well for the equalization functions for the local contrast of the segments. It is observed that the original dynamic range of the contrast lies between –3 and +3. 5. Discussion

The proposed algorithm compares well against conventional histogram equalization methods. This is due to the fact that each segment of the image is allocated a dynamic range according to the relevant information that is significant for medical diagnosis and not according to the percentage of the pixels that it contains with respect to the whole image. This is a subjective decision met by the examining physicians who participated in this study. Furthermore, fuzzification allows for smooth blending of the boundaries of the segments without deteriorating the quality of the image. The proposed method does not

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Equ

aliz

ed p

ixel

val

ue

Figure 11: Comparison between the equalization

functions resulting from the global histogram (--) and the local histograms of the mean values for Region 1 (+) & 2 (o)

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ixel

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Figure 12: Equalization functions resulting from the

local histograms of the differential values for Region 1 (+) & 2 (o)

depend upon the number of segments that result after the segmentation of the original image or the fuzzy classification algorithm to be used. The medical information, which is present in the original images, is preserved and outlined in the enhanced images according to the medical doctors who used the enhanced images in their diagnosis. The algorithm is easily extended to cases in which the dynamic ranges of the individual segments overlap not only at the boundaries but, instead, they overlap throughout the whole dynamic range of the original image. Mapping is more complex in such cases and the enhanced dynamic ranges, which correspond to the segments of the image, do not need to be consecutive. 6. References [1] H. R. Tizhoosh, “Fuzzy Logic in Image Processing”, Springer-Verlag, Berlin, Germany, 1997.

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[6] G. Anastassopoulos, I. Stephanakis, and S. Gardikis, “Evaluation of Histogram Enhancement Techniques Used in Conjunction With Wavelet Compression Methods For Improved Signal Processing Of Child Trauma Images”, Proceedings of the Seventh Australian and New Zealand Intelligent Information Systems Conference, The University

of Western Australia, Perth, Western Australia, Nov. 2001, pp. 73-76.

[7] G. Anastassopoulos, S. Gardikis and I. Stephanakis, “Quality Assessment Of Child Trauma Images Compressed With Wavelet Compression Techniques In A Telemedicine Environment”, Proc. of the 4th International Conference in Neural Networks and Expert Systems in Medicine and Healthcare, June 2001, pp. 369-373.

[8] G. J. Mandellos, M. Koukias, D. K. Lymberopoulos, and G. K. Anastassopoulos, “Medical Image Quality Evaluation Of A Telemedicine Service Provided By Hellenic PTT”, Proc. of the 2nd IASTED International Conference in Visualization, Imaging and Image Processing, ACTA Press, Malaga, Spain, Sept. 2002, pp. 344-348.

[9] H. D. Cheng, and Y. M. Lui, “Automatic Bandwidth Selection of Fuzzy Membership Functions”, Information Sciences 103, 1997, pp. 1-21.

[10] Liang-Kai Huang, and Mao-Jiun J. Wang, “Image Thresholding By Minimizing the Measures Of Fuzziness”, Pattern Recognition, Vol. 28, No. 1, 1995, pp. 41-51.