Evaluation of Hepatic Cystic Echinococcosis ’ CT image in Xinjiang Uygur Autonomous Region based on Kolmogorov Complexity Model *

Designing and developing computer-assisted image processing techniques to help doctors improve their diagnosis has received considerable interests over the past years. In this paper, we used the kolmogorov complexity model to analyze the CT images of the healthy liver and multiple daughter hydatid cysts. Before the complexity characteristic calculating, the image preprocessing methods had been used for image standardization. From the kolmogorov complexity model, complexity characteristic were calculated in order to quantify the complexity, between healthy liver and multiple daughter hydatid cysts. Then we use statistical method to analyze the complexity characteristic of those two types of images. Our preliminary results show that the complexity characteristic has statistically significant (p<0.05) to analyze these two types CT images, between the healthy liver and the multiple daughter hydatid cysts. Furthermore, the result leads us to the conclusion that the kolmogorov complexity model could use for analyze the hydatid disease and will also extend the analysis the other lesions of liver.


Introduction
Cystic echinococcosis (CE), also known as hydatid disease, is an infection of larval stage animal tapeworm, Echinococcus, has a wide geographical distribution [1].The liver is the most common site of the echinococcal cyst of the pastoral strains (> 65%) [2].The greatest prevalence of cystic echinococcosis in human and animal hosts is found in countries of the temperate zones, including southern South America, the entire Mediterranean littoral, southern and central parts of the former Soviet Union, central Asia, China, Australia, and parts of Africa [3].In China, human CE has been recorded in 22 Provinces and Administrative Regions, with a particularly high endemic level over large areas of north-western provinces [4].The Xinjiang Uygur Autonomous Region, multi-ethnic province in northwestern China, is one of the most important foci of human CE in the world [5].The definitive diagnosis for most cases of CE in man is by physical imaging methods, such as radiology, ultrasonography, computed axial tomography, and magnetic resonance imaging.The ability of CT to reveal hepatic lesions in experimental and clinical settings has been well documented and has high accuracy in the diagnosis of complications in CE of the liver [6].Designing and developing computer-assisted image processing techniques to help doctors improve their diagnosis has received considerable interests in recent years.
Medical imaging is clearly very important to extract the maximum possible information from any image obtained.Mul-tivesicular cysts manifest as well-defined fluid collections in a honeycomb pattern, with multiple septa representing the walls of the daughter cysts.When daughter cysts are separated by the hydatid matrix (a material with mixed echogenicity), they show a "wheel spoke" pattern [7].The CT image of multiple daughter hydatid cysts showed a multiloculated appearance with the density of fluid in the daughter cysts lower than the density of fluid in the mother cyst.Fig. 1 shows typical a large cystic lesion, which included many small round shaped cystic lesions.We propose to focuse on using Kolmogorov Complexity model for calculate the complexity of the CT image, both the healthy liver and the multiple daughter hydatid cysts.
The evaluation of the complexity of an observed object is an old but outstanding problem.The notion of Kolmogorov complexity was defined independently by G. Chaitin, R. Solomono, and A. Kolmogorov [8].Kolmogorov proposed a complexity measure of a specified binary sequence, in which the complexity is given by the length of the shortest algorighm which can produce this sequence [10].This definition of complexity is usually called Kolmogorov Complexity (KC).Kasper and Schuster [11] proposed a computationally simple measure of the algorithmic complexity which was analyzed mathematically by Lempel and Ziv [12].The complexity of a finite string from the Kaspar-Schuster's method can be considered as a realization of the Kolmogorov Complexity.Kolmogorov Complexity and other complexity measures have been applied in many fields, such as time series analysis [13], [14], handwritten characters recognition [15], image compression [9] and statistic complexity [16].These applications have shown that the com-plexity measure is a useful tool for signal and image processing.To author's knowledge, the present study of kolmogorov complexity has not been applied in the hepatic cystic echinococcosis.
Based on the above observations, we proposed use the kolmogorov complexity model to analyze the CT image of healthy liver and multiple daughter hydatid cysts (presented in Figure 1).For the purpose of complexity analysis, the original image needs to be preprocessed.Our approach first preprocessed the image, including color transformation, normalize the scale, remove noise and enhance the contrast, shown in Figure 1.Then, followed by calculate of the complexity characteristic.
From the kolmogorov complexity model, complexity characteristic were calculated in order to quantify the complexity, between healthy liver and multiple daughter hydatid cysts, and the complexity was analyzed by SPSS, the statistical analysis software.Furthermore, we discussed the usefulness of the proposed complexity model for analyzing a series of healthy liver and multiple daughter hydatid cysts.

Image Acquisition
Abdominal CT images, from both patients and healthy controls, were acquired at First Affiliated Hospital, Xinjiang Medical University of China, using a CT scanner.Digitized CT images of the abdomen, used as input for this study, were grouped into two classes: (a) healthy liver and (b) multiple daughter hydatid cysts.Furthermore, a number of 200 images provided for the experiment, 100 images of healthy liver and 100 images of multiple daughter hydatid cysts.

Image Preprocessing
A captured image contains not only the information of useful but also some noise and the variation caused by the rotation and translation.So, the image cannot be used directly.In order to keep the useful information of the CT images under different conditions, image preprocessing approaches were used to preprocess images before the analysis algorithm was applied.For the purpose of complexity analysis, the original image needs to be preprocessed to color transformation, normalize the scale, remove noise and enhance the contrast, reduce the influence of the factors mentioned above.The result of image preprocessing was shown in Figure 2 and Figure 3.
Step 1 Color transformation: Convert RGB image to the grayscale intensity image, by eliminating the hue and saturation information while retaining the luminance.The original image is in RGB color space.That is, the color image is formed by the combination of three digital images of the same region shot through red, green, and blue filters.This color space is fine for digitization, but transformation to another color space may be advantageous for subsequent steps in the analysis [17].Step 2 Normalizing scale: Abdominal CT image from different people and different CT scanner may be captured in different size.We propose to give a four-element position vector that specifies the size and position of the crop rectangle.These images were digitized into1024 × 1024 array with spatial resolu- tion of 256 grey levels.
Step 3 Removing noise: Median filtering is a nonlinear operation often used in image processing and more effective than convolution when the goal is to simultaneously reduce noise and preserve edges.Median filtering uses a sliding window.It finds the median value of the population of pixels inside the window, and assigns this value to the corresponding output pixel.
Step 4 Enhancing contrast: In CT images, hydatid lesions located in a liver are generally identified by intensity difference between lesions and liver.The intensity of the hydatid lesions can be lower and or higher than that of the liver.Therefore, the objective of our work is to enhance contrast of CT image containing liver and hydatid lesions as a necessary preprocessing so that we are able to keep more useful information in CT images.We propose to enhance the contrast of CT image by transforming the values using contrast-limited adaptive histogram equalization (CLAHE) [18].

Kolmogorov Complexity Measure
An image can be first converted into a one-dimensional binary sequence by scanning it either horizontally or vertically.In our proposal, we evaluate the complexity of each vector in the horizontal direction and get the complex value of each row vector.Then composed the complexity of each row into a vector of complexity and we calculate the complexity of the complex vector as the characteristic complexity of image.
For simplicity, we consider strings consisting of '0' and '1' only, that is, binary sequences.Assume that the complexity of a finite string of length N is denoted by c(N).
Theoretical study has shown that [11], Obviously, we have 0 1 KC ≤ ≤ .Kolmogorov only gave a general definition of the Kolmogorov Complexity.To compute the KC measure, Kaspar and Schuster proposed an explicit algorithm [13].In their approach, two operations, copying and inserting: were used for computing 6. ( ) 9. If ( ) where c is used to count the number of inserting operations, that is, the complexity of the sequence ( ) ( ) . Note that the last copy step is also counted if measure is then calculated using Equation 2.

Experimental Result
We present the preliminary results of our studies on the usefulness of the proposed complexity model for analyzing a series of healthy liver as shown in Figure 2 and multiple daughter hydatid cysts as shown in Figure 3.

Descriptive Statistical Analysis of Kolmogorov Complexity Characteristic
In Kolmogorov complexity characteristic, there are 200 images available, 100 healthy liver images and 100 multiple daughter hydatid cyst images.According to the calculated complexity, we use the statistical analysis software: SPSS, descriptive analysis the complexity data.The sample size, mean value, standard deviation and standard error of mean for both healthy liver and multiple daughter hydatid cysts are given in Table 1.The box plots (shown in Figure 4) depicted the minimum, first quartile, median, third quartile and maximum of healthy liver and multiple daughter hydatid cysts.

Independent-Samples T Test for Complexity Characteristic
To evaluate the effectiveness of the complexity data, we use the statistical analysis method of Independent-Samples T Test to analyze the complexity data.In the result, the significance (p=0.002) is less than 0.05 indicating that the complexity characteristic has differences between healthy liver and multiple daughter hydatid cysts.

Conclusion
In this paper, we propose an image analysis technique based on Kolmogorov Complexity model for characterizing healthy liver and multiple daughter hydatid cysts.A statistical description and analysis of complexity characteristic for two types of CT images has been presented.Preliminary experimental study demonstrated the feasibility of the proposed technique in analysis the healthy liver and multiple daughter hydatid cysts.

Figure 1 .
Figure 1.Description of the proposed model for complexity analysis of CT image for both healthy liver and multiple daughter hydatid cysts.

Figure 2 .
Figure 2. CT image of healthy liver.(a) An original image.(b) The image after color transformation.(c) The image after normalized the scale.(d)The image after applied median filter.(e) The image after application the CLAHE enhancing.

Figure 3 .
Figure 3. CT image of multiple daughter hydatid cyst.(a) An original image.(b) The image after color transformation.(c) The image after normalized the scale.(d)The image after applied median filter.(e) The image after application the CLAHE enhancing.

Figure 4 .
Figure 4. Box plots of healthy liver and multiple daughter hydatid cysts.