|Year : 2011 | Volume
| Issue : 3 | Page : 237-245
Analysis of Three-dimensional Magnetic Resonance Human Liver Images
Michal Strzelecki1, Malrey Lee2
1 Institute of Electronics, Technical University of Lódz, ul. Wólczanska 211/215, 90-924 Lódz, Poland
2 Center for Advanced Image and Information Technology, Chonbuk National University, Division of Electronics and Information Engineering, 561-756 Jeonju, South Korea
|Date of Web Publication||9-Aug-2011|
Institute of Electronics, Technical University of Lódz, ul. Wólczanska 211/215, 90-924 Lódz
| Abstract|| |
Recent development in three-dimensional (3D) imaging techniques such as magnetic resonance imaging or computed tomography with application in medical science demands the development of appropriate 3D image processing methods. It is therefore of interest to develop methods of image analysis, which would make use of this additional information. This article presents the classification and segmentation of 3D MR human liver images. The described experiments investigate whether it is possible to improve the accuracy of homogenous texture classification with the use of 3D analysis. Classification was performed both for 3D and two-dimensional data samples using Gray Level Co-occurrence Matrices. The proposed segmentation method is based on the 3D network of synchronized oscillators applied for 3D data. The principles of oscillator network operation are described here. The network was tested on sample 3D artificial images, and the segmentation results were compared with those obtained with the use of multilayer feedforward perceptron. It is demonstrated that the advantage of the discussed approach is its resistance to changes of visual image information caused, for example, by noise, that are very often present in biomedical images. The proposed technique was applied for segmentation of 3D liver images, and the sample results are presented and discussed.
Keywords: 3D magnetic resonance, Classification, Human liver images, Multilayer feedforward perceptron
|How to cite this article:|
Strzelecki M, Lee M. Analysis of Three-dimensional Magnetic Resonance Human Liver Images. IETE J Res 2011;57:237-45
| 1. Introduction|| |
Recently, the medical imaging techniques have improved dramatically offering not only the best photographic image quality but also three-dimensional (3D) images (such as 3D image acquisition protocols developed for computed tomography [CT] or magnetic resonance imaging [MRI ]), used, for example, in medical diagnosis. This significantly improved medical diagnosis, introducing new useful information that is not available in the classical two-dimensional (2D) imaging. On the other hand, analysis of 3D images requires appropriate methods in order to benefit from this additional information. This concerns image classification and segmentation. Thus development shows of a new technique for analysis of 3D data is considered as a very important research topic.
The objective of this article is to present the analysis methods for 3D MR human liver images. Healthy and diseased livers, with different stages of liver fibrosis and cirrhosis were observed. Two types of image analysis were performed: classification of healthy and diseased samples and segmentation of the 3D liver data.
For image classification, a texture analysis was performed. Texture is a key feature for image classification and segmentation . It is useful in the analysis of images ranging from aerial and satellite photos to microscopic images of food samples. It is especially important in biomedical image processing, as gray level information turns out to be insufficient for distinguishing different types and conditions of human tissues. There has been a considerable amount of research in this field and numerous methods have been proposed related to texture description and classification. These include among others, run-length and co-occurrence matrices , discrete wavelet transforms , stochastic models , and fractal dimension .
The experiment described in this study investigates whether statistical analysis of 3D images can improve texture classification as compared with traditional 2D analysis, assuming the same texture class. The gray level co-occurrence matrix (GLCM)  proved to be a reliable tool for discrimination and segmentation of 2D textured images  ; however, not much research has been done to explore its performance on 3D images (mostly due to its low time efficiency). To compare 2D vs 3D classification, another experiment was performed on 3D artificial textured images. They were synthesized using 3D Markov random field (MRF) image model. In case of MR and synthesized images, classification was performed both for original 3D data and for 2D cross-sections, to check if additional dimension is able to improve discrimination results. Furthermore, this approach was applied to MR 2D and 3D liver data. Image classification was performed using 1-nearest neighbor (1-NN) classifier  and nonlinear discriminant analysis (NDA), which is based on multilayer perceptron (MLP) neural network .
Another analysis was related to 3D liver image segmentation. It is a very important aspect of visual perception, and remains a challenging task for many image analysis problems. Several approaches to this problem have been described in the literature. For CT images, extended active contour method was used to segment mouse spleen ; a knowledge-based approach based on Bayes' rule was used  for segmentation of coronary arteries. Statistical segmentation method with the use of deterministic annealing was proposed for the classification of brain tissues in multiple sclerosis MR brain images . MR brain tumor images were segmented by means of 3D Markov mesh models . An interesting approach was presented , where usually not visible for human vision system, 3D boundary of brain tumor was detected by computing gradients in the third and higher order statistics of the MR data.
This article presents a different 3D segmentation technique, which implements a network of synchronized oscillators (SON) . This recently developed tool is based on "temporary correlation" theory , which attempts to explain scene recognition, as it would be performed by a human brain. This theory assumes that different groups of neural cells encode different properties of homogenous image regions (eg, shape, color, and texture). Monitoring of temporal activity of cell groups allows the detection of such image regions, and consequently leads to scene segmentation. Oscillator network was successfully used for segmentation of gray level  and textured images , including also biomedical ones . The advantage of this network is its adaptation to local image changes (related both to the image intensity and texture), which in turn ensures correct segmentation of noisy and blurred image fragments. Another advantage is that synchronized oscillators do not require any training process, unlike the artificial neural networks.
The network of synchronized oscillators is also suitable for hardware realization, providing very fast image segmentation due to parallel oscillator operation. Such Very Large Scale of Integration (VLSI) network chips were recently realized as Complementaly Mental-oxide Semiconductor (CMOS) Application-specific Integrated Circuit (ASICs) ,. They are able to perform segmentation of 2D images.
The article is organized as follows: Section 2 describes the classification experiment performed on artificial data; in Section 3, quantification of texture feature is presented, which is further used for classification of 2 types of liver images; Section 4 describes operation principles of the 3D oscillator network; Section 5 presents segmentation results of sample 3D MR liver images; and Section 6 contains discussion and concludes the article.
| 2. Classification of Artificial Data|| |
The MRF image model has been frequently used in several aspects of image processing, including texture classification and segmentation , and also for 3D images . It is possible to extend standard 2D MRF model to 3D case. Assume X[i,j,k] is an image array of size N×N×N and x[i,j,k] denotes the integer gray level value in the range of [0, L1 ] at location (i,j,k), where L is the number of image gray levels. If X[i,j,k] is a first-order MRF, the conditional probability for pixel x[i,j,k] is given by  :
where b=[b1, b2, b3 ] is spatial-dependency parameter vector corresponding to first-order neighborhood T of pixel x[i,j,k], as illustrated in [Figure 1]. Z is a partition function used for formula (1) normalization.
In this case
The 3D images used in the experiment were 4-gray level 1st order MRF realizations with a size of 100×100×40 voxels. To generate these images, modified Gibbs sampler procedure was used. Analyzed images, shown in [Figure 2]a-f represent 6 different texture classes obtained for different b parameter vectors. The 2D images were of 256×256 pixels, 4 gray levels. They were obtained by use of 1st order 2D MRF model with the same parameter values as in the case of 3D textures. They are presented in [Figure 2]g-l.
|Figure 2: Middle cross-sections of 3D textures generated for the following model parameters b1=b2=b3 equal to: 0.0 (uniform noise) (a), 0.2 (b), 0.4 (c), 0.6 (d), 0.8 (e), and 1.0 (f). Images of 2D textures generated for MRF parameters b1=b2 equal to: 0.0 (uniform noise) (g), 0.2 (h), 0.4 (i), 0.6 (j), 0.8 (k), and 1.0 (l).|
Click here to view
Such artificial textures provide large number of data samples, thus the reliability of a given classifier can be evaluated. Moreover, features used for the description of analyzed textures (estimated MRF parameters) are optimal (as they describe the probabilistic model used for texture generation), thus accurate classification results are expected. There is no need in this case to consider the search and then the selection of most discriminant features.
For feature classification, an NDA was applied . It transforms the input features into a new nonlinear feature space to provide further feature reduction and its linear separability. Another advantage of NDA is reduction of input data variance in the new space . This neural network-based approach allows for validation of classification results. The whole data set was divided into 2 parts-training set and test set. NDA network was learned using training set to minimize its classification error, and the obtained network weights were stored. Next, the test set was fed into network inputs (network weights were the same as obtained during the learning phase) and its classification was performed. Test set classification results evaluate the ability of network generalization, which is a neural classifier quality measure. Correct classification of the test set means that network weights were able to adapt to class distribution in the feature space for the analyzed data set. This in consequence confirms a reliability of NDA network classifier. The following NDA network structure was applied for 3D images: 3D 3-6-2-6 (3 inputs corresponding to 3 features, 6 neurons in 1st hidden layer, 2 neurons in 2nd hidden layer corresponding to 2 NDA features, 6 neurons in output layer, which corresponds to 6 texture classes) for 2D images: 2-6-2- 6. This network is shown in [Figure 3]. The training set contained 32 data vectors (with 3 or 2 elements depending on image dimension) of estimated MRF parameters (6×32=192 vectors altogether). The estimation was performed for each texture in nonoverlapping regions with the following sizes:
Classification errors obtained for training sets are presented in [Table 1].
- 10×10×10 voxels (3D images, this rather small basic region size was assumed, as in real biomedical images larger regions are usually not available)
- 33×33 pixels (2D images, number of region pixels corresponds to number of voxels in basic region for 3D images). The ratio of Linear Discriminate Analysis (LDA) network weights to the number of samples in training data set was as follows:56:192, thus it was lower than 1/3, as suggested .
|Figure 3: Structure of the neural network used for the classification of 3D textures.|
Click here to view
|Table 1: Number of misclassified samples [misclassification error in %] for NDA classifier obtained for training and test data sets|
Click here to view
| 3. Classification of MR Liver Images|| |
Similar classification method was also applied for the discrimination of 3D liver images, obtained using magnetic resonance tomography (Philips Medical System, Netherlands). These images were recorded at the University of Rennes, France. Image size was equal to 192×192×60 voxels, with a resolution of 2.08×2.08×2.0 mm/voxel. These images were acquired using 3D acquisition protocol and stored in DICOM format. There were 4 healthy liver images and 10 with different liver diseases (fibrosis and cirrhosis). Sample images are shown in [Figure 4]. The long-range objective of this research is to check, if morphologic changes, which occur in the human liver (caused by fibrosis or cirrhosis), are reflected in their MR images. Thus classification task was to check, if it is possible to discriminate healthy and diseased livers based on their texture.
Two approaches for texture feature extraction were assumed: one for 3D data and second for 2D image slices. In case of 3D data analysis, the cubic ROIs were defined with size 10×10×10 voxels. Small Region of Interest (ROI) size was caused by rather low image resolution. For each 3D image, 10 such nonoverlapping ROIs were used to calculate texture features. In case of 2D images also 10 ROIs were used for texture feature evaluation. In this case, defined ROIs were 2D, of elliptic shape, with area equal to 576 pixels. The ROI shape and size was selected to fit to the lower liver cross-sections. The ROIs were evenly distributed over different slices of the 3D image. Sample ROIs for 3D and 2D analysis are shown in [Figure 5]. Thus the number of data samples was 40 for healthy liver and 100 for liver diseases.
|Figure 5: ROI distribution for sample analyzed image: 3D case (cross-sections of 5 ROIs are visible) (a) and 2D case (one ROI) (b). Distribution of 2D ROIs in the 3D image (coronal view, white lines correspond to elliptic ROI cross-sections) (c).|
Click here to view
For each ROI, the number of texture features was estimated, depending on the type of analysis performed (3D or 2D). The number and type of texture features are listed in [Table 2]. For each ROI, ±3σ normalization was performed. Each ROI was normalized by calculating the mean value (m) and standard deviation (σ) of ROI gray levels. Normalization involved ROI mean value subtraction and division of the difference by the standard deviation. Subsequently, the ROI gray levels were quantified to the range of m±3σ. Further analysis included only data from this range, in order to minimize the influence of possible MR signal alterations that might have been present during acquisition, and to eliminate the dependency on different mean values of ROIs representing the same tissue .
Distribution of 3 features with the lowest 1-NN classification error (found using feature selection based on the optimal subset search for feature triplets)  for data obtained by 3D and 2D analysis is presented in [Figure 6]. Such a feature selection method provided feature set with a lower classification error rate when compared with other feature reduction techniques, such as Fisher coefficient  or minimization of classification error .
|Figure 6: Distribution of suboptimal features for 3D (a) and 2D (b) data classification. The same data in NDA feature space, for 3D (c) and 2D (d). Class marks: 1-healthy, 2-deseased.|
Click here to view
MaZda , a software package developed at the Institute of Electronics, Technical University of Lodz, Lodz, Poland, for quantitative texture analysis was used for both ROI definition and feature calculation and selection. Data classification and visualization were performed using b11 program (a part of MaZda package) .
Next, the check classification reliability, the analyzed samples were divided arbitrarily into training and test sets (both for 3D and 2D data). Both sets contained the same number of samples, 50 corresponding to healthy liver and 20 of diseased ones. NDA networks were learned using samples from training sets, and then the obtained network weights were stored. In this case, the NDA network 1st layer was reduced to 3 neurons only to maintain appropriate ratio of the number of network weights and size of the training set (26-80). Then samples from the test set were fed into NDA network inputs and classification was performed. Classification errors for whole, test, and training data sets (for 3D images and 2D cross-sections) are presented in [Table 3].
1-NN, 1-nearest neighbor; NDA, nonlinear discriminant analysis.
| 4. The Architecture of 3D Oscillators Network|| |
To implement the image segmentation technique based on temporary correlation theory, an oscillator network was proposed . Each network oscillator is defined by 2 differential equations , :
where x is referred to as an excitatory variable, while y is an inhibitory variable. IT is a total stimulation of an oscillator and ε, γ, β are parameters. Oscillators defined by Equation (1) are connected in 3D network, in the simplest case each oscillator is connected only to its 6 nearest neighbors, as shown in [Figure 7] (larger neighborhood sizes are also possible). Network dimensions are equal to dimensions of analyzed image and each oscillator represents single image pixel. Each oscillator in the network is connected with so-called global inhibitor (GI in [Figure 7]), which receives information from oscillators and in turn eventually can inhibit whole network. Generally, the total oscillator stimulation IT is given by Equation (2) , :
where Wik are synaptic dynamic weights connecting oscillator i and k. Number of these weights depends on neighborhood size N(i). In the case presented in [Figure 7], N(i) contains 6 nearest neighbors of ith oscillator (except for these located on network boundaries).
|Figure 7: A fragment of 3D oscillator network. GI means the global inhibitor, connected to each network oscillator.|
Click here to view
Due to these local excitatory connections an active oscillator spreads its activity over the whole oscillator group, which represents image object. This provides synchronization of this group. θX is a threshold, above which oscillator k becomes active. H is a Heaviside function, it is equal to one if its argument is higher than zero, and zero otherwise. Wz is a weight of inhibitor GI, it is equal one if at least one network oscillator is in active phase (x>0) and it is equal to zero otherwise. The role of global inhibitor is to provide desynchronization of oscillator groups representing different objects from this one which is actually being under synchronization. Global inhibitor will not affect any synchronized oscillator group because the sum in Equation (2) has greater value than Wz.
The weight Wik connecting 2 neighbor oscillators, which represent image pixels i and k is defined by formula (3):
where fi and fk are gray levels of pixels i and k, respectively, No is the number of active oscillators in the neighborhood N(i) and L is the number of image gray levels. Hence, weights are high for homogenous regions and low for region boundaries. Because excitation of any oscillator depends on the sum of weights of its neighbors, all oscillators in the homogenous region oscillate in synchrony. Different oscillator groups represent each region. Oscillator's activation is switching sequentially between groups in such a way, that at a given time only one group (representing given region) is synchronously oscillating.
A segmentation algorithm using oscillator network was presented . It is based on simplified oscillator model and does not require solution of (1) for each oscillator; it can be also easily adapted to 3D network. This algorithm was used for segmentation of different biomedical images ,.
Oscillator network was tested on sample artificial image with a size of 256×256×80 voxels and 256 gray levels. It consists of 2 equal quadratic prisms with different gray levels and a sphere located centrally in the image. Although real images often suffer from noise and distortions, the same was applied for the analyzed ones. The image was corrupted by a Gaussian noise with zero mean value and standard deviation equal to 20. Additionally, an additive nonuniform image illumination was simulated. This illumination increases its brightness by one for each image row (starting from image top to its bottom). Middle cross-section of such distorted image is shown in [Figure 8]a. The second image used for analysis represents a mosaic of 4 3D textures generated using MRF model, as described in Section 2. For the generation of each texture, different 1st order model parameter values were assumed. It is with a size of 80×80×40 voxels and 4 gray levels. A middle cross-section of this image is presented in [Figure 8]d. For segmentation, each image texture was described by 3 MRF parameters. These parameters were estimated for each image point (except for lateral ones) in a box of size 10×10×10 voxels. The parameter values were used in formula (4) instead of the image gray level to obtain network weights.
|Figure 8: Artificial images used for segmentation: distorted image with 3 regions (a), textured image (b). Proportions of image sizes are not maintained, images (d, e, f) were enlarged. Segmentation results: oscillator network (b, e), MLP (c, f).|
Click here to view
For both the images, neighborhood N(i) contained 28 oscillators (corresponding to 28 pixels surrounding each pixel i). Segmentation results are presented in [Figure 8]b and e. It can be observed that in the case of the image from [Figure 8]a segmentation was performed correctly, for all image objects. For the textured image, the segmentation was correct for homogenous region, and some misclassified regions can be. It can be observed that in the case of the image from [Figure 8]a segmaenation was performed correctly for all image objects.
The same images were segmented using feedforward MLP network . MLP with 2 neurons in the hidden layer and 3 [Figure 8]a or 4 [Figure 8]d neurons in the output layer was trained using b11 software . [Figure 8]a image shows training set containing 96 samples, randomly drawn from each image region (32 samples from the middle part for each of the 2 quadratic prisms and 32 for the sphere, respectively). In [Figure 8]d, there are 128 samples in the training set (32 samples randomly selected for each texture). After network learning (correct classification was obtained for both training sets), and image segmentation was performed using obtained network weights. Each image pixel was assigned to the given image region or texture based on network classification decision. Segmentation results are shown in [Figure 8]c and f. In case of the first image, totally missing segmentation was obtained. A large range of gray levels in each region (due to nonuniform image illumination) was not considered by training set. In case of such image distortions, each region possesses similar gray level distribution, thus it not possible to provide a correct boundary between these regions by means of MLP. For textured image, much better segmentation results were observed; however, some misclassified fragments could be found not only close to texture boundaries but also in the homogenous texture regions. Quantitative analysis of correctly classified image area results in 81% and 73% of oscillator network [Figure 8]e and MLP [Figure 8]f, respectively.
| 5. Analysis of 3D Liver Image|| |
The proposed segmentation method was also applied for segmentation of 3D liver images, described in Section 3. [Figure 9] presents sample segmented axially oriented liver cross-sections. [Figure 9]a, d, g, and j shows liver of a healthy patient, [Figure 9]b, e, h, and k displays a liver affected by fibrosis, and in [Figure 9]c, f, i and l a cirrhotic liver is presented. The objective of this research is to automatically detect a liver region from the rest of the image. Another purpose of this segmentation is estimation of liver volume. This parameter is very important for diagnosis of liver diseases. For this purpose, the SON was used. Network weights were set according to (3) and neighborhood N(i)=28 was assumed, as in case of artificial images. Segmentation results are marked with white outlines in [Figure 9]a-l. Only liver region was marked, other detected organs were neglected based on volume criterion (liver represents the largest organ in analyzed 3D images). Although the liver region is detected correctly, some segmentation errors are visible close to the liver boundary, where some other tissues are classified as liver. White regions, which can be observed in some of the segmented images [Figure 9]g and j inside of the liver represent larger liver veins.
|Figure 9: Segmentation results (white outline) for sample cross-sections of MR human liver images extracted from 3D data (a fragment of top and bottom image background was clipped). Healthy liver (a, d, g, j), a liver with fibrosis (b, e, h, k), and cirrhotic livers (c, f, i, l). Numbers indicate the slice number.|
Click here to view
| 6. Discussion and Conclusion|| |
The first conclusion emerging from the performed experiment states that it is possible to classify 3D human liver images into healthy and diseased ones with the use of GLCM features developed originally for 2D images. Furthermore, it is possible to improve the classification of homogenous texture by performing the analysis of the 3D images. It was demonstrated that the better classification results were obtained for analyzed 3D artificial textures than for their 2D cross-sections. 3D data are found to be more useful in the classification than 2D data. This is indicated by lower classification errors [Table 3]. It should be also mentioned that the number of 3D features was smaller than those calculated for 2D. Classification errors can be caused by low image resolution. If one image voxel contains information from the cube of approximately 2×2×2 mm of liver, this size is probably too large to preserve full liver texture characteristics.
Similar results were obtained for classification of artificial textures. It was found that also 3D MRF data contain more information when compared with 2D. This is shown by the classification results obtained for regions 10×10×10 voxels and 33×33 pixels. Even when the number of region pixels/voxels was the same, classification results obtained for 3D data are almost 3 times better when compared with 2D [Table 1].
Another advantage of 3D analysis is the possibility of ROI size reduction. In case of biomedical MR images, due to a relatively low image resolution, available region of the given tissue or organ is usually rather small, thus only limited ROIs are attainable.
The experiments described in this article indicate that 3D network of synchronized oscillators can be used for segmentation of 3D images. Also, it was demonstrated that in case of artificial distorted and textured images, SON provides better segmentation results when compared to MLP. It is caused by the fact that the SON weights are calculated based on the differences between image gray levels (or features used for texture description) considered for some pixel neighborhood. In case of small gray level (or feature value) changes, network weights remain similar and the analyzed image region is segmented correctly. In case of MLP, their weights have constant values, defined during learning procedure for the given training set. Thus a change of some image region brightness, which was not considered in the training set, may cause their wrong segmentation. Resistance to changes of visual image information and to noise, often present in biomedical images, as an important advantage of the oscillator network.
Preliminary segmentation results for sample liver 3D MR images are also promising. Automatic detection of liver volume in 3D MR image will allow classification of different liver diseases. This classification will consider texture information extracted from the 3D data. It is expected that properly selected texture features used for characterization of analyzed tissues will lead to reliable discrimination of liver tissue, which is a topic of further research.
| 7. Acknowledgments|| |
The authors thank Professor Jacques de Certaines from the University of Rennes, France, for delivering human liver images.
This work was performed within the framework of COST B21 European project: "Physiological Modeling of MR Image Formation."
| References|| |
|1.||M Hajek, M Dezertova, A Materka, and R Lerski,, "Texture analysis for magnetic resonance imaging", In: M Hajek, M Dezertova, A Materka, R Lerski, editors. Prague: Med4 publishing, 2006. |
|2.||R Haralick, "Statistical and Structural Approaches to Texture", Proc. IEEE, Vol. 67, No. 5, pp. 786-804, 1979. |
|3.||P Mojsilovic, M Popovic, and D Rackov, "On the selection of optimal wavelet basis for texture characterisation", IEEE Trans. on Image Processing, Vol. 9, No. 12, pp. 2043-50, 2000. |
|4.||H Derin, and H Elliot, "Modeling and segmentation of noisy and textured images using Gibbs random fields", IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 9, No. 1, pp. 39-55, 1987. |
|5.||L Kaplan, "Extended fractal analysis for texture classification and segmentation", IEEE Trans. on Image Processing, Vol. 8, No. 11, pp. 1572-82, 1999. |
|6.||M Strzelecki. "Segmentation of image texture using network of synchronised oscillators and statistical methods", Scientific Letters no 946, Technical University of Lodz, 2004. |
|7.||J Schürmann, "Pattern Classification", John Wiley and Sons, NewYork, 1996. |
|8.||K Fukunaga, "Introduction to Statistical Pattern Recognition", New york: Academic Press, 1991. |
|9.||D Aykac, JR Price, and JS Wall, "3D segmentation of the mouse spleen in microCT via active contours", Nuclear Science Symposium Conference Record, 3 CD ROM, 2005. |
|10.||Y Yang, A Tannenbaum, and D Giddens, "Knowledge-based 3D segmentation and reconstruction of coronary arteries using CT images", Proc. of 26th Annual International Conference of the IEEE Engineering in Medicine and Biology, Vol. 1, pp. 1664-6, 2004. |
|11.||G Zhanyu, V Venkatesan, and S Mitra, "A statistical 3-D segmentation algorithm for classifying brain tissues in multiple sclerosis", Proc. 14th IEEE Symposium on Computer-Based Medical Systems, pp. 455-60, 2001. |
|12.||C Fassnacht, and PA Devijver, "Medical image segmentation with a 3D nearest neighbor Markov mesh", Proc. of the 18th Annual International Conference of the IEEE Engineering in Medicine and Biology, Vol. 3, pp. 1049-50, 1996. |
|13.||M Petrou, VA Kovalev, and JR Reichenbach, "Three-dimensional nonlinear invisible boundary detection", IEEE Trans. on Image Processing, Vol. 15, pp. 3020-32, 2006. |
|14.||E Çesmeli, and D Wang, "Texture segmentation using Gaussian- Markov random fields and neural oscillator networks", IEEE Trans. on Neural Networks, Vol. 12, pp. 394-404, 2001. |
|15.||D Wang, "Emergent synchrony in locally coupled neural oscillators", IEEE Trans. on Neural Networks, Vol. 4, pp. 941-8, 1995. |
|16.||N Shareef, D Wang, and R Yagel, "Segmentation of medical images using LEGION", IEEE Trans. on Med. Imag, Vol. 18, pp. 74-91, 1999. |
|17.||M Strzelecki, "Texture boundary detection using network of synchronised oscillators", Electronics Letters, Vol. 40, pp. 466-7, 2004. |
|18.||J Cosp, J Madrenas, E Alarcón, E Vidal, and G Villar, "Synchronization of nonlinear electronic oscillators for neural computation", IEEE Trans. on Neural Networks, Vol. 15, pp. 1315-27, 2004. |
|19.||J Kowalski, and M Strzelecki, "CMOS VLSI chip for segmentation of binary images", Proc. of IEEE Workshop on Signal Processing, pp. 251-6, 2005. |
|20.||H Kovalev, F Kruggel, H Gertz, and Y Cramon, "Three-dimensional texture analysis of MRI brain datasets", IEEE Trans. on Biomedical Imaging, Vol. 20, No. 5, pp. 424-33, 2001. |
|21.||Y Hu, and J Hwang, "Handbook of neural network signal processing", Boca Raton: CRC Press; 2002. |
|22.||A Materka, MaZda Users Manual, Available from: https://www.eletel.p.lodz.pl/merchant/mazda/order1_pl.epl [Last cited on 2006 ]. |
|23.||A Mucciardi, and E Gose, "A comparison of seven techniques for choosing subsets of patter recognition properties", IEEE Trans. On Computers, Vol. c-20, No. 9, pp. 1023-31, 1971. |
|24.||P Linsay, and D Wang, "Fast numerical integration of relaxation oscillator networks based on singular limit solutions", IEEE Trans. On Neural Networks, Vol. 9, pp. 523-32, 1998. |
| Authors|| |
Michal Strzelecki received the M.Sc. degree in electrical engineering from the Technical University of Lodz (TUL) Poland in 1983, the Ph.D. degree in technical sciences from the same University in 1995. In 2006 he received D.Sc. degree (Habilitation) in computer science from the AGH University of Science and Technology, Krakow. Currently, he is with the Medical Electronics Division in the Institute of Electronics. His research interests include: Michal Strzelecki holds memberships in the Association for Image Processing and the Polish Society of Medical Informatics. He is also a member of Board of Directors of European Campus Card Association. Since 2004 dr Strzelecki has been vice director for teaching of the Institute of Electronics.
Malrey Lee received a Ph.D. in Computer Science from the University of Chung-Ang. She has been a Professor at the ChonBuk National University in Korea. She has over forty publications in various areas of Computer Science, concentrating on Artificial Intelligence, Robotics, Medical Healthcare and Software Engineering.
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9]
[Table 1], [Table 2], [Table 3]