212 Third International Conference on Theoretical and Mathematical Foundations of Computer Science Lecture Notes in Information Technology, Vol.38 Applying Kohonen Network in Organising Unstructured Data for Talus Bone Seng Poh Lim * a and Habibollah Haron b Department of Modeling and Industrial Computing, Faculty of Computer Science and Information System, Universiti Teknologi Malaysia, Skudai, Johor, Malaysia. a lawrencess87@yahoo.com, b habib@utm.my Keywords: Kohonen Network, Unstructured Data, Talus Bone, Surface Reconstruction, Visualisation Abstract. Incorrect result will be produced during visualisation due to the connectivity between the unstructured data is unknown. This is the main problem in the surface reconstruction because correct topology is important in representing the object shape. So, the dataset should be reorganised by finding the correct topology of the data before visualising it. Besides that, most of the medical image are organised and visualised by using the scanning software in determining the shape of the object. In addition, soft computing methods are seldom used in dealing with medical field data. Therefore, this paper proposed Kohonen Network by testing the availability of this method in organising the medical image data because this method is mostly used in constructing engineering field data. Based on the experimental result obtained, this method is proved to be able in dealing with the medical field data. 1. Introduction As mentioned in [1], data collection and surface representation are important in surface reconstruction because they will determine the methods used and represent the topology of the data. Unstructured data will produce different shape compared to the original object shape due to the connectivity of the data is unknown. This is the main problem in surface reconstruction as we want to obtain the correct shape with the correct topology information. Hence, reorganise process should be performed on the data collected and structured data is obtained at the end of the process. So, the shape obtained will be better due to fewer points are used to represent the same shape compared to the original data. Currently, most of the medical image are organised and visualised by using the scanning software in determining the object shape. Hence, we do not know the accuracy of the result because the software will form the connectivity of the points automatically and represent the shape. For some reasons, some of the medical image is traced manually by performing segmentation. This process is very time consuming since each of the bone data is joined manually and separately by the healthcare worker. However, this will increase the accuracy since connectivity of every point is determined manually. The shape obtained will represent what kind of disease was suffered by the patient. Therefore, the accuracy and the shape are important in medical field. This paper applied Kohonen Network in organising the unstructured data for talus bone. The aim of applying this method is to test the availability of the method in organising the medical field data since this method is mostly used in constructing engineering field data. For Kohonen Network, it will preserve the topology of the shape during the learning process is carried out. Besides that, soft computing methods are seldom used in dealing with medical field data. If computer science method 978-1-61275-51-4/1/$25. 213 IERI ICTMF 212
is applied and the results obtained are similar with the result generated by using the software, hence this method is proved to be good. For this paper, accuracy of the result produced is not concern because currently we only want to test the method. Hence, this paper will only focus in organising the unstructured data and visualising the shape of the result produced. This paper is structured as follows. In Section 2, we review previous works on Kohonen Network method. Section 3 describes flow of experiment by using Kohonen Network in organising the unstructured data. For Section 4, discussion is done on the result produced. Conclusions and future work are presented in the last section. 2. Review on Kohonen Network Kohonen Network, or known as Self Organizing Map (SOM) was introduced by Professor Teuvo Kohonen in 1982. This method can be used to analyse high-dimensional data and also as visualisation method [2,3]. It is a two-layer unsupervised continuous valued Neural Network [2,4]. Kohonen Network contains n input and m output nodes in its training steps and there is a weight associated to the connection from the input nodes to the output nodes. Minimum output node will be the winning node whereby the weights of this connection and their neighbours will be updated in a well-defined way [2]. In general, competition, cooperation and adaptation are the 3 phases involved in Kohonen Network. For Kohonen Network theory, please refer to [5]. SOM can be used to define some standard to modulate the function of a data set [6]. In [7], Kohonen training algorithm is applied to improve the overall performance at multiple resolution of the mesh. As discussed in [8], Kohonen Self Organizing Feature Map is used to estimate the parameter for Permanent Magnet Synchronous Motor (PMSM) drive. While for [2], different kinds of B-spline surfaces have been created continuously by using Kohonen Neural Network. As mentioned by [9], Kohonen Network is often used in solving the unodered data problems. In [1], Kohonen Growing Grid is used in organising the unstructured data. Besides that, Kohonen Network is merged with PSO in obtaining better surface. However, they did not state that when there are more than two nodes which containing the same number of winning counter, how the algorithm will be performed. In [6], the vertices of the initially mesh is moved by using SOM toward the point set. For [11], Kohonen learning rule is used for the adaptation process and the topological neigbourhood is obtained by using graph representation. Learning process is used in [12] work to generate a mesh model of the surface by building the connectivity between the points. While in [13], parameterisation method is developed by using Kohonen Network in creating an initial base surface. Based on the literature review, Kohonen Network is proposed because it is able to deal with unstructured data. This is proof in [1] work where they deal the unstructured data by using Kohonen Network. Besides that, they also merged it with other techniques and represented as hybrid method. It can also deal with data points because of its network layer characteristics. As done by [7], he considered the vertices as the cells for neural network while coordinates as the weight vector for each cell. 3. Flow of Experiment This section will explain the flow of the experiment. The data used for this experiment was obtained from the Ethical Committee from the Clinical Research Centre (CRC), Hospital Tengku Ampuan Afzan, Kuantan, Malaysia. A four-row multi-slice CT scanner (Somatom, Volume Zoom, SIEMENS) was used with 3mm slice thickness and recon increment of 1.5mm. This data contains 5253 points and there are no any standard dataset for talus bone because each person talus bone size is different and based on their body size. Fig. 1 shows the visualisation of raw data by using GNUPlot. Based on Fig.1, it shows that the data is in unstructured type and it needs to be reorganised so that the surface generated is similar to the original object shape.
The reorganise process will be done by using Kohonen network. In order to fit as the input for Kohonen Network, hence the data should be in Coordinates X, Y and Z. So, based on the input type, hence the output generated will be the same as the input. Table 1 shows the example of raw data for talus bone in 3D with Coordinates X, Y and Z. Table 1. Example of raw data for talus bone No Coordinates X Y Z 1.262362.1969676.5568 2.26818.194817.55893 3.2629733.1972524.5597 4.2621266.19683.5511 5.26834.1957758.551362 Fig. 1. Visualisation of raw data 6.2624499.1974173.551372 The result produced will be different for every times because random function is used in generating the weight for the Kohonen Network. Three nodes will be assigned as the input layer for the Kohonen Network and for the input vector, it contains of three values (Coordinates X, Y and Z) which will be chosen randomly by the algorithm. For output layer, which are the weights of the Kohonen Network will be dependent on the grid size. The dataset value will not change whereas the weights for Kohonen Network will be updated at the end of the process. This is because the dataset will be chosen as the input vector by the algorithm and the weights will learn based on the dataset chosen. The weights will approximate to the input vector during the learning process and become the output at the end of the process. This section will explain the reorganise process by applying Kohonen Network in organising the data. Fig. 2 shows the flow chart for the experiment. Refer to [5] for Equation 1 until Equation 6. Start Choose one input randomly Read the data (sample) Initialize grid size, initial learning rate, number of iterations and initial radius. Generate the weight of the nodes No Find the winning node Nearest to input vector? Yes Update the weight of the winning node and neighbours node Yes Produce output Yes Reach max iterations? No End Fig. 2. Flow chart of experiment The algorithm is performed as below: 1) Unstructured data are collected in the form of X, Y and Z. Read the input vector (unstructured data) into the algorithm.
2) Grid size, m, n and number of node, m x n are initialised. Weights of the nodes, W are generated randomly. Initial learning rate,, number of iterations, t and initial radius, are assigned. 3) Competition: One random input vector, P s is selected. Find the closest node from the P s by using Euclidean s distance formula. The node which contains the smallest distance from the P s will be the winning node. Euclid i n i ( X i W i where X i is the input vector and W i is the weight unit. 4) Cooperation and Adaptation: The weight of the neighbourhood nodes will be updated along with the weight of the winning node by using Gaussian function. W ( t 1 ) W ( t ) G s X ( t ) W ( t ) (2) ) 2 (1) G s ( t ) exp 2 dist, 2 2 ( ) t t (3) 1, 2,3... t ( t ) exp, t 1, 2,3... (4) t ( t ) exp, t 1, 2,3... (5) T (6) where, X is the input vector W is the weight of nodes Gs is the Gaussian function dist is the distance between winning node and the nearest node is the radius, is the initial radius is the learning rate, is the initial learning rate T is the maximum iteration, t is the iteration is the time constant 5) The learning process will return to 3 until the maximum iteration is reached. After the reorganise process was completed, hence the output is plotted by using GNUPlot in order to visualise the shape of the output. 4. Result Discussion This section will discuss the results produced by using Kohonen Network. The data used is the talus bone of a patient which contains 5253 points. It is very dense and is in unstructured type. Table 2 shows the results produced after the experiment was completed. Two parameters have been tested in order to prove the efficiency of the method, which is the grid size and number of iterations. Based on the results in Table 2, the grid size and number of iterations are directly proportional to the time taken to generate the result. When the grid size and iterations are increasing, the time taken to generate the result is longer. Besides that, the visualisation result shows that when the grid size is increasing and the number of iterations remain constant, hence the result produced will be not good
since not all the nodes were updated. However, the coverage of the surface is wider if the grid size is increasing because more points were used in representing the shape. When the grid size remain constant and the number of iterations is increasing, the surface is smoother based on the visualisation result shown in Table 2. This is because more data are included into the learning process and hence the approximation toward the input is more accurate. The result generated for each time will be different because random function is performed in generating the result. Although the grid size is increasing, but it is still unable to cover the whole surface of the object and the points are not joining together. Based on the statements given, this implies that the results of the experiment are affected by the parameters. Based on the result generated, Kohonen Network is proved to be able in organising the medical image data although there are some limitations and drawbacks. Since it is able to organise the unstructured data, hence improvement can be done to the method by solving the drawbacks. Hybrid with other methods can be done in order to decrease the time taken to produce the result. For this stage, no comparison can be done with the shape produced because the scanning software is just for the hospital usage. This result is only to prove the method availability to organise the dataset. Table 2. Result for experiments Grid size, No. of Time [s] m x n iterations, t 1 x 1 1.735 Visualisation 1 x 1 3 1.819 1 x 1 5 2.581 2 x 2 1 1.971 2 x 2 3 5.57 2 x 2 5 9.64 3 x 3 1 4.125 3 x 3 3 11.918 3 x 3 5 19.722 5. Conclusion and Future Works
In this paper, Kohonen Network is applied in organising the unstructured data for talus bone. Several experiments have been carried out in order to test the efficiency of the technique toward medical image data. Based on the experiments result, this technique is proof to be able in organising the data well. But the limitation is it cannot cover the whole surface of that object. The target for this paper in the future will be enhanced and improved the technique used. Several grids can be merged as a square or rectangle shape and applied in constructing the unstructured data. This is because the experiment results proof that soft computing methods are able to organise medical image data. Maybe computer science method can save up a lot of time and also provided better result compared by using medical software. So, based on the suggestions given, the shape obtained might be better since the object can be covered by the closed surface and maybe the termination criteria can be fulfilled faster. The accuracy of the result and comparison with other methods can be considered when the enhancement has been done on the method used. 6. Acknowledgements This work is financed by UTM Zamalah. The medical data is provided by Rosdi Daud, Medical Implant Technology Group (MEDITEG), UTM. Authors would like to thank the anonymous referees for their valuable comments and suggestions. References [1] S. P. Lim and H. Haron. Surface Reconstruction Techniques: A Review. Artif Intell Rev, DOI: 1.17/s1462-12-9329-z, Springer. 1-2. (212) [2] M. Hoffmann. Numerical Control Of Kohonen Neural Network For Scattered Data Approximation. Numerical Algorithm, Vol.39. 175-186. (25) [3] T. Kohonen and T. Honkela. Kohonen Network. [Online]. Available at: http://www.scholarpedia.org/article/kohonen_network [Accessed 19 Aug 211]. (27) [4] G. F. Luger. Artificial Intelligence Structures and Strategies for Complex Problem Solving Fifth Edition. Pearson Education Limited. (25) [5] T. Kohonen. The Self-Organizing Map. Proceedings of the IEEE, Vol. 78, No. 9, September 199.1464-148. (199) [6] A. d. M. B. Júnior, A. D. D. Neto, J. D. d. Melo and L. M. G. Gonçalves. An Adaptive Learning Approach for 3-D Surface Reconstruction From Point Clouds. IEEE Transactions On Neural Networks. 1-11. (28) [7] Y. Yu. Surface Reconstruction from Unorganized Points Using Self-Organizing Neural Networks. IEEE Visualization 99, Conference Proceedings (1999): 61-64. (1999) [8] B. Jaganathan, S. Venkatesh, Y. Bhardwaj and C. A. Prakash. Kohonen s Self Organizing Map Method of Estimation of Optimal Parameters of a Permanent Magnet Synchronous Motor Drive. India International Conference on Power Electronics (IICPE). 1-6. (211) [9] M. Hoffmann. Modified Kohonen Neural Network for Surface Reconstruction, Publ. Math. 54 (1999). 857-864. (1999) [1]F. Forkan and S. M. Shamsuddin. Kohonen Swarm Algorithm for Unstructured Data in Surface Reconstruction. Fifth International Conference on Computer Graphics, Imaging and Visualization. 5 11. (28)
[11] F. Boudjemaï, P. B. Enberg and J. G. Postaire. Dynamic Adaptation And Subdivision In 3D- SOM Application To Surface Reconstruction. Proceedings of the 17th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 5). 6-43. (25) [12]F. Boudjemaï, P. B. Enberg and J. G. Postaire. Surface modeling by using self organizing maps of Kohonen. IEEE International Conference on Systems, Man and Cybernetics, 23. Vol.3. 2418-2423. (23) [13]J. Barhak and A. Fischer. Parameterization and Reconstruction from 3D Scattered Points Based on Neural Network and PDE Techniques. IEEE Transactions On Visualization and Computer Graphics, Vol. 7, No. 1, January-March 21. 1-16. (21)