Spatial Fuzzy Clustering with Simultaneous Estimation of Markov Random Field Parameters and Class

Unsupervised Fuzzy C-Means (FCM) clustering technique has been widely used in image segmentation. However, conventional FCM algorithm has an intrinsic limitation: no spatial information is taken into account. This causes the FCM algorithm to work only on well-defined images with low level of noise. In this document a improvement to fuzzy clustering is described. A prior spatial con-straint is introduced into FCM algorithm through Markov random field theory and its equivalent Gibbs random field theory, in which the spatial information is encoded through mutual influences of neighboring sites. This unsupervised fuzzy Bayesian image segmentation method using fuzzy Markov random fields (FRMFs), which provides an improved segmentation re-sults when compared to the ‘hard ’ MRF method, has two groups of parameters to be estimated: the MRF parameters and class parameters for each pixel in the image. Typically, these two parameters are treated separately, and estimated in an alternating fashion. In this work, a method to estimate the parameters defining the Markovian distribution of the measured data while performing the data clustering simultaneously is developed. That is possible by defining esti-mates of the MRF parameters as functions of the class parameters resulting in a cost function that depends only on the class parameters of each pixel. The Conjugate Gradient method (CGM) is applied to search the optimizer of the resulting non-linear cost function. We perform computer simulations on synthetic test images to demonstrate the efficacy and efficiency of the proposed method and also provide a comparison with some of the commonly used methods. This work is only a little part of a more complex project based on predictive an-alytics. This big project works with geospatial data, therefore some knowledge about this type of data and how it has to be processed in order to be clustered by our method is also included. 3Acknowledgements I would like to acknowledge all the people who have helped me realize this The-sis. Specially, I want to thank my advisors, Prof. Dr. Miles N. Wernick an