Browsing by Subject "Markov random fields"
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Item Open Access Generation and parameter estimation of Markov random field textures and a parallel network for texture generation(Bilkent University, 1990) Gürelli, Mehmet İzzetIn this thesis, a special class of Markov random fields (MRF), which is defined on two dimensional pixel arrays and represented by a few numbers called the MRF parameters, is studied as a texture model. Specifically, the generation of sample MRF textures and estimation of MRF texture parameters are considered. For the generation of sample MRF textures, an algorithm that can be implemented in a parallel manner is developed together with a parallel network which implements the algorithm. A mathematical description of the algorithm, based on finite state Markov chains is given and the structure of the network is explained. For the estimation of MRF texture parameters, a method based on histogramming of a sample MRF texture is studied cind a mathematical justification of the. method is given. Generation and parameter estimation methods studied in this thesis are tested by some computer programs and the results are observed to be satisfactory for many purposes.Item Open Access Modeling economic activities and random catastrophic failures of financial networks via gibbs random fields(Springer, 2020) Onural, Levent; Pınar, Mustafa Çelebi; Fırtına, CanThe complicated economic behavior of entities in a population can be modeled as a Gibbs random field (GRF). Even with simple GRF models, which restrict direct statistical interactions with a small number of neighbors of an entity, real life economic and financial activities may be effectively described. A computer simulator is developed to run empirical experiments to assess different coupling structures and parameters of the presented model; it is possible to test many economic and financial models and policies in terms of their transient and steady-state consequences.Item Open Access Object-based 3-d motion and structure analysis for video coding applications(Bilkent University, 1997) Alatan, A. AydinNovel 3-D motion analysis tools, which can be used in object-based video codecs, are proposed. In these tools, the movements of the objects, which are observed through 2-D video frames, are modeled in 3-D space. Segmentation of 2-D frames into objects and 2-D dense motion vectors for each object are necessary as inputs for the proposed 3-D analysis. 2-D motion-based object segmentation is obtained by Gibbs formulation; the initialization is achieved by using a fast graph-theory based region segmentation algorithm which is further improved to utilize the motion information. Moreover, the same Gibbs formulation gives the needed dense 2-D motion vector field. The formulations for the 3-D motion models are given for both rigid and non- rigid moving objects. Deformable motion is modeled by a Markov random field which permits elastic relations between neighbors, whereas, rigid 3-D motion parameters are estimated using the E-matrix method. Some improvements on the E-matrix method are proposed to make this algorithm more robust to gross errors like the consequence of incorrect segmentation of 2-D correspondences between frames. Two algorithms are proposed to obtain dense depth estimates, which are robust to input errors and suitable for encoding, respectively. While the former of these two algorithms gives simply a MAP estimate, the latter uses rate-distortion theory. Finally, 3-D motion models are further utilized for occlusion detection and motion compensated temporal interpolation, and it is observed that for both applications 3-D motion models have superiority over their 2-D counterparts. Simulation results on artificial and real data show the advantages of the 3-D motion models in object-based video coding algorithms.