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In this paper, we propose a supervised color image segmentation using homotopy continuation method and Markov random field (MRF) model. We propose a constrained compound MRF model to take care of color texture and scene images. Ohta (I1, I2, I3) model is used as the color for image segmentation. We also have extended the proposed model to inter-color-planes as well as intra-color-planes of the color model and thus a double constrained compound MRF (DCCMRF) model is proposed. The a priori MRF model parameters are estimated using the proposed homotopy continuation based method. The model parameters are the maximum pseudo likelihood estimates. The DCCRMRF model with estimated model parameters exhibited improved segmentation accuracy as compared to DCMRF, MRF, double MRF (DMRF) and JSEG method.