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An iterative split-and-merge framework for the segmentation of planar surfaces in the disparity space is presented. Disparity of a scene is modeled by approximating various surfaces in the scene to be planar. In the split phase, the number of planar surfaces along with the underlying plane parameters is assumed to be known from the initialization or from the previous merge phase. Based on these parameters, planar surfaces in the disparity image are labeled to minimize the residuals between the actual disparity and the modeled disparity. The labeled planar surfaces are separated into spatially continuous regions which are treated as candidates for the merging that follows. The regions are merged together under a maximum variance constraint while maximizing the merged area. A multistage branch-and-bound algorithm is proposed to carry out this optimization efficiently. Each stage of the branch-and-bound algorithm separates a planar surface from the set of spatially continuous regions. The multistage merging estimates the number of planar surfaces and their labeling. The splitting and the multistage merging is repeated till convergence is reached or satisfactory results are achieved. Experimental results are presented for variety of stereo image data.