One of the initial steps in the analysis of 3-D/4-D images is Segmentation, which entails partitioning the images into relevant subsets such as object and background. In this paper, we present a multidimensional segmentation algorithm to extract object surfaces from Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) scans. The algorithm is formulated in the framework of Mathematical Morphology. We propose the Generalized Morphological operators for segmentation in multidimensions. Apriori knowledge of the approximate location of the object surface is commu-nicated to the algorithm via the definition of the Search Space. The algorithm uses this definition of the Search Space to obtain the Surface Candidate elements. The search space specification reduces the computational cost and increases the reliability of the detected features. The detected surface is represented as a hierarchical combination of patches. Initial results obtained by using the algorithm to segment the Brain from cranial MRI scans is presented.