In this paper we extend previous techniques we developed for efficient morphological processing of 2D document images to the analysis of 3D voxel data obtained by Computed Tomography (CT) scans. The proposed approach is based on a directional interval coding scheme of the voxel data and a basic set of operations that can be employed directly to the encoded data. The scan lines can be chosen to be in an arbitrary direction so as to fit directionality inherent to the data. Morphological operations are obtained by manipulating pairs of intervals belonging to the data and the kernel, where such manipulation can result in the addition, removal, or change of existing intervals. In addition to the implementation of ordinary morphological operations we develop a convolution operation that can be applied directly to the encoded data thus enabling the implementation of regulated morphological operations which incorporate a variable level of strictness. The computational complexity of the proposed operations is evaluated and compared to that of the standard implementation. The paper concludes with simulation results in which the execution time of iterative application of different morphological operations based on a standard implementation and the proposed encoded implementation are compared.