This paper presents a sub-voxel analysis method for multi- parameter volumetric images such as MRI to provide partial volume estimation. The proposed method finds a continuous function for a neighboring structure of each voxel. The estimation function and neighboring structure are chosen from the quadratic/cubic polynomials and a set of 2D/3D symmetric neighborhood architectures, respectively. Then, a new form of the eigenimage method, based on Gram-Schmidt orthogonalization, is derived for each choice of estimation function and neighboring structure. Finally, the above estimators are applied to a simulation model consisting of materials similar to CSF, WM, and GM of the human brain in T1- , T2-, and PD-weighted MRI. In the presence of noise, the examined continuous estimators show a smaller standard deviation (up to 40%) than the standard eigenimage method. Also the chosen estimators have analytical solution for their Gram-Schmidt filters, so their execution times are comparable with that of the standard eigenimage method. In addition, the proposed approach can determine the 3D distribution of each material and extract the connecting surfaces of the materials within each voxel.