The present invention relates to a method and system for constructing isosurfaces from 3D data sets, such as 3D image data that are based on a cubic grid (voxel image data). Specifically, 3D image is rendered from a voxel image that can be generated by a variety of medical modalities. The present invention is a modification of the MCA that allows for constructing an isosurface without holes resulting from some cubes having ambiguous isosurface topology. Specifically, to avoid holes resulting from ambiguities, multiple isosurfaces having different resolution levels are generated for ambiguous cubes to resolve the ambiguity.