In a method and apparatus for detecting and displaying arbitrary interior surfaces of a three-dimensional body from a regular array of values of at least one physical property in the interior of the body, the physical property measurements are made with systems such as computerized tomographic x-ray imaging, or magnetic resonance imaging. A recursive algorithm starts with a seed voxel in the surface of interest and continues to all adjacent voxels having a common face which is penetrated by the surface of interest. The common surface penetrations are derived from a look-up table which lists the adjacent voxels having a common penetrated face for each voxel index. The voxel index, in turn, is the string of binary digits representing the voxel vertices whose vertex values exceed the surface value of the surface of interest. The resulting list of voxels can be processed by conventional processors to display the surface of interest with greatly reduced interference from nearby, closely intermingled surfaces with the same or similar surface values.