Abstract In many three-dimensional imaging applications the three-dimensional scene is represented by a three-dimensional array of volume elements, or voxels for short. A subset Q of the voxels is specified by some property. The objects in the scene are then defined as subsets of Q formed by voxels which are “connected” in some appropriate sense. It is often of interest to detect and display the surface of an object in the scene, specified, say, by one of the voxels in it. A set of topological definitions is given for object surfaces and associated concepts. Some results are also proved which allow detection of object surfaces in a three-dimensional scene in a computationally efficient way.