A new approach to the problem of object segmentation and isosurface detection is introduced. Drawing on the fundamental marching cubes algorithm of Lorensen and Cline, it operates with one space sweep through the voxels (hence it is called the voxel-sweep). It detects all isosurfaces and partitions the objects into connected components on the basis of the continuity of the surfaces. The surface of each connected component is obtained as an oriented triangular mesh, and is thus amenable as input to mesh-processing programs and hardware. Each separate component is automatically associated with its topological holes. These properties enable accurate volume and surface-area estimation of each component, as well as noise reduction (by eliminating "small" components). The runtime of the voxel-sweep is just a negligible increase over the runtime of the marching cubes algorithm. Another option of the voxel-sweep is to visualize the resulting surfaces at the same time as they are being formed. Ideally, this option should enable realtime modification of the iso-values defining the surfaces.