This paper presents a new approach to carry out erosion, dilation and connected component labeling. We use the Extreme Vertices Model (EVM), an orthogonal polyhedra representation, to describe binary images and volume datasets in a very efficient way. Our proposal does not use a voxel-based approach but deals with the inner sections of the object. It allows to treat images and volumes indistinctly using the same algorithm and data structure with no overhead of memory and can be applied to manifold as well as non-manifold data. The connected component labeling algorithm actually detects non-manifold zones and permits to break or not the objects at these zones by an user-specified parameter.