Topological features constitute the highest abstraction in object representation. Euler characteristic is one of the most widely used topological invariants. The computation of the Euler characteristic is mainly based on three well-known mathematical formulae, which calculate either on the boundary of object or on the whole object. However, as digital objects are often non-manifolds, none of the known formulae can correctly compute the genus of digital surfaces. In this paper, we show that a new topological surface invariant of 3D digital objects, called BIUP{3}, can be obtained through a special homeomorphic transform: front propagation at a constant speed. BIUP{3} overcomes the theoretic weakness of the Euler characteristic and it applies to both manifolds and non-manifolds. The computation of BIUP{3} can be done efficiently through a virtual front propagation, leaving the images unaffected.