BIUP3: boundary topological invariant of 3D objects through front propagation at a constant speed

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 BIUP³, can be obtained through a special homeomorphic transform: front propagation at a constant speed. BIUP³ overcomes the theoretic weakness of the Euler characteristic and it applies to both manifolds and non-manifolds. The computation of BIUP³ can be done efficiently through a virtual front propagation, leaving the images unaffected.