Two filtrations of ribbon 2-knots

We have constructed a ‘Vassiliev-like’ filtration on the free abelian group generated by the set of ribbon 2-knots in 4-space in two ways: one is from a ribbon 2-disk, and the other from a projection of a ribbon 2-knot onto a generic 3-space whose singular set consists of only double points. Each filtration determines a notion of finite type invariants for ribbon 2-knots. We prove that the two filtrations are the same, and thus, the two finite type invariants are coincident.