This paper presents a more robust reconstruction algorithm to solve the genus restriction of displaced subdivision surface (DSS) from unorganized points. DSS is a useful mesh representation to guarantee the memory efficiency by storing a vertex position as one scalar displacement value, which is measured from the original mesh to its parametric domain. However, reconstructing DSS from unorganized points has some defects such as the incorrect approximation of concave region and the limited application of genus-0. Based on volumetric approach, our new cell carving method can easily and quickly obtain the shape of point clouds and preserve its genus. In addition, using interpolatory subdivision scheme, our displaced butterfly subdivision surface is also effective multiresolution representation, because it samples exclusively new odd vertices at each level, compared with previous works to resample all vertices of every level. We demonstrate that displaced butterfly subdivision surface is an effective multiresolution representation that overcome the topological restriction and preserve the detailed features nicely.