In this paper, we present a deformable surface geometric model for segmenting targets from volumetric data. This model deforms under external forces only, and changes its geometry and topology by using improved geometric constraints. External forces are calculated by using the sum of inflation forces, whose contributions take place on internal regions of objects, and the gradient forces, which play a key role when the surface is near the boundary of objects. A new set of geometric constraints is proposed which includes constraints on vertices, edges and faces. Once a constraint is broken, the corresponding topological transformation will occur to keep the geometric and topological integrity of the surface unaltered. We demonstrate that our model can efficiently segment complex anatomic structures from medical 3D images, and achieve the requirements of accuracy and geometry for image segmentation.