Biomedical Engineering Reference
In-Depth Information
Figure 8.3: (a) Interactively positioning a CSG model relative to a Marching
Cubes mesh. (b) Isosurface of a binary scan conversion of the initialization CSG
model. (c) Final internal embryo structures.
O α by first applying an erosion followed by a dilation of φ , i.e. O α φ = D α
E α φ , which removes small pieces or thin appendages. A closing is defined
as C α φ = E α D α φ , and closes small gaps or holes within objects. Both
operations have the qualitative effect of low-pass filtering the isosurfaces in
φ —an opening by removing material and a closing by adding material. Both
operations tend to distort the shapes of the surfaces on which they operate,
which is acceptable for the initialization because it will be followed by a
surface deformation.
User-specified : For some applications it is desirable and easier for the user to
interactively specify the initial model. Here, the user creates a Constructive
Solid Geometry (CSG) model which defines the shape of the initial surface.
In Fig. 8.3(a) the CSG model in blue is interactively positioned relative to a
Marching Cubes mesh extracted from the original dataset. The CSG model is
scan-converted into a binary volume, with voxels simply marked as inside (1)
or outside (0), using standard CSG evaluation techniques [40]. An isosurface
of the initialization volume dataset generated from the torus and sphere is
presented in Fig. 8.3(b). This volume dataset is then deformed to produce
the final result seen in Fig. 8.3(c).
8.3.2 Level Set Surface Deformation
The initialization should position the model near the desired solution while re-
taining certain properties such as smoothness, connectivity, etc. Given a rough
initial estimate, the surface deformation process moves the surface model to-
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