Automated Meshing of Anatomical Shapes for Deformable Medial Modeling: Application to the Placenta in 3D Ultrasound

Strain estimation in aortic roots from 4D echocardiographic images using medial modeling and deformable registration

“…For thin cylindrical shapes like the aortic root, the estimated medial axis aligns well with the ridge of the signed distance transform shown in Figure 3C. For anatomies with larger shape variation, m can alternatively be updated through constrained optimization as described in [66], such that the values of q U and q L are optimized to align the medial axis with the ridge of the signed distance transform.…”

“…For example, deterministic skeletonization algorithms estimate an object's medial geometry directly from its boundary representation (e.g., [61][62][63]), while inverse skeletonization algorithms approximate an object's medial geometry by fitting a pre-defined deformable model with fixed medial topology to the object (e.g., [64,65]). In this work, we use a boundary contour resampling scheme adapted from [66] to generate a 3D triangulated medial mesh of the aortic root based on the geometry of its boundary (similar to deterministic algorithms) while assuming a non-branching medial 8 axis topology (similar to inverse skeletonization approaches). The meshing algorithm is specific to 3D shapes with non-branching medial geometry, meaning that the 3D shape can be sliced into 2D cross-sections that are oblong and homeomorphic to a disk (e.g., placentas, cardiac ventricles, kidneys).…”