Date of Award

Summer 2017

Document Type


Degree Name

Doctor of Philosophy (PhD)

Committee Director

Michel A. Audette

Committee Member

Frederic D. McKenzie

Committee Member

Khan M. Iftekharuddin

Committee Member

Gregory S. Fischer


The Dual Contouring algorithm (DC) is a grid-based process used to generate surface meshes from volumetric data. However, DC is unable to guarantee 2-manifold and watertight meshes due to the fact that it produces only one vertex for each grid cube. We present a modified Dual Contouring algorithm that is capable of overcoming this limitation. The proposed method decomposes an ambiguous grid cube into a set of tetrahedral cells and uses novel polygon generation rules that produce 2-manifold and watertight surface meshes with good-quality triangles. These meshes, being watertight and 2-manifold, are geometrically correct, and therefore can be used to initialize tetrahedral meshes.

The 2-manifold DC method has been extended into the multi-material domain. Due to its multi-material nature, multi-material surface meshes will contain non-manifold elements along material interfaces or shared boundaries. The proposed multi-material DC algorithm can (1) generate multi-material surface meshes where each material sub-mesh is a 2-manifold and watertight mesh, (2) preserve the non-manifold elements along the material interfaces, and (3) ensure that the material interface or shared boundary between materials is consistent. The proposed method is used to generate multi-material surface meshes of deep brain anatomical structures from a digital atlas of the basal ganglia and thalamus. Although deep brain anatomical structures can be labeled as functionally separate, they are in fact continuous tracts of soft tissue in close proximity to each other. The multi-material meshes generated by the proposed DC algorithm can accurately represent the closely-packed deep brain structures as a single mesh consisting of multiple material sub-meshes. Each sub-mesh represents a distinct functional structure of the brain.

Printed and/or digital atlases are important tools for medical research and surgical intervention. While these atlases can provide guidance in identifying anatomical structures, they do not take into account the wide variations in the shape and size of anatomical structures that occur from patient to patient. Accurate, patient-specific representations are especially important for surgical interventions like deep brain stimulation, where even small inaccuracies can result in dangerous complications. The last part of this research effort extends the discrete deformable 2-simplex mesh into the multi-material domain where geometry-based internal forces and image-based external forces are used in the deformation process. This multi-material deformable framework is used to segment anatomical structures of the deep brain region from Magnetic Resonance (MR) data.