Reconstructing Cell Complexes From Cross-sections

Abstract. Many interesting segmentations take the form of cell complexes. We present a method to infer a 3D cell complex from of a series of 2D cross-sections. We restrict our attention to the class of complexes whose duals resemble triangulations. This class includes microstructures of polycrystalline materials, as well as other cellular structures found in nature. Given a prescribed matching of 2D cells in adjacent cross-sections we produce a 3D complex spanning these sections such that matched 2-cells are contained in the interior of the same 3-cell. The reconstruction method considers only the topological structure of the input. After an initial 3D complex is recovered, the structure is altered to accommodate geometric properties of the dataset. We evaluate the method using ideal, synthetic datasets as well as serial-sectioned micrographs from a sample of tantalum metal

Construction of simplified boundary surfaces from serial-sectioned metal micrographs

We present a method for extracting boundary surfaces from segmented cross-section image data. We use a constrained Potts model to interpolate an arbitrary number of region boundaries between segmented images. This produces a segmented volume from which we extract a triangulated boundary surface using well-known marching tetrahedra methods. This surface contains staircase-like artifacts and an abundance of unnecessary triangles. We describe an approach that addresses these problems with a voxel-accurate simplification algorithm that reduces surface complexity by an order of magnitude. Our boundary interpolation and simplification methods are novel contributions to the study of surface extraction from segmented cross-sections. We have applied our method to construct polycrystal grain boundary surfaces from micrographs of a sample of the metal tantalum

Multi-Material Mesh Representation of Anatomical Structures for Deep Brain Stimulation Planning

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

Toward Controllable and Robust Surface Reconstruction from Spatial Curves

Reconstructing surface from a set of spatial curves is a fundamental problem in computer graphics and computational geometry. It often arises in many applications across various disciplines, such as industrial prototyping, artistic design and biomedical imaging. While the problem has been widely studied for years, challenges remain for handling different type of curve inputs while satisfying various constraints. We study studied three related computational tasks in this thesis. First, we propose an algorithm for reconstructing multi-labeled material interfaces from cross-sectional curves that allows for explicit topology control. Second, we addressed the consistency restoration, a critical but overlooked problem in applying algorithms of surface reconstruction to real-world cross-sections data. Lastly, we propose the Variational Implicit Point Set Surface which allows us to robustly handle noisy, sparse and non-uniform inputs, such as samples from spatial curves