549 research outputs found
Watertight and 2-Manifold Surface Meshes Using Dual Contouring With Tetrahedral Decomposition of Grid Cubes
The Dual Contouring algorithm (DC) is a grid-based process used to generate surface meshes from volumetric data. The advantage of DC is that it can reproduce sharp features by inserting vertices anywhere inside the grid cube, as opposed to the Marching Cubes (MC) algorithm that can insert vertices only on the grid edges. 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. Our method decomposes an ambiguous grid cube into a maximum of twelve tetrahedral cells; we introduce novel polygon generation rules that produce 2-manifold and watertight surface meshes. We have applied our proposed method on realistic data, and a comparison of the results of our proposed method with results from traditional DC shows the effectiveness of our method
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
Algorithms and methods for discrete mesh repair
Computational analysis and design has become a fundamental part of product research, development, and manufacture in aerospace, automotive, and other industries. In general the success of the specific application depends heavily on the accuracy and consistency of the computational model used. The aim of this work is to reduce the time needed to prepare geometry for mesh generation. This will be accomplished by developing tools that semi-automatically repair discrete data. Providing a level of automation to the process of repairing large, complex problems in discrete data will significantly accelerate the grid generation process. The developed algorithms are meant to offer semi-automated solutions to complicated geometrical problems—specifically discrete mesh intersections and isolated boundaries. The intersection-repair strategy presented here focuses on repairing the intersection in-place as opposed to re-discretizing the intersecting geometries. Combining robust, efficient methods of detecting intersections and then repairing intersecting geometries in-place produces a significant improvement over techniques used in current literature. The result of this intersection process is a non-manifold, non-intersecting geometry that is free of duplicate and degenerate geometry. Results are presented showing the accuracy and consistency of the intersection repair tool. Isolated boundaries are a type of gap that current research does not address directly. They are defined by discrete boundary edges that are unable to be paired with nearby discrete boundary edges in order to fill the existing gap. In this research the method of repair seeks to fill the gap by extruding the isolated boundary along a defined vector so that it is topologically adjacent to a nearby surface. The outcome of the repair process is that the isolated boundaries no longer exist because the gap has been filled. Results are presented showing the precision of the edge projection and the advantage of edge splitting in the repair of isolated boundaries
Surface Extraction from Neural Unsigned Distance Fields
We propose a method, named DualMesh-UDF, to extract a surface from unsigned
distance functions (UDFs), encoded by neural networks, or neural UDFs. Neural
UDFs are becoming increasingly popular for surface representation because of
their versatility in presenting surfaces with arbitrary topologies, as opposed
to the signed distance function that is limited to representing a closed
surface. However, the applications of neural UDFs are hindered by the notorious
difficulty in extracting the target surfaces they represent. Recent methods for
surface extraction from a neural UDF suffer from significant geometric errors
or topological artifacts due to two main difficulties: (1) A UDF does not
exhibit sign changes; and (2) A neural UDF typically has substantial
approximation errors. DualMesh-UDF addresses these two difficulties.
Specifically, given a neural UDF encoding a target surface to be
recovered, we first estimate the tangent planes of at a set of sample
points close to . Next, we organize these sample points into local
clusters, and for each local cluster, solve a linear least squares problem to
determine a final surface point. These surface points are then connected to
create the output mesh surface, which approximates the target surface. The
robust estimation of the tangent planes of the target surface and the
subsequent minimization problem constitute our core strategy, which contributes
to the favorable performance of DualMesh-UDF over other competing methods. To
efficiently implement this strategy, we employ an adaptive Octree. Within this
framework, we estimate the location of a surface point in each of the octree
cells identified as containing part of the target surface. Extensive
experiments show that our method outperforms existing methods in terms of
surface reconstruction quality while maintaining comparable computational
efficiency.Comment: ICCV 202
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