Topology-controlled Reconstruction of Multi-labelled Domains from Cross-sections
SIGGRAPH 2017, ACM Transactions on Graphics
Zhiyang Huang, Ming Zou, Nathan Carr, Tao Ju
In this work we present the first algorithm for reconstructing multi-labeled material interfaces the allows for explicit topology control. Our algorithm takes in a set of 2D cross-sectional slices (not necessarily parallel), each partitioned by a curve network into labeled regions representing different material types. For each label, the user has the option to constrain the number of connected components and genus. Our algorithm is able to not only produce a material interface that interpolates the curve networks but also simultaneously satisfy the topological requirements. Our key innovation is defining a space of topology-varying material interfaces, which extends the family of level sets in a scalar function, and developing discrete methods for sampling distinct topologies in this space. Besides specifying topological constraints, the user can steer the algorithm interactively, such as by scribbling. We demonstrate, on synthetic and biological shapes, how our algorithm opens up new opportunities for topology-aware modeling in the multi-labeled context.
Topology-Constrained Surface Reconstruction From Cross-sections
SIGGRAPH 2015, ACM Transactions on Graphics
Ming Zou, Michelle Holloway, Nathan Carr, Tao Ju
In this work we detail the first algorithm that provides topological control during surface reconstruction from an input set of planar cross-sections. Our work has broad application in a number of fields including surface modeling and biomedical image analysis, where surfaces of known topology must be recovered. Given curves on arbitrarily oriented cross-sections, our method produces a manifold interpolating surface that exactly matches a user-specified genus. The key insight behind our approach is to formulate the topological search as a divide-and-conquer optimization process which scores local sets of topologies and combines them to satisfy the global topology constraint. We further extend our method to allow image data to guide the topological search, achieving even better results than relying on the curves alone. By simultaneously satisfying both geometric and topological constraints, we are able to produce accurate reconstructions with fewer input cross-sections, hence reducing the manual time needed to extract the desired shape.
Anisotropic geodesics for live-wire mesh segmentation
Pacific Graphics 2014, Computer Graphics Forum
Yixin Zhuang, Ming Zou, Nathan Carr, Tao Ju
We present an interactive method for mesh segmentation that is inspired by the classical live-wire interaction for image segmentation. The core contribution of the work is the definition and computation of wires on surfaces that are likely to lie at segment boundaries. We define wires as geodesics in a new tensor-based anisotropic metric, which improves upon previous metrics in stability and feature-awareness. We further introduce a simple but effective mesh embedding approach that allows geodesic paths in an anisotropic path to be computed efficiently using existing algorithms designed for Euclidean geodesics. Our tool is particularly suited for delineating segmentation boundaries that are aligned with features or curvature directions, and we demonstrate its use in creating artist-guided segmentations.
An Algorithm for Triangulating Multiple 3D Polygons
Eurographics Symposium on Geometry Processing (SGP) 2013, Computer Graphics Forum
Ming Zou, Tao Ju, Nathan Carr
We present an algorithm for obtaining a triangulation of multiple, non-planar 3D polygons.
The output minimizes additive weights, such as the total triangle areas or the total dihedral angles between adjacent triangles.
Our algorithm generalizes a classical method for optimally triangulating a single polygon.
The key novelty is a mechanism for avoiding non-manifold outputs for two and more input polygons without compromising optimality.
For better performance on real-world data, we also propose an approximate solution by feeding the algorithm with a reduced set of triangles.
In particular, we demonstrate experimentally that the triangles in the Delaunay tetrahedralization of
the polygon vertices offer a reasonable trade off between performance and optimality.
A general and efficient method for finding cycles in 3D curve networks
SIGGRAPH Asia 2013, ACM Transactions on Graphics
Yixin Zhuang, Ming Zou, Nathan Carr, Tao Ju
Generating surfaces from 3D curve networks has been a longstanding problem in computer graphics.
Recent attention to this area has resurfaced as a result of new sketch based modeling systems.
In this work we present a new algorithm for finding cycles that bound surface patches.
Unlike prior art in this area, the output of our technique is unrestricted,
generating both manifold and non-manifold geometry with arbitrary genus.
The novel insight behind our method is to formulate our problem as finding local mappings at the vertices and curves of our network,
where each mapping describes how incident curves are grouped into cycles.
This approach lends us the efficiency necessary to present our system in an interactive design modeler,
whereby the user can adjust patch constraints and change the manifold properties of
curves while the system automatically re-optimizes the solution.
Automatic Landmark Mapping Using Subdivision Meshes
Landmarks are very important in medical studies on bones.
In a typical comparison experiment on bones, researchers usually need to repeatedly identify landmarks for hundreds of similar bones,
which could take hours of a well-trained expert.
This project aims at replacing this repetitive labor work with an automatic landmark generation procedure by applying computational geometry methods.
Given a standard bone and a set of surface landmarks, our algorithm automatically generates a corresponding set of surface landmarks on another bone.
We have been using this algorithm processing bio-medical data for
School of Medicine of WUSTL.
This work is based on a previous work of Prof. Tao Ju
and Dr. Lu Liu,
about using subdivision meshes as deformable atlases [Paper Link].
If you are interested, please contact Prof. Tao Ju for more information.