Topology-controlled Reconstruction of Multi-labelled Domains from Cross-sections

ACM Transactions on Graphics (Proc. ACM Siggraph 2017)
Zhiyang Huang*, Ming Zou*, Nathan Carr^, Tao Ju*
*Washington University in St. Louis,  ^Adobe


Teaser: Given several multi-labeled planes depicting the anatomical regions of a mouse brain (a), reconstruction without topology control (b1) leads to redundant handles for the red and yellow labels (black arrows in c1, d1) and disconnection for the green label (e1). Our method (b2) allows the user to prescribe the topology such that the red label has one tunnel (gray arrow in c2), the yellow label has no tunnels (d2), and the green label is connected (e2). The legends in (b1,b2) report, for each label in the reconstruction, the genus of each surface component bounding that label (e.g., “0,0” means two surfaces each with genus 0). User-specified constraints are colored red.


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.



 author = {Huang, Zhiyang and Zou, Ming and Carr, Nathan and Ju, Tao},
 title = {Topology-controlled Reconstruction of Multi-labelled Domains from Cross-sections},
 journal = {ACM Trans. Graph.},
 issue_date = {July 2017},
 volume = {36},
 number = {4},
 month = jul,
 year = {2017},
 issn = {0730-0301},
 pages = {76:1--76:12},
 articleno = {76},
 numpages = {12},
 url = {},
 doi = {10.1145/3072959.3073644},
 acmid = {3073644},
 publisher = {ACM},
 address = {New York, NY, USA},
 keywords = {contour interpolation, material interfaces, surface reconstruction, topology},

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