Constraints on deformable models: recovering 3D shape and nongrid motion
Artificial Intelligence
Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
On Three-Dimensional Surface Reconstruction Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Fat surfaces: a trivariate approach to triangle-based interpolation on surfaces
Computer Aided Geometric Design
Modeling scattered function data on curved surfaces
Pacific Graphics '94 Proceedings of the second Pacific conference on Fundamentals of computer graphics
Surface Approximation and Geometric Partitions
SIAM Journal on Computing
An efficient algorithm for terrain simplification
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A constant factor approximation algorithm for a class of classification problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A simple algorithm for homeomorphic surface reconstruction
Proceedings of the sixteenth annual symposium on Computational geometry
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Approximation algorithms for the metric labeling problem via a new linear programming formulation
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Detecting undersampling in surface reconstruction
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
An efficient algorithm for image segmentation, Markov random fields and related problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Visualizing and Modeling Scattered Multivariate Data
IEEE Computer Graphics and Applications
The Pseudoflow Algorithm and the Pseudoflow-Based Simplex for the Maximum Flow Problem
Proceedings of the 6th International IPCO Conference on Integer Programming and Combinatorial Optimization
Image Segmentation with Monotonicity and Smoothness Constraints
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Instant Recognition of Half Integrality and 2-Approximations
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Space and Time Shape Constrained Deformable Surfaces for 4D Medical Image Segmentation
MICCAI '00 Proceedings of the Third International Conference on Medical Image Computing and Computer-Assisted Intervention
Segmentation by Grouping Junctions
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Markov Random Fields with Efficient Approximations
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Optimal Surface Segmentation in Volumetric Images-A Graph-Theoretic Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the twenty-fourth annual symposium on Computational geometry
Electric Field Theory Motivated Graph Construction for Optimal Medical Image Segmentation
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Graph search with appearance and shape information for 3-D prostate and bladder segmentation
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
Optimal graph based segmentation using flow lines with application to airway wall segmentation
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Efficient algorithms for segmenting globally optimal and smooth multi-surfaces
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Faster segmentation algorithm for optical coherence tomography images with guaranteed smoothness
MLMI'11 Proceedings of the Second international conference on Machine learning in medical imaging
Segmentation of the surfaces of the retinal layer from OCT images
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Simultaneous segmentation of multiple closed surfaces using optimal graph searching
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
The matrix orthogonal decomposition problem in intensity-modulated radiation therapy
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
The layered net surface problems in discrete geometry and medical image segmentation
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Lung tumor segmentation using electric flow lines for graph cuts
ICIAR'12 Proceedings of the 9th international conference on Image Analysis and Recognition - Volume Part II
A survey of graph theoretical approaches to image segmentation
Pattern Recognition
Bayesian segmentation of atrium wall using globally-optimal graph cuts on 3D meshes
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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In this paper, we study an interesting geometric graph called multi-column graph in the d-D space (d 驴 3), and formulate two combinatorial optimization problems called the optimal net surface problems on such graphs. Our formulations capture a number of important problems such as surface reconstruction with a given topology, medical image segmentation, and metric labeling. We prove that the optimal net surface problems on general d-D multicolumn graphs (d 驴 3) are NP-hard. For two useful special cases of these d-D (d 驴 3) optimal net surface problems (on the so-called proper ordered multi-column graphs) that often arise in applications, we present polynomial time algorithms. We further apply our algorithms to some surface reconstruction problems in 3-D and 4-D, and some medical image segmentation problems in 3-D and 4-D, obtaining polynomial time solutions for these problems. The previously best known algorithms for some of these applied problems, even for relatively simple cases, take at least exponential time. Our approaches for these applied problems can be extended to higher dimensions.