Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
New methods to color the vertices of a graph
Communications of the ACM
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Level Set Evolution without Re-Initialization: A New Variational Formulation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Coupled Parametric Active Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
Level set analysis for leukocyte detection and tracking
IEEE Transactions on Image Processing
Segmenting and tracking fluorescent cells in dynamic 3-D microscopy with coupled active surfaces
IEEE Transactions on Image Processing
Cell Spreading Analysis with Directed Edge Profile-Guided Level Set Active Contours
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
Four-Color Theorem and Level Set Methods for Watershed Segmentation
International Journal of Computer Vision
Segmentation and Classification of Cell Cycle Phases in Fluorescence Imaging
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
Accurate spatial neighborhood relationships for arbitrarily-shaped objects using Hamilton-Jacobi GVD
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Moving object segmentation using the flux tensor for biological video microscopy
PCM'07 Proceedings of the multimedia 8th Pacific Rim conference on Advances in multimedia information processing
Fast graph partitioning active contours for image segmentation using histograms
Journal on Image and Video Processing
Multiphase level set for automated delineation of membrane-bound macromolecules
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Fast globally optimal segmentation of cells in fluorescence microscopy images
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Robust tracking of migrating cells using four-color level set segmentation
ACIVS'06 Proceedings of the 8th international conference on Advanced Concepts For Intelligent Vision Systems
Learning to detect cells using non-overlapping extremal regions
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Hierarchical partial matching and segmentation of interacting cells
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
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Current level-set based approaches for segmenting a large number of objects are computationally expensive since they require a unique level set per object (the N-level set paradigm), or $\lceil\text{log}_2 N\rceil$ level sets when using a multiphase interface tracking formulation. Incorporating energy-based coupling constraints to control the topological interactions between level sets further increases the computational cost to O(N2). We propose a new approach, with dramatic computational savings, that requires only four, or fewer, level sets for an arbitrary number of similar objects (like cells) using the Delaunay graph to capture spatial relationships. Even more significantly, the coupling constraints (energy-based and topological) are incorporated using just constant O(1) complexity. The explicit topological coupling constraint, based on predicting contour collisions between adjacent level sets, is developed to further prevent false merging or absorption of neighboring cells, and also reduce fragmentation during level set evolution. The proposed four-color level set algorithm is used to efficiently and accurately segment hundreds of individual epithelial cells within a moving monolayer sheet from time-lapse images of in vitro wound healing without any false merging of cells.