Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Watershed of a continuous function
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Topographic distance and watershed lines
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Unsupervised cell nucleus segmentation with active contours
Signal Processing - Special issue on deformable models and techniques for image and signal processing
Digital Image Processing
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
International Journal of Computer Vision
Watersnakes: Energy-Driven Watershed Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Active Contour Model for Segmentation Based on Cubic B-splines and Gradient Vector Flow
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Energy Partitions and Image Segmentation
Journal of Mathematical Imaging and Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Journal of Computational Physics
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
Journal of Mathematical Imaging and Vision
An improved watershed algorithm based on efficient computation of shortest paths
Pattern Recognition
An efficient immersion-based watershed transform method and its prototype architecture
Journal of Systems Architecture: the EUROMICRO Journal
A piecewise constant level set method for elliptic inverse problems
Applied Numerical Mathematics
Level set methods for watershed image segmentation
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Cell segmentation using coupled level sets and graph-vertex coloring
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Energy minimization based segmentation and denoising using a multilayer level set approach
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Spatially adaptive wavelet thresholding with context modeling for image denoising
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Segmenting and tracking fluorescent cells in dynamic 3-D microscopy with coupled active surfaces
IEEE Transactions on Image Processing
A binary level set model and some applications to Mumford-Shah image segmentation
IEEE Transactions on Image Processing
High-throughput analysis of multispectral images of breast cancer tissue
IEEE Transactions on Image Processing
Predictive watershed: a fast watershed algorithm for video segmentation
IEEE Transactions on Circuits and Systems for Video Technology
Geometric attraction-driven flow for image segmentation and boundary detection
Journal of Visual Communication and Image Representation
ECM-aware cell-graph mining for bone tissue modeling and classification
Data Mining and Knowledge Discovery
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A marker-controlled and regularized watershed segmentation is proposed for cell segmentation. Only a few previous studies address the task of regularizing the obtained watershed lines from the traditional marker-controlled watershed segmentation. In the present formulation, the topographical distance function is applied in a level set formulation to perform the segmentation, and the regularization is easily accomplished by regularizing the level set functions. Based on the well-known Four-Color theorem, a mathematical model is developed for the proposed ideas. With this model, it is possible to segment any 2D image with arbitrary number of phases with as few as one or two level set functions. The algorithm has been tested on real 2D fluorescence microscopy images displaying rat cancer cells, and the algorithm has also been compared to a standard watershed segmentation as it is implemented in MATLAB. For a fixed set of markers and a set of challenging images, the comparison of these two methods shows that the present level set formulation performs better than a standard watershed segmentation.