Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Level Set Methods and Image Segmentation
MIAR '01 Proceedings of the International Workshop on Medical Imaging and Augmented Reality (MIAR '01)
Handbook of Biomedical Image Analysis: Volume 3: Registration Models (International Topics in Biomedical Engineering)
A visual pathway for shape-based invariant classification of gray scale images
Integrated Computer-Aided Engineering - Artificial Neural Networks
Integrated Computer-Aided Engineering
View invariant head recognition by Hybrid PCA based reconstruction
Integrated Computer-Aided Engineering
Topological derivative: A tool for image processing
Computers and Structures
Shape-Based Level Set Method for Image Segmentation
HIS '09 Proceedings of the 2009 Ninth International Conference on Hybrid Intelligent Systems - Volume 01
Solving the Chan-Vese model by a multiphase level set algorithm based on the topological derivative
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
An incremental-encoding evolutionary algorithm for color reduction in images
Integrated Computer-Aided Engineering
Distance regularized level set evolution and its application to image segmentation
IEEE Transactions on Image Processing
Teeth segmentation in digitized dental X-ray films using mathematical morphology
IEEE Transactions on Information Forensics and Security
Shape recovery algorithms using level sets in 2-D/3-D medical imagery: a state-of-the-art review
IEEE Transactions on Information Technology in Biomedicine
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
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In this paper we propose a segmentation approach that applies the topological derivative as a pre-processing step. The obtained result is used for initializing a Level Set model in order to get the final result. First, the method uses a low-pass filter and the topological derivative to get a rough definition of the boundaries of interest. Then, morphological operators are applied to fill holes and discard artifacts. Next, a Level Set model is used to improve the result giving the desired approximation. We test the pipeline for cell image segmentation. Finally, we provide a full mathematical justification for the topological asymptotic expansion.