Visual reconstruction
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Hierarchy in Picture Segmentation: A Stepwise Optimization Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Integrating Region Growing and Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
On active contour models and balloons
CVGIP: Image Understanding
Variational methods in image segmentation
Variational methods in image segmentation
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Study of a Convex Variational Diffusion Approach for Image Segmentation and Feature Extraction
Journal of Mathematical Imaging and Vision
Game-Theoretic Integration for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Markov Pixon Information Approach for Low-Level Image Description
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Cooperative Robust Estimation Using Layers of Support
IEEE Transactions on Pattern Analysis and Machine Intelligence
Coupled Geodesic Active Regions for Image Segmentation: A Level Set Approach
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Calibrating Parameters of Cost Functionals
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Globally Optimal Regions and Boundaries
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
A Level Line Selection Approach for Object Boundary Estimation
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Bayesian Object Detection through Level Curves Selection
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
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We propose a variational framework for determining global minimizers of rough energy functionals used in image segmentation. Segmentation is achieved by minimizing an energy model, which is comprised of two parts: the first part is the interaction between the observed data and the model, the second is a regularity term. The optimal boundaries are the set of curves that globally minimize the energy functional. Our motivation comes from the observation that energy functionals are traditionally complex, for which it is usually difficult to precise global minimizers corresponding to "best" segmentations. Therefore, we focus on basic energy models, which global minimizers can be explicitly determined. In this paper, we prove that the set of curves that minimizes the image moment-based energy functionals is a family of level lines, i.e. the boundaries of level sets (connected components) of the image. For the completeness of the paper, we present a non-iterative algorithm for computing partitions with connected components. It leads to a sound initialization-free algorithm without any hidden parameter to be tuned.