Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Mathematical morphology on complete semilattices and its applications to image processing
Fundamenta Informaticae - Special issue on mathematical morphology
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Fundamenta Informaticae - Special issue on mathematical morphology
Nonlinear PDEs and Numerical Algorithms for Modeling Levelings and Reconstruction Filters
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Inf-semilattice approach to self-dual morphology
Inf-semilattice approach to self-dual morphology
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
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This paper begins with analyzing the theoretical connections between levelings on lattices and scale-space erosions on reference semi-lattices. They both represent large classes of self-dual morphological operators that exhibit both local computation and global constraints. Such operators are useful in numerous image analysis and vision tasks ranging from simplification, to geometric feature detection, to segmentation. Previous definitions and constructions of levelings were either discrete or continuous using a PDE. We bridge this gap by introducing generalized levelings based on triphase operators that switch among three phases, one of which is a global constraint. The triphase operators include as special cases reference semilattice erosions. Algebraically, levelings are created as limits of iterated or multiscale triphase operators. The subclass of multiscale geodesic triphase operators obeys a semigroup, which we exploit to find a PDE that generates geodesic levelings. Further, we develop PDEs that can model and generate continuous-scale semilattice erosions, as a special case of the leveling PDE. We discuss theoretical aspects of these PDEs, propose discrete algorithms for their numerical solution which are proved to converge as iterations of triphase operators, and provide insights via image experiments.