Minimal representations for translation-invariant set mappings by mathematical morphology
SIAM Journal on Applied Mathematics
Optimal mean-square N-observation digital morphological filters: i. optimal binary filters
CVGIP: Image Understanding
Model-based morphology: the opening spectrum
Graphical Models and Image Processing
Optimal Binary Morphological Bandpass Filters Induced byGranulometric Spectral Representation
Journal of Mathematical Imaging and Vision
| Hi-index | 0.00 |
A classical single-parameter τ-opening is a union ofopenings in which each structuring element is scaled by the sameparameter. Multiparameter binary τ-openings generalize themodel in two ways: first, parameters for each opening areindividually defined; second, a structuring element can beparameterized relative to its overall shape, not merely sized. The reconstructive filter corresponding to an opening is defined byfully passing any grain (connected component) that is not fullyeliminated by the opening and deleting all other grains. Adaptivedesign results from treating the parameter vector of a reconstructivemultiparameter τ-opening as the state space of a Markov chain.Signal and noise are modeled as unions of randomly parameterized andrandomly translated primary grains, and the parameter vector istransitioned depending on whether an observed grain is correctly orincorrectly passed. Various adaptive models are considered,transition probabilities are discussed, the state-probabilityincrement equations are deduced from the appropriateChapman-Kolmogorov equations, and convergence of the adaptation ischaracterized by the steady-state distribution relating to the Markovchain.