Optimal Morphological Pattern Restoration from Noisy Binary Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Theoretical aspects of morphological filters by reconstruction
Signal Processing
Optimal Binary Morphological Bandpass Filters Induced byGranulometric Spectral Representation
Journal of Mathematical Imaging and Vision
Optimal and adaptive reconstructive granulometric bandpass filters
Signal Processing
Secondarily constrained Boolean filters
Signal Processing
Multiresolution Analysis for Optimal Binary Filters
Journal of Mathematical Imaging and Vision
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
Automatic Programming of Morphological Machines by PAC Learning
Fundamenta Informaticae
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This paper examines binary filter design by jointly applying multiresolution design and envelope constraint. In multiresolution design, the value of the designed filter for a configuration is defined at a resolution sufficiently low to have observed the configuration. Preference is given to higher resolutions, but the number of training observations is taken into account. In envelope design, the designed filter is constrained to lie in the envelope between two humanly designed filters. For small samples, the envelope-designed filter has the benefit of being in accord with expert knowledge, whereas for large samples statistical training provides more accurate filter design. To obtain the advantages of both approaches, they can be applied in combination. This can be done in more than a single way. This paper explores joint multiresolution-envelope design, extends the basic propositions for envelope design to the multiresolution setting, considers design consistency, and provides experimental support for the joint approach.