Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological methods in image and signal processing
Morphological methods in image and signal processing
A Representation Theory for Morphological Image and Signal Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
The analysis of morphological filters with multiple structuring elements
Computer Vision, Graphics, and Image Processing
Decomposition of gray-scale morphological structuring elements
Pattern Recognition
Separable decompositions and approximations of greyscale morphological templates
CVGIP: Image Understanding
Theoretical Aspects of Gray-Level Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
The algebraic basis of mathematical morphology
CVGIP: Image Understanding
The Geometry of Basis Sets for Morphologic Closing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Minimal representations for translation-invariant set mappings by mathematical morphology
SIAM Journal on Applied Mathematics
Pattern Recognition Letters
Pattern Recognition Letters
Morphological Filtering as Template Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological Filtering as Template Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
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The choice and detailed design of structuring elements plays a pivotal role in the morphologic processing of images. A broad class of morphological operations can be expressed as an equivalent supremum of erosions by a minimal set of basis filters. Diverse morphological operations can then be expressed in a single, comparable framework. The set of basis filters are data-like structures, each filter representing one type of local change possible under that operation. The data-level description of the basis set is a natural starting point for the design of morphological filters. This paper promotes the use of the basis decomposition of gray-scale morphological operations to design and apply morphological filters. A constructive proof is given for the basis decomposition of general gray-scale morphological operations, as are practical algorithms to find all of the basis set members for these operations.