CVGIP: Image Understanding
Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
Journal of Mathematical Imaging and Vision
Connectivity on Complete Lattices
Journal of Mathematical Imaging and Vision
Connections for sets and functions
Fundamenta Informaticae - Special issue on mathematical morphology
Shape Connectivity: Multiscale Analysis and Application to Generalized Granulometries
Journal of Mathematical Imaging and Vision
Connectivity on complete lattices: new results
Computer Vision and Image Understanding
A multiscale approach to connectivity
Computer Vision and Image Understanding
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Grayscale level connectivity: theory and applications
IEEE Transactions on Image Processing
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
Object-Based Image Analysis Using Multiscale Connectivity
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiscale Connected Operators
Journal of Mathematical Imaging and Vision
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In a recent paper, we have proposed a novel theory that extends connectivity to a multiscale framework. Although we have presented several examples, we have not provided a systematic approach for constructing multiscale connectivities. In this paper, we introduce three general techniques for constructing multiscale connectivities. The first two start from a given base connectivity and produce multiscale connectivities by applying pyramids of clusterings or granulometries. The third technique starts from a given multiscale connectivity and constructs a new one by means of a clustering or an opening. Several examples illustrate the utility of the proposed techniques for constructing multiscale connectivities.