Pattern Spectrum and Multiscale Shape Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Connected morphological operators for binary images
Computer Vision and Image Understanding
Connections for sets and functions
Fundamenta Informaticae - Special issue on mathematical morphology
Connectivity on complete lattices: new results
Computer Vision and Image Understanding
A Theoretical Tour of Connectivity in Image Processing and Analysis
Journal of Mathematical Imaging and Vision
Geodesy and connectivity in lattices
Fundamenta Informaticae
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Antiextensive connected operators for image and sequence processing
IEEE Transactions on Image Processing
A Theoretical Tour of Connectivity in Image Processing and Analysis
Journal of Mathematical Imaging and Vision
Object-Based Image Analysis Using Multiscale Connectivity
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiscale Connected Operators
Journal of Mathematical Imaging and Vision
Constructing multiscale connectivities
Computer Vision and Image Understanding
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Attribute-space connectivity and connected filters
Image and Vision Computing
The Strong Property of Morphological Connected Alternated Filters
Journal of Mathematical Imaging and Vision
A New Fuzzy Connectivity Measure for Fuzzy Sets
Journal of Mathematical Imaging and Vision
Constructing multiscale connectivities
Computer Vision and Image Understanding
Adjacency stable connected operators and set levelings
Image and Vision Computing
Hyperconnections and openings on complete lattices
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Component-hypertrees for image segmentation
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
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The concept of connectivity is fundamental in image analysis and computer vision problems, and particularly in problems of image segmentation and object detection. In this paper, we introduce a novel theory of connectivity, which considers traditional concepts in a multiscale framework. The proposed theory includes, as a single-scale special case, the notion of connectivity classes in complete lattices. Following mathematical preliminaries, we introduce multiscale connectivity by means of two alternative, but equivalent, approaches. The first approach is based on the notion of a connectivity measure, which quantifies the degree of connectivity of a given object, whereas the second approach is based on the notion of a connectivity pyramid. We also introduce the notion of σ-connectivity openings and show that these operators define multiscale connectivities. Moreover. we introduce the notion of σ-reconstruction operators and show that, under certain conditions, these operators define multiscale connectivities as well. Based on the proposed theory, we show that fuzzy topological and fuzzy graph-theoretic connectivities are multiscale analogs of the classical notions of topological and graph-theoretic connectivity, respectively. We also discuss a generalization of the proposed multiscale connectivity concept which leads to the notion of multiscale level connectivity for grayscale images. Examples illustrate several key points of our approach.