A New Fuzzy Connectivity Measure for Fuzzy Sets

Nempont, Olivier; Atif, Jamal; Angelini, Elsa D.; Bloch, Isabelle

doi:10.1007/s10851-009-0136-3

Cited by 18 publications

(16 citation statements)

References 36 publications

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“…It was initially defined in [136], and then exploited in fuzzy connectedness notions [151], now widely used for instance in medical image segmentation and incorporated in freely available softwares such as ITK. 4 More general classes of fuzzy connectivity have later been developed, with again applications in medical imaging [44,115,124]. Using both topology and metrics, the notion of skeleton and medial axis was also extended to fuzzy sets [84,102,118,123].…”

Section: Intermediate Levelmentioning

confidence: 99%

Fuzzy sets for image processing and understanding

Bloch

2015

Fuzzy Sets and Systems

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Section: Intermediate Levelmentioning

confidence: 99%

Fuzzy sets for image processing and understanding

Bloch

2015

Fuzzy Sets and Systems

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“…In [20], the authors presented a specific type of h-connection and proposed the notion of segmentation by similarity zones (further developed in [21]). The work in [22] defined a new hconnection based on the theory of fuzzy connectivity measures and developed the notion of fuzzy attribute filtering. In [23] and [24], the authors proposed to modify the reconstruction step of the traditional attribute filter with the Max-Tree by using a specific h-connection called the k-flat zones.…”

Section: Related Workmentioning

confidence: 99%

“…These theoretical developments are illustrated by their application on a fuzzy h-connection recently proposed in [22]. Our new approach allows us to represent the different fuzzy h-connected components of an image in a single tree structure.…”

Section: Contributionsmentioning

confidence: 99%

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Hyperconnections and Hierarchical Representations for Grayscale and Multiband Image Processing

Perret

Lefèvre

Collet

et al. 2012

IEEE Trans. on Image Process.

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Connections in image processing are an important notion that describes how pixels can be grouped together according to their spatial relationships and/or their gray-level values. In recent years, several works were devoted to the development of new theories of connections among which hyperconnection (h-connection) is a very promising notion. This paper addresses two major issues of this theory. First, we propose a new axiomatic that ensures that every h-connection generates decompositions that are consistent for image processing and, more precisely, for the design of h-connected filters. Second, we develop a general framework to represent the decomposition of an image into h-connections as a tree that corresponds to the generalization of the connected component tree. Such trees are indeed an efficient and intuitive way to design attribute filters or to perform detection tasks based on qualitative or quantitative attributes. These theoretical developments are applied to a particular fuzzy h-connection, and we test this new framework on several classical applications in image processing, i.e., segmentation, connected filtering, and document image binarization. The experiments confirm the suitability of the proposed approach: It is robust to noise, and it provides an efficient framework to design selective filters.

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“…In this paper, the theory is extended to the compete lattice framework, and the infinite case. The new theory provides deeper understanding of hyperconnectivity, and provides a theoretical basis for grey-scale hyperconnected filters such as those developed in [5,4]. I will first define some basic notions and notation, and then recall the theory of connectivity classes or connections, as developed by Serra in the complete lattice case [8].…”

Section: Introductionmentioning

confidence: 99%

Hyperconnections and Openings on Complete Lattices

Wilkinson

2011

Mathematical Morphology and Its Applications to Image and Signal Processing

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Abstract. In this paper the notion of hyperconnectivity, which is an extension of connectivity is explored in the lattice theoretical framework. It is shown that a fourth axiom is needed when moving from connections to hyperconnections, in order to define hyperconnected components meaningfully, which is important for the definition of, e.g., viscous levellings. New hyperconnectivity openings, which are the hyperconnected equivalents of connectivity openings are then defined. It then shown that all algebraic openings which are translation and grey-scale invariant can be described as hyperconnected attribute filters. This means that hyperconnectivity lies at the heart of a vast range of morphological filters.

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A New Fuzzy Connectivity Measure for Fuzzy Sets

Cited by 18 publications

References 36 publications

Fuzzy sets for image processing and understanding

Fuzzy sets for image processing and understanding

Hyperconnections and Hierarchical Representations for Grayscale and Multiband Image Processing

Hyperconnections and Openings on Complete Lattices

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