Spatially-variant mathematical morphology

Charif-Chefchaouni, M.; Schonfeld, Dan

doi:10.1109/icip.1994.413632

Cited by 21 publications

(21 citation statements)

References 12 publications

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“…The mathematical morphology operators defined in this paper have strong links with previous works by Charif-Chefchaouni [10] and Roerdink [5,9], as discussed hereafter.…”

Section: Discussionmentioning

confidence: 79%

“…For the more intuitive operators defined here, one needs to swap θ and θ in equations (53) and (54). Nevertheless, all properties proved in [10] also hold for the operators of this paper.…”

Section: Link With Charif-chefchaouni's Workmentioning

confidence: 94%

“…In [10], Charif-Chefchaouni and Schonfeld propose a general framework for spatially varying mathematical morphology. The structuring element around a pixel p is the set θ(p) and the spatially-varying erosion ε θ , dilation δ θ , opening Γ θ and closing Φ θ are defined as…”

Section: Link With Charif-chefchaouni's Workmentioning

confidence: 99%

“…Finally, Charif-Chefchaouni and Schonfeld [10] propose a comprehensive theory of spatially-variant binary mathematical morphology where the structuring elements can vary both in size and shape. While they prove important theoretical properties of these operators, they offer no efficient way to implement them.…”

Section: Introductionmentioning

confidence: 99%

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Locally adaptable mathematical morphology using distance transformations

Cuisenaire

2006

Pattern Recognition

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We investigate how common binary mathematical morphology operators can be adapted so that the size of the structuring element can vary across the image pixels.We show that when the structuring elements are balls of a metric, locally adaptable erosion and dilation can be efficiently implemented as a variant of distance transformation algorithms. Opening and closing are obtained by a local threshold of a distance transformation, followed by the adaptable dilation.

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“…The mathematical morphology operators defined in this paper have strong links with previous works by Charif-Chefchaouni [10] and Roerdink [5,9], as discussed hereafter.…”

Section: Discussionmentioning

confidence: 79%

Section: Link With Charif-chefchaouni's Workmentioning

confidence: 94%

Section: Link With Charif-chefchaouni's Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Locally adaptable mathematical morphology using distance transformations

Cuisenaire

2006

Pattern Recognition

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“…Serra defined the concept of a structuring function, which associates to each point in the space a structuring element. Charif-Chefchaouni and Schonfeld [34], [35] pursued the investigation of SV mathematical morphology in a systematic way. They introduced the basic SV morphological operators and investigated their properties.…”

mentioning

confidence: 99%

Spatially Variant Morphological Restoration and Skeleton Representation

Bouaynaya

Charif-Chefchaouni

Schonfeld

2006

IEEE Trans. on Image Process.

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Abstract-The theory of spatially variant (SV) mathematical morphology is used to extend and analyze two important image processing applications: morphological image restoration and skeleton representation of binary images. For morphological image restoration, we propose the SV alternating sequential filters and SV median filters. We establish the relation of SV median filters to the basic SV morphological operators (i.e., SV erosions and SV dilations). For skeleton representation, we present a general framework for the SV morphological skeleton representation of binary images. We study the properties of the SV morphological skeleton representation and derive conditions for its invertibility. We also develop an algorithm for the implementation of the SV morphological skeleton representation of binary images. The latter algorithm is based on the optimal construction of the SV structuring element mapping designed to minimize the cardinality of the SV morphological skeleton representation. Experimental results show the dramatic improvement in the performance of the SV morphological restoration and SV morphological skeleton representation algorithms in comparison to their translation-invariant counterparts.

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