A new approach to morphological color image processing

Louverdis, G.; Vardavoulia, Maria I.; Andreadis, Ioannis; Tsalides, Ph.

doi:10.1016/s0031-3203(01)00166-2

Cited by 92 publications

(49 citation statements)

References 6 publications

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“…These invaluable properties have led to the widespread use of lexicographical ordering with the purpose of establishing multivariate morphological operators, especially in the field of colour morphology [1,4,12,14,21].…”

Section: Lexicographical Orderingmentioning

confidence: 99%

“…As far as its theoretical properties are concerned, α-modulus lexicographical ordering, appears to be the most pertinent among the variations presented in section 2.3, as it provides an effective means of shifting priority away from the first vector dimension, while preserving the desirable characteristics of lexicographical ordering that have made it popular within the morphological context [1,4,12,14,21].…”

Section: Imagesmentioning

confidence: 99%

“…As a more concrete example, let us return to the aforementioned case of colour morphology in the HSL colour space. Polar colour spaces exhibit an inherent prioritisation of channels, as they model the higher levels of human colour vision, and thus luminance is most often used in the first position of the lexicographical cascade when developing morphological operators [1,4,14,19]. However, non trivial relations are present among the three channels (luminance, saturation and hue), that are totally ignored using expression (5).…”

Section: Imagesmentioning

confidence: 99%

See 2 more Smart Citations

On lexicographical ordering in multivariate mathematical morphology

Aptoula

Lefèvre

2008

Pattern Recognition Letters

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Since mathematical morphology is based on complete lattice theory, a vector ordering method becomes indispensable for its extension to multivariate images. Among the several approaches developed with this purpose, lexicographical orderings are by far the most frequent, as they possess certain desirable theoretical properties. However, their main drawback consists of the excessive priority attributed to the first vector dimension. In this paper, the existing solutions to solving this problem are recalled and two new approaches are presented. First, a generalisation of α-modulus lexicographical ordering is introduced, making it possible to accommodate any quantisation function. Additionally, an input specific method is suggested, based on the use of a marker image. Comparative application results on colour noise reduction and texture classification are also provided.

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Section: Lexicographical Orderingmentioning

confidence: 99%

Section: Imagesmentioning

confidence: 99%

Section: Imagesmentioning

confidence: 99%

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On lexicographical ordering in multivariate mathematical morphology

Aptoula

Lefèvre

2008

Pattern Recognition Letters

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“…The main difficulty of the application of morphological methods into color image processing lies in the required vector ordering scheme [3,79,80]. The definitions of the basic mathematical morphology operations were generalized in various ways, so that they can work on color images and can be applied for impulsive noise suppression [81][82][83][84][85][86].…”

Section: Introductionmentioning

confidence: 99%

Adaptive rank weighted switching filter for impulsive noise removal in color images

Smołka

Malik

2012

J Real-Time Image Proc

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In this paper, a novel approach to the problem of impulsive noise removal in color digital images is presented. The described switching filter is based on the rank weighted, cumulated pixel dissimilarity measures, which are used for the detection of image samples contaminated by impulsive noise process. The introduced adaptive design enables the filter to tune its parameters to the amount of impulsive noise corrupting the image. The comparison with existing denoising schemes shows that the new technique more efficiently removes the impulses introduced by the noise process, while better preserving image details. An important feature of the new filter is its low computational complexity, which allows for its application in real-time applications.

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“…[26,34,47,48,51], and conference proceedings, e.g. [21,22,27,32,53], bear testimony to the variety and the success of mathematical morphology. Recently, the fundamental morphological operations of dilation and erosion, and with it some other basic morphological operators, have been made available for matrix-valued data, matrix fields for short [11].…”

Section: Introductionmentioning

confidence: 99%

PDE-based Morphology for Matrix Fields: Numerical Solution Schemes

Burgeth

Breuß

Didas

et al. 2009

Tensors in Image Processing and Computer Vision

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Tensor fields are important in digital imaging and computer vision. Hence there is a demand for morphological operations to perform e.g. shape analysis, segmentation or enhancement procedures. Recently, fundamental morphological concepts have been transferred to the setting of fields of symmetric positive definite matrices, which are symmetric rank two tensors. This has been achieved by a matrixvalued extension of the nonlinear morphological partial differential equations (PDEs) for dilation and erosion known for grey scale images. Having these two basic operations at our disposal, more advanced morphological operators such as top hats or morphological derivatives for matrix fields with symmetric, positive semidefinite matrices can be constructed. The approach realises a proper coupling of the matrix channels rather than treating them independently. However, from the algorithmic side the usual scalar morphological PDEs are transport equations that require special upwind-schemes or novel high-accuracy predictor-corrector approaches for their adequate numerical treatment. In this chapter we propose the non-trivial extension of these schemes to the matrix-valued setting by exploiting the special algebraic structure available for symmetric matrices. Furthermore we compare the performance and juxtapose the results of these novel matrix-valued high-resolution-type (HRT) numerical schemes by considering top hats and morphological derivatives applied to artificial and real world data sets.

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A new approach to morphological color image processing

Cited by 92 publications

References 6 publications

On lexicographical ordering in multivariate mathematical morphology

On lexicographical ordering in multivariate mathematical morphology

Adaptive rank weighted switching filter for impulsive noise removal in color images

PDE-based Morphology for Matrix Fields: Numerical Solution Schemes

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