Spatially-Variant Mathematical Morphology

Charif-Chefchaouni, M.; Schonfeld, Dan

doi:10.1007/978-1-4613-0469-2_7

Cited by 3 publications

(3 citation statements)

References 4 publications

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“…For example, setting w ij = log(1 B j (i)) with B j a set representing a structuring element at pixel j, we get the usual flat dilation and erosion. If the family (B j ) 1≤j≤n is not translation invariant, we get the so called adaptive morphology framework [6,7,15,26]; if B j is not a spatial neighborhood of j, we get the typical nonlocal operators [23,30]. In general, the formulation of Equation ( 8) defines non-flat, adaptive and possibly non-local morphological operators, and the structuring function at each pixel j is contained in the j-th column of matrix W , that we will note W •j .…”

Section: Morphological Operatorsmentioning

confidence: 99%

“…The need to analyze and filter shapes without corrupting them naturally gave rise to the so called adaptive or spatially variant mathematical morphology [6,7,15,26], in which structuring elements could vary in space so as to adapt to the local structures of the images being processed. This framework was applied to design edge-preserving filters in general [9,10,18,33], but also showed to be particularly relevant to the processing of thin anisotropic objects in images [29,32], such as vessels, fibers or roads in satellite images.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Anisotropic Morphological Filtering Based on Co-Circularity of Local Orientations

Blusseau¹,

Velasco-Forero²,

Angulo³

et al. 2022

Image Processing on Line

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The algorithm presented in this paper is an application of a general framework for morphological processing of signals on weighted graphs. Here we apply it to images by defining what we call a co-circularity graph. In this graph, the vertices are the pixels and the weighted edges depend on a consistency criterion (co-circularity) between local orientations estimated from the structure tensors. This graph induces anisotropic adaptive morphological operators which are related both to anisotropic diffusion in images and path optimality in graphs. We present several applications such as the enhancement of fiber-like structures, completion of interrupted edges and the regularization of grayscale images. We also discuss the parameters setting depending on the application. Source CodeThe reviewed source code and documentation for this algorithm are available from the web page of this article 1 . Compilation and usage instructions are included in the README.txt file of the archive.

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Section: Morphological Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive Anisotropic Morphological Filtering Based on Co-Circularity of Local Orientations

Blusseau¹,

Velasco-Forero²,

Angulo³

et al. 2022

Image Processing on Line

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“…Spatially-variant morphology has been addressed afterwards by Banon and Barrera in [3] where they proposed a kernel representation as well as by Charif-Chefchaouni and Schonfeld [4], moreover a minimal basis representation has been pursued in [3,5]. Applications based on spatiallyvariant morphology can be found e.g.…”

Section: Introductionmentioning

confidence: 98%

Comparison of orientated and spatially variant morphological filters vs mean/median filters for adaptive image denoising

Verdú‐Monedero

Angulo²,

Larrey-Ruiz

et al. 2010

2010 IEEE International Conference on Image Processing

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Presentation available at http://www.tic.upct.es/rafael.verdu/slides/slides2010icip.pdf
ISBN: 978-142447994-8International audienceThis paper shows a comparison of spatially-variant discrete operators for denoising gray-level images. These non-iterative operators use a neighborhood that varies over space, adapting their shape and orientation according to the data of the image under study. The orientation of the neighborhood is computed by means of a diffusion process of the average square gradient field, which regularizes and extends the orientation information from the edges of the objects to the homogeneous areas of the image; and the shape of the orientated neighborhood can be either a linear segment or a rectangle of anisotropy given by the distance to relevant edges of the objects. Results on gray-level images show the ability of spatially-variant morphological operators for adaptively preserving the main structures in the image while reducing the noise

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Anisotropic Morphological Filters With Spatially-Variant Structuring Elements Based on Image-Dependent Gradient Fields

Verd-Monedero

Angulo

Serra

2011

IEEE Trans. on Image Process.

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This paper deals with the theory and applications of spatially-variant discrete mathematical morphology. We review and formalize the definition of spatially variant dilation/erosion and opening/closing for binary and gray-level images using exclusively the structuring function, without resorting to complement. This theoretical framework allows to build morphological operators whose structuring elements can locally adapt their shape and orientation across the dominant direction of the structures in the image. The shape and orientation of the structuring element at each pixel are extracted from the image under study: the orientation is given by means of a diffusion process of the average square gradient field, which regularizes and extends the orientation information from the edges of the objects to the homogeneous areas of the image; and the shape of the orientated structuring elements can be linear or it can be given by the distance to relevant edges of the objects. The proposed filters are used on binary and gray-level images for enhancement of anisotropic features such as coherent, flow-like structures. Results of spatially-variant erosions/dilations and openings/closings-based filters prove the validity of this theoretical sound and novel approach.

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Spatially-Variant Mathematical Morphology

Cited by 3 publications

References 4 publications

Adaptive Anisotropic Morphological Filtering Based on Co-Circularity of Local Orientations

Adaptive Anisotropic Morphological Filtering Based on Co-Circularity of Local Orientations

Comparison of orientated and spatially variant morphological filters vs mean/median filters for adaptive image denoising

Anisotropic Morphological Filters With Spatially-Variant Structuring Elements Based on Image-Dependent Gradient Fields

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