Locally adaptable mathematical morphology using distance transformations

Cuisenaire, O.

doi:10.1016/j.patcog.2005.07.009

Cited by 53 publications

(37 citation statements)

References 17 publications

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“…-positions in the image, as in Beucher et al (1987); Cuisenaire (2006); -local regularity including the morphological amoebas (Lerallut et al, 2007), adaptive geodesic neighborhoods (Grazzini and Soille, 2009), bilateral structuring function (Angulo, 2013), nonlocal structuring function (Velasco-Forero and Angulo, 2013);…”

Section: Motivation and Goalmentioning

confidence: 99%

Multiscale Image Analysis Based on Robust and Adaptive Morphological Scale-Spaces

Diop

Angulo

2014

Image Anal Stereol

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Mathematical morphology is a powerful tool for image analysis; however, classical morphological operators suffer from lacks of robustness against noise, and also intrinsic image features are not accounted at all in the process. We propose in this work a new and different way to overcome such limits, by introducing both robustness and locally adaptability in morphological operators, which are now defined in a manner such that intrinsic image features are accounted. Dealing with partial differential equations (PDEs) for generalized Cauchy problems, we show that proposed PDEs are equivalent to impose robustness and adaptability of corresponding sup-inf operators, to structuring functions. Accurate numerical schemes are also provided to solve proposed PDEs, and experiments conducted for both synthetic and real images, show the efficiency and robustness of our approach.

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Section: Motivation and Goalmentioning

confidence: 99%

Multiscale Image Analysis Based on Robust and Adaptive Morphological Scale-Spaces

Diop

Angulo

2014

Image Anal Stereol

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“…1 is straightforward, it is hard to develop an algorithm that calculates the DT quickly [7,25,[44][45][46][47]. In practice, the calculation of DT starts with the initialization of the algorithm.…”

Section: Distance Transformmentioning

confidence: 99%

“…[6][7][8]). Their work introduces a "zone of interest (ZOI)", a bounding box that limits the neighborhood in which calculations have to be executed.…”

Section: Patent Applicationsmentioning

confidence: 99%

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Distance Transforms: Academics Versus Industry

Broek

Schouten²

2011

CSENG

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Abstract:In image and video analysis, distance transformations (DT) are frequently used. They provide a distance image (DI) of background pixels to the nearest object pixel. DT touches upon the core of many applications; consequently, not only science but also industry has conducted a significant body of work in this field. However, in a vast majority of the cases this has not been published in major scientific outlets but has been filed as a patent application. This article provides a brief introduction into DT, including a specification of a few of the most prominent algorithms in the field. Next, a few interesting algorithms from the last decade are discussed. A benchmark including eight DT algorithms (i.e., city block, Danielsson's algorithm, chamfer 3-4, hexadecagonal region growing, a recent claimed true Euclidean DT, and three exact Euclidean DT) has been executed, which illustrates the intriguing complexity of DT in terms of precision and computational complexity. Subsequently, a selection of key patent applications are discussed that have emerged in this field, including their scientific merit and areas of application. Finally, this article's findings are summarized and discussed, with an emphasis on both the common ground of scientific articles and patent applications as well as the added value they can have to each other.

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“…-On the one hand, a variability on the support space E: spatially variable shape of structuring functions according to i) the geometric position in the image: perspective-adapted Morphology by Beucher et al (1987) and by Cuisenaire (2006), ii) the local regularity of image values: morphological amoebas by Lerallut et al (2005), intrinsic structuring elements by Debayle and Pinoli (2005) morphological bilateral filtering by Angulo (2011), iii) the orientation: curvilinear morphohessian filter by Tankyevych et al (2008), locally-variant anisotropic morphological filters by Verdu-Monedero et al (2011).…”

Section: Introductionmentioning

confidence: 99%

Structurally Adaptive Mathematical Morphology Based on Nonlinear Scale-Space Decompositions

Angulo¹,

Velasco-Forero²

2011

Image Anal Stereol

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Standard formulation of morphological operators is translation invariant in the space and in the intensity: the same processing is considered for each point of the image. A current challenging topic in mathematical morphology is the construction of adaptive operators. In previous works, the adaptive operators are based either on spatially variable neighbourhoods according to the local regularity, or on size variable neighbourhoods according to the local intensity. This paper introduces a new framework: the structurally adaptive mathematical morphology. More precisely, the rationale behind the present approach is to work on a nonlinear multi-scale image decomposition, and then to adapt intrinsically the size of the operator to the local scale of the structures. The properties of the derived operators are investigated and their practical performances are compared with respect to standard morphological operators using natural image examples.

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Locally adaptable mathematical morphology using distance transformations

Cited by 53 publications

References 17 publications

Multiscale Image Analysis Based on Robust and Adaptive Morphological Scale-Spaces

Multiscale Image Analysis Based on Robust and Adaptive Morphological Scale-Spaces

Distance Transforms: Academics Versus Industry

Structurally Adaptive Mathematical Morphology Based on Nonlinear Scale-Space Decompositions

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