Set Operator Decomposition and Conditionally Translation Invariant Elementary Operators

Banon, Gerald Jean Francis; Barrera, Júnior

doi:10.1007/978-94-011-1040-2_2

Cited by 2 publications

(2 citation statements)

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“…The mathematical morphology [7,8,9] refers to nonlinear processing and analysis of geometric structures of images. Morphology is based on the study of decompositions of operators between complete lattices in terms of two classes of elementary operators known as erosion and dilation [10]. The language of mathematical morphology is "set theory", where the sets represent the shapes in an image [11].…”

Section: Mathematical Morphologymentioning

confidence: 99%

An Approach to Extracting Facade Features Using the Intensity Value of Terrestrial Laser Scanner with Mathematical Morphology

Soria-Medina¹,

Martínez²,

Buffara-Antunes³

et al. 2011

28th International Symposium on Automation and Robotics in Construction (ISARC 2011)

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Nowadays, Terrestrial Laser Scanner (TLS) is a crucial device in order to acquire geographical data easily. In recent years, advances in accuracy and velocity have enhanced 3D models, but these stand-alone data do not provide the feature extraction. High density point clouds can be obtained with terrestrial laser scanner and by means of modelling and processing techniques, objects features can be constructed. Generally researchers use the geometric information for extracting object characteristics. This paper describes a methodology to use not only the geometrical information but also the intensity data provided during the scan process. The aim of this paper is to present a methodology to extract façades from laser scanner data. The proposed method uses mathematical morphology to classify, segment and extract the borders of principal features of the building "Quiñones de León country mansion" in the city of Vigo, Galicia, Spain. Furthermore, the final result shows huge potential of the intensity data solution to extract the main features of façades and together with the K-means algorithm for segmentation and mathematical morphology operators. It suggests keeping the effort going on combining them as successful tools employed for feature extraction of historical buildings.

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Section: Mathematical Morphologymentioning

confidence: 99%

An Approach to Extracting Facade Features Using the Intensity Value of Terrestrial Laser Scanner with Mathematical Morphology

Soria-Medina¹,

Martínez²,

Buffara-Antunes³

et al. 2011

28th International Symposium on Automation and Robotics in Construction (ISARC 2011)

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“…We know (see [1]) that δ a and are, respectively, a dilation and an erosion, a and b being their respective structuring functions. When applying these operators to an image we get two expanded images as shown in Figure 1.…”

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confidence: 99%

New Insight on Digital Topology

Banon

Mathematical Morphology and Its Applications to Image and Signal Processing

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Abstract. The traditional approach of digital topology consists of using two different kinds of neighborhood for the black and white pixels of a binary image, and consequently two kinds of connectedness. In this paper, we are proposing to define connectedness in terms of a bounded subcollection of sets and to analyze the topological aspect of a binary image in an expanded domain in which it is sufficient to consider only one kind of connectedness. In the first part, we recall the definitions of neighborhood and connectedness of the traditional digital topology approach. In the second part, we define the notions of "bounded space", "connected bounded space" and of "connected subset of a bounded space". In the last part, we introduce two image operators (a dilation and an erosion) that produce expanded images whose connectedness is analyzed in relation to a bounded space obtained from the invariance domain of an opening. We show how the traditional two kinds of connectedness can be derived from this analysis. . IntroductionDigital topology provides the theoretical foundations for image analysis and more specifically advanced image segmentation.Traditionally, digital topology is based on the neighborhood concept. From it, other concepts, like connectedness and connected components, are derived.When the pixels of a binary image are arranged along lines and columns, the need for using two kinds of neighborhood, one for the black pixels and one for the white, appears in the early studies on digital topology.In this paper, we propose the notion of bounded space as first concept, instead of neighborhood. Then we can use the traditional topological approach (not digital) to define connectedness.Our contribution consists of showing that it is possible to derive the traditional 4-connectedness and 8-connectedness from a unique connectedness defined on an expanded image domain. This is obtained by using two expansion operators (one dilation and one erosion) and by studying connectedness in the expanded domain.In the first section, we recall the definitions of neighborhood and connectedness of the traditional digital topology approach, and we show the need for two definitions.

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Set Operator Decomposition and Conditionally Translation Invariant Elementary Operators

Cited by 2 publications

References 4 publications

An Approach to Extracting Facade Features Using the Intensity Value of Terrestrial Laser Scanner with Mathematical Morphology

An Approach to Extracting Facade Features Using the Intensity Value of Terrestrial Laser Scanner with Mathematical Morphology

New Insight on Digital Topology

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