A first parallel algorithm to compute the morphological tree of shapes of nD images

Crozet, Sébastien; Géraud, Thierry

doi:10.1109/icip.2014.7025593

Cited by 25 publications

(14 citation statements)

References 27 publications

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“…The algorithm computes the tree of shapes with quasi-linear time complexity when data quantization is low (typically 12 bits or less) and it works for nD images. Moreover, Crozet et al [38] presented the first parallel algorithm to compute the morphological tree of shapes based on the previous algorithm [37]. The tree of shapes is a more general representation of the image with respect to the min-tree and max-tree and it has many advantages.…”

Section: A Tree Of Shapesmentioning

confidence: 99%

Remote Sensing Image Classification Using Attribute Filters Defined Over the Tree of Shapes

Cavallaro¹,

Mura²,

Benediktsson³

2016

IEEE Trans. Geosci. Remote Sensing

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Abstract-Remotely sensed images with very high spatial resolution provide a detailed representation of the surveyed scene with a geometrical resolution that at the present can be up to 30 cm (WorldView-3). A set of powerful image processing operators have been defined in the mathematical morphology framework. Among those, connected operators (e.g., attribute filters) have proven their effectiveness in processing very high resolution images. Attribute filters are based on attributes which can be efficiently implemented on tree-based image representations. In this work, we considered the definition of min, max, direct and subtractive filter rules for the computation of attribute filters over the tree of shapes representation. We study their performance on the classification of remotely sensed images. We compare the classification results over the tree of shapes with the results obtained when the same rules are applied on the component trees. The random forest is used as a baseline classifier and the experiments are conducted using multispectral data sets acquired by QuickBird and IKONOS sensors over urban areas.

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Section: A Tree Of Shapesmentioning

confidence: 99%

Remote Sensing Image Classification Using Attribute Filters Defined Over the Tree of Shapes

Cavallaro¹,

Mura²,

Benediktsson³

2016

IEEE Trans. Geosci. Remote Sensing

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“…The algorithm computes the ToS with quasi-linear time complexity when data quantization is low (typically 12 bits or less) and it works for nD images. Moreover, Crozet et al [20] presented the first parallel algorithm to compute the morphological ToS based on the previous algorithm [19].…”

Section: Tree Of Shapesmentioning

confidence: 99%

Region-based classification of remote sensing images with the morphological tree of shapes

Cavallaro

Mura

Carlinet

et al. 2016

2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS)

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International audienceSatellite image classification is a key task used in remote sensing for the automatic interpretation of a large amount of information. Today there exist many types of classification algorithms using advanced image processing methods enhancing the classification accuracy rate. One of the best state-of-the-art methods which improves significantly the classification of complex scenes relies on Self-Dual Attribute Profiles (SDAPs). In this approach, the underlying representation of an image is the Tree of Shapes, which encodes the inclusion of connected components of the image. The SDAP computes for each pixel a vector of attributes providing a local multi-scale representation of the information and hence leading to a fine description of the local structures of the image. Instead of performing a pixel-wise classification on features extracted from the Tree of Shapes, it is proposed to directly classify its nodes. Extending a specific interactive segmentation algorithm enables it to deal with the multi-class classification problem. The method does not involve any statistical learning and it is based entirely on morphological information related to the tree. Consequently, a very simple and effective region-based classifier relying on basic attributes is presented

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“…Last let us recall that a quasi-linear algorithm exists to compute the tree of shapes, that has the property of also working in the nD case [10]. A parallel version of this algorithm is available [9].…”

Section: The Morphological Tree Of Shapesmentioning

confidence: 99%

Self-duality and Digital Topology: Links Between the Morphological Tree of Shapes and Well-Composed Gray-Level Images

Géraud

Carlinet

Crozet

2015

Lecture Notes in Computer Science

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International audienceIn digital topology, the use of a pair of connectivities is required to avoid topological paradoxes. In mathematical morphology, self-dual operators and methods also rely on such a pair of connectivities. There are several major issues: self-duality is impure, the image graph structure depends on the image values, it impacts the way small objects and texture are processed, and so on. A sub-class of images defined on the cubical grid, well-composed images, has been proposed, where all connectivities are equivalent, thus avoiding many topological problems. In this paper we unveil the link existing between the notion of well-composed images and the morphological tree of shapes. We prove that a well-composed image has a well-defined tree of shapes. We also prove that the only self-dual well-composed interpolation of a 2D image is obtained by the median operator. What follows from our results is that we can have a purely self-dual representation of images, and consequently, purely self-dual operators

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A first parallel algorithm to compute the morphological tree of shapes of nD images

Cited by 25 publications

References 27 publications

Remote Sensing Image Classification Using Attribute Filters Defined Over the Tree of Shapes

Remote Sensing Image Classification Using Attribute Filters Defined Over the Tree of Shapes

Region-based classification of remote sensing images with the morphological tree of shapes

Self-duality and Digital Topology: Links Between the Morphological Tree of Shapes and Well-Composed Gray-Level Images

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