Some links between extremum spanning forests, watersheds and min-cuts

Allène, Cédric; Audibert, Jean-Yves; Couprie, Michel; Keriven, Renaud

doi:10.1016/j.imavis.2009.06.017

Cited by 72 publications

(79 citation statements)

References 14 publications

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“…7c) is an Ç-shortest path 2. This result has been independently presented in two papers [43], [45] published at the same conference. spanning forest relative to the graph X (Fig.…”

Section: Shortest Path Forestssupporting

confidence: 54%

“…Due to relative MSFs and M-kernels, we provide a mathematical comparison among watershed cuts, shortest path forests (the theoretical basis of the Image Foresting Transform [4] and of the fuzzy connected image segmentation [5], [40]), and topological watersheds [12], [23]. Furthermore, in [43], based on the framework of this paper, a link between min-cuts [2] and watershed cuts is provided.…”

Section: Watersheds Shortest Path Forests and Topological Watershedsmentioning

confidence: 99%

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Watershed Cuts: Thinnings, Shortest Path Forests, and Topological Watersheds

Cousty

Bertrand²,

Najman³

et al. 2010

IEEE Trans. Pattern Anal. Mach. Intell.

153

126

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Abstract-We recently introduced watershed cuts, a notion of watershed in edge-weighted graphs. In this paper, our main contribution is a thinning paradigm from which we derive three algorithmic watershed cut strategies: The first one is well suited to parallel implementations, the second one leads to a flexible linear-time sequential implementation, whereas the third one links the watershed cuts and the popular flooding algorithms. We state that watershed cuts preserve a notion of contrast, called connection value, on which several morphological region merging methods are (implicitly) based. We also establish the links and differences between watershed cuts, minimum spanning forests, shortest path forests, and topological watersheds. Finally, we present illustrations of the proposed framework to the segmentation of artwork surfaces and diffusion tensor images.

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“…7c) is an Ç-shortest path 2. This result has been independently presented in two papers [43], [45] published at the same conference. spanning forest relative to the graph X (Fig.…”

Section: Shortest Path Forestssupporting

confidence: 54%

Section: Watersheds Shortest Path Forests and Topological Watershedsmentioning

confidence: 99%

Watershed Cuts: Thinnings, Shortest Path Forests, and Topological Watersheds

Cousty

Bertrand²,

Najman³

et al. 2010

IEEE Trans. Pattern Anal. Mach. Intell.

153

126

View full text Add to dashboard Cite

show abstract

“…Such behaviour can be explained by taking a look at the central region of Figure 2b reveals similar colours, tough representing different sediment classes. One of the strongest skills of the OPF classifier turns out to be its main weakness: a theoretical property says OPF minimizes the classification error over the training set, which can be close to zero depending on the configuration (distribution of samples) of the training set [16]. Roughly speaking, OPF training step aims at partition the graph induced by the dataset samples by means of a competition process among prototype samples (key samples chosen from each class).…”

Section: Methodsmentioning

confidence: 99%

River sediment yield classification using remote sensing imagery

Pisani

Costa

Rosa

et al. 2016

2016 9th IAPR Workshop on Pattern Recogniton in Remote Sensing (PRRS)

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The monitoring of water quality is essencial to the mankind, since we strongly depend on such resource for living and working. The presence of sediments in rivers usually indicates changes in the land use, which can affect the quality of water and the lifetime of hydroelectric power plants. In countries like Brazil, where more than 70% of the energy comes from the water, it is crucial to keep monitoring the sediment yield in rivers and lakes. In this work, we evaluate some stateof-the-art supervised pattern recognition techniques to classify different levels of sediments in Brazilian rivers using satellite images, as well as we make available an annotated dataset composed of two images to foster the related research.

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“…In a framework of edge-weighted graphs, the watershed is defined as a cut relative to the regional minima/maxima of the weight function. Couprie et al showed that GC and RW converge to maximum spanning forest (MSF) cuts [6,7]. The MSF computation is a key factor in this computational efficiency.…”

Section: Methodsmentioning

confidence: 99%

Using Power Watersheds to Segment Benign Thyroid Nodules in Ultrasound Image Data

Kollorz

Angelopoulou

Beck

et al. 2011

Bildverarbeitung Für Die Medizin 2011

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Abstract. Thyroid nodule segmentation is a hard task due to different echo structures, textures and echogenicities in ultrasound (US) images as well as speckle noise. Currently, a typical clinical evaluation involves the manual, approximate measurement in two section planes in order to obtain an estimate of the nodule's size. The aforementioned nodule attributes are recorded on paper. We propose instead the semi-automatic segmentation of 2D slices of acquired 3D US volumes with power watersheds (PW) independent of the nodule type. We tested different input seeds to evaluate the potential of the applied algorithm. On average we achieved a 76.81 % sensitivity, 88.95 % precision and 0.81 Dice coefficient. The runtime on a standard PC is about 0.02 s which indicates that the extension to 3D volume data should be feasible.

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Some links between extremum spanning forests, watersheds and min-cuts

Cited by 72 publications

References 14 publications

Watershed Cuts: Thinnings, Shortest Path Forests, and Topological Watersheds

Watershed Cuts: Thinnings, Shortest Path Forests, and Topological Watersheds

River sediment yield classification using remote sensing imagery

Using Power Watersheds to Segment Benign Thyroid Nodules in Ultrasound Image Data

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