2010
DOI: 10.1016/j.imavis.2009.06.017
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Some links between extremum spanning forests, watersheds and min-cuts

Abstract: Minimum cuts, extremum spanning forests and watersheds have been used as the basis for powerful image segmentation procedures. In this paper, we present some results about the links which exist between these different approaches. Especially, we show that extremum spanning forests are particular cases of watersheds from arbitrary markers and that min-cuts coincide with extremum spanning forests for some particular weight functions.

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Cited by 74 publications
(81 citation statements)
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References 14 publications
(24 reference statements)
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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%
See 1 more Smart Citation
“…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%
“…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%
“…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%