The Watershed Transform: Definitions, Algorithms and Parallelization Strategies

Roerdink, Jos B. T. M.; Meijster, Arnold

doi:10.3233/fi-2000-411207

Cited by 1,103 publications

(498 citation statements)

References 33 publications

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“…Note that in this paper, we did not address the issue of shot noise that has for long been known to be a problem for most segmentation algorithms, and in particular for Watershed techniques (see e.g. Roerdink & Meijster 2001 for a review on the subject). In fact, shot noise often leads to over segmentation, and numerous complex techniques have been developed to try and compensate for it.…”

Section: Discussionmentioning

confidence: 99%

The fully connectedN-dimensional skeleton: probing the evolution of the cosmic web

Sousbie¹,

Colombi²,

Pichon³

2009

Monthly Notices of the Royal Astronomical Society

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A method to compute the full hierarchy of the critical subsets of a density field is presented. It is based on a Watershed technique and uses a probability propagation scheme to improve the quality of the segmentation by circumventing the discreteness of the sampling. It can be applied within spaces of arbitrary dimensions and geometry. This recursive segmentation of space yields, for a d‐dimensional space, a d− 1 succession of n‐dimensional subspaces that fully characterize the topology of the density field. The final one‐dimensional manifold of the hierarchy is the fully connected network of the primary critical lines of the field: the skeleton. It corresponds to the subset of lines linking maxima to saddle points, and provides a definition of the filaments that compose the cosmic web as a precise physical object, which makes it possible to compute any of its properties such as its length, curvature, connectivity etc. When the skeleton extraction is applied to initial conditions of cosmological N‐body simulations and their present‐day non‐linear counterparts, it is shown that the time evolution of the cosmic web, as traced by the skeleton, is well accounted by the Zel'dovich approximation (ZA) provided the small‐scale artificial smoothing introduced by the displacement field computation is taken into account. This scale is shown to be well modelled as in units of the non‐linear scale, a being the expansion factor. Comparing this skeleton to the initial skeleton undergoing the Zel'dovich mapping shows that two effects are competing during the formation of the cosmic web: a general dilation of the larger filaments that is captured by a simple deformation of the skeleton of the initial conditions on the one hand, and the shrinking, fusion and disappearance of the more numerous smaller filaments on the other hand. The net result corresponds to a decrease of the cosmic skeleton's length with time. Other applications of the N‐dimensional skeleton and its peak patch hierarchy are discussed.

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Section: Discussionmentioning

confidence: 99%

The fully connectedN-dimensional skeleton: probing the evolution of the cosmic web

Sousbie¹,

Colombi²,

Pichon³

2009

Monthly Notices of the Royal Astronomical Society

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“…The ROI identification was divided into two different steps. First, we performed identification of foreground objects by applying the watershed algorithm to the normalized images (53,54). One of the requirements for an object to be considered as a CTC is that it has an intact nucleus that can be identified.…”

Section: Roi Identificationmentioning

confidence: 99%

Automated detection of circulating tumor cells with naive Bayesian classifiers

et al. 2014

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Personalized medicine is a modern healthcare approach where information on each person's unique clinical constitution is exploited to realize early disease intervention based on more informed medical decisions. The application of diagnostic tools in combination with measurement evaluation that can be performed in a reliable and automated fashion plays a key role in this context. As the progression of various cancer diseases and the effectiveness of their treatments are related to a varying number of tumor cells that circulate in blood, the determination of their extremely low numbers by liquid biopsy is a decisive prognostic marker. To detect and enumerate circulating tumor cells (CTCs) in a reliable and automated fashion, we apply methods from machine learning using a naive Bayesian classifier (NBC) based on a probabilistic generative mixture model. Cells are collected with a functionalized medical wire and are stained for fluorescence microscopy so that their color signature can be used for classification through the construction of Red-Green-Blue (RGB) color histograms. Exploiting the information on the fluorescence signature of CTCs by the NBC does not only allow going beyond previous approaches but also provides a method of unsupervised learning that is required for unlabeled training data. A quantitative comparison with a state-of-the-art support vector machine, which requires labeled data, demonstrates the competitiveness of the NBC method. (5-7), much emphasis has been put on techniques that effectively collect CTCs from peripheral blood. Currently, the majority of studies use anti-epithelial-cell-adhesionmolecule (EpCAM) antibody-coated isolation systems (8-10), whereas other types of immunomagnetic devices (11-13), density gradient centrifugation (14) or membrane filtration (15,16), are also used for CTC enrichment. The subsequent CTC detection is realized by either immunocytological staining or polymerase chain reaction (17). Due to the extraordinary rarity of CTCs in patients, which have a typical ratio of one CTC per 10 8 blood cells (18), classical flow cytometry has proven unreliable and methods using intravital multiphoton flow cytometry and photoacoustic flowmetry are currently being developed (17,(19)(20)(21)(22). Although these methods have already successfully identified CTCs in control blood specimens spiked with cancer cell lines, they are not yet ready for use in detection of CTC in patients with cancer.The data of this study were generated by a technology that can collect CTCs in vivo using a functionalized and structured medical wire (FSMW) (23). Medical guidewires are widely used for angiography and insertion of venous catheters (24)

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“…The concept has been applied in a variety of applications such as remeshing of triangular surfaces using quadrilaterals [DBG * 06], analyzing and visualizing scalar [PCM03] and vector fields [HH89], or identification of handles and tunnels in surfaces [GW01]. The watershed algorithm [RM00] is closely related to topology and often applied in image analysis. However, although topological concepts have become standard tools in other areas and despite the possible algorithmic advantages due to derivative-free and purely combinatorial computations, almost no approaches exist to apply this scheme for the extraction of salient edges.…”

Section: Introductionmentioning

confidence: 99%

Separatrix Persistence: Extraction of Salient Edges on Surfaces Using Topological Methods

Weinkauf

Günther

2009

Computer Graphics Forum

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Salient edges are perceptually prominent features of a surface. Most previous extraction schemes utilize the notion of ridges and valleys for their detection, thereby requiring curvature derivatives which are rather sensitive to noise. We introduce a novel method for salient edge extraction which does not depend on curvature derivatives. It is based on a topological analysis of the principal curvatures and salient edges of the surface are identified as parts of separatrices of the topological skeleton. Previous topological approaches obtain results including non-salient edges due to inherent properties of the underlying algorithms. We extend the profound theory by introducing the novel concept of separatrix persistence, which is a smooth measure along a separatrix and allows to keep its most salient parts only. We compare our results with other methods for salient edge extraction.

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The Watershed Transform: Definitions, Algorithms and Parallelization Strategies

Cited by 1,103 publications

References 33 publications

The fully connectedN-dimensional skeleton: probing the evolution of the cosmic web

The fully connectedN-dimensional skeleton: probing the evolution of the cosmic web

Automated detection of circulating tumor cells with naive Bayesian classifiers

Separatrix Persistence: Extraction of Salient Edges on Surfaces Using Topological Methods

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