Watershed of a continuous function

Najman, Laurent; Schmitt, Michel

doi:10.1016/0165-1684(94)90059-0

Cited by 249 publications

(164 citation statements)

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“…It must be specify that here the standard framework of watershed transform based on the flooding algorithm is adopted despite to there are other alternative frameworks based on a continuous formulation using topographic distance [25,26]; the topological watershed based on discrete geometry tools [27,28]; graph-based watershed using minimum spanning-tree algorithms [29,30]; the power watershed algorithm [31]; the viscous watershed [32]; etc.…”

Section: Introductionmentioning

confidence: 99%

Liver segmentation in MRI: A fully automatic method based on stochastic partitions

López-Mir

Naranjo

Angulo

et al. 2014

Computer Methods and Programs in Biomedicine

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There are few fully automated methods for liver segmentation in magnetic resonance images (MRI) despite the benefits of this type of acquisition in comparison to other radiology techniques such as computed tomography (CT). Motivated by medical requirements, liver segmentation in MRI has been carried out. For this purpose, we present a new method for liver segmentation based on the watershed transform and stochastic partitions. The classical watershed over-segmentation is reduced using a marker-controlled algorithm. To improve accuracy of selected contours, the gradient of the original image is successfully enhanced by applying a new variant of stochastic watershed. Moreover, a final classifier is performed in order to obtain the final liver mask. Optimal parameters of the method are tuned using a training dataset and then they are applied to the rest of studies (17 datasets). The obtained results (a Jaccard coefficient of .91 ± .02) in comparison to other methods demonstrate that the new variant of stochastic watershed is a robust tool for automatic segmentation of the liver in MRI.

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Section: Introductionmentioning

confidence: 99%

Liver segmentation in MRI: A fully automatic method based on stochastic partitions

López-Mir

Naranjo

Angulo

et al. 2014

Computer Methods and Programs in Biomedicine

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Section: Minimum Cost Path Saliencymentioning

confidence: 99%

“…(12)) is di!erent from the one proposed in [15] which constituted the basis for the dynamics of contours. In [15] the use of the line integral expresses a measure of the work needed to move a point a towards another point b, following a steepest descent path. For this purpose, the gradient vector "eld is used to combine the work calculation and the notion of topographic distance, as introduced in [13].…”

Section: Minimum Cost Path Saliencymentioning

confidence: 99%

“…Several advantageous characteristics are ensured by applying the watershed transformation: (i) watersheds form closed curves providing a full partitioning of the image domain (thus, we get a pure region-based segmentation which does not require any closing or connection of the edges); (ii) watersheds on the image of gradient modulus can play the role of a multiple point detector [15], thus treating well all cases of multiple regions which meet at the same multiple point; (iii) there is a 1}1 relationship between the minima and the catchment basins. Therefore, we can represent a whole region by its minimum.…”

Section: Introductionmentioning

confidence: 99%

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Low level image partitioning guided by the gradient watershed hierarchy

1999

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In this paper, we study the construction of hierarchies for gradient watersheds. The underlying analysis is based on the fact that the gradient image provides information with respect to local discontinuity and similarity. Two algorithms which utilize this type of information are analyzed. The "rst one is an extended version of the dynamics of contours and the second is the algorithm which considers the minimum cost path saliency between two adjacent regional minima. For both algorithms, a stopping criterion which de"nes and extracts automatically each hierarchical level is proposed. An important hint to determine which one of the two algorithms has a superior behavior is the domination of the pro"le type of the surface (convex or concave) formed by the gradient image. Tests are discussed on arti"cially generated and real images. The proposed bottom-up procedure provides an essential aid to the precise classi"cation of anatomical objects when used together with a user-interface environment.1999 Elsevier Science B.V. All rights reserved. ZusammenfassungIm folgenden Beitrag werden wir die Konstruktion von Hierarchien fuK r Wendepunkte untersuchen. Die zugrundeliegende Analyse beruht auf da{ Gradientenbilder Informationen uK ber lokale DiskontinuitaK ten und A G hnlichkeiten beinhalten. Es werden zwei Algorithmen untersucht, die diese Art von Information nutzen. Der erste ist eine erweiterte Version der Dynamik von Konturen und der zweite Algorithmus betrachtet minimale SpruK nge der Kostenfunktion zwischen zwei benachbarten regionalen Minima. FuK r beide Algorithmen wird ein Abbruchkriterium vorgestellt, das automatisch jede hierarchische Stufe de"niert und extrahiert. Ein wichtiger Hinweis dafuK r, welcher der beiden Algorithmen ein besseres Verhalten liefert, ist die Dominanz des Pro"ltyps der Ober#aK che (konvex oder konkav), gegeben durch das Gradientenbild. Tests mit kuK nstlichen und realen Bildern werden diskutiert. Die vorgestellte bottom-up Methode liefert eine entscheidende Hilfe zur praK zisen Klassi"zierung anatomischer Objekte, wenn sie im Zusammenhang mit einer Benutzerschnittstelle eingesetzt wird.1999 Elsevier Science B.V. All rights reserved. Re2 sume2Dans cet article, nous eH tudions la construction de hieH rarchies pour les lignes de partage des eaux du gradient. L'analyse sous-jacente repose sur le fait que l'image gradient fournit de l'information relative aux discontinuiteH s et aux similariteH s 0165-1684/99/$ -see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 -1 6 8 4 ( 9 8 ) 0 0 2 3 2 -1 locales. Deux algorithmes qui utilisent ce type d'information sont analyseH s. Le premier est une version eH tendue de la dynamique des contours et le deuxie`me est un algorithme qui conside`re le chemin de cou( t minimum entre deux minima reH gionaux adjacents. Pour les deux algorithmes, nous proposons un crite`re d'arre( t qui deH "nit et extrait automatiquement chaque niveau hieH rarchique. Une indication importante pour deH terminer lequel des deux algorithmes a un...

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“…In the continuous domain and assuming that the image is smooth and has isolated critical points, the continuous watershed is equivalent to finding a skeleton by influence zones with respect to a weighted distance function that uses points in the regional minima of the image as sources and η = ||∇f || as the field of indices [9,7]. If other markers different than the minima are to be used as sources, then the homotopy of the function must be modified via morphological reconstruction to impose these markers as the only minima.…”

Section: Continuous Watershed and Eikonal Pdementioning

confidence: 99%

Multiscale Morphological Segmentations Based on Watershed, Flooding, and Eikonal PDE

Meyer

Maragos

1999

Scale-Space Theories in Computer Vision

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Abstract. The classical morphological segmentation paradigm is based on the watershed transform, constructed by flooding the gradient image seen as a topographic surface. For flooding a topographic surface, a topographic distance is defined from which a minimum distance algorithm is derived for the watershed. In a continuous formulation, this is modeled via the eikonal PDE, which can be solved using curve evolution algorithms. Various ultrametric distances between the catchment basins may then be associated to the flooding itself. To each ultrametric distance is associated a multiscale segmentation; each scale being the closed balls of the ultrametric distance.

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Watershed of a continuous function

Cited by 249 publications

References 10 publications

Liver segmentation in MRI: A fully automatic method based on stochastic partitions

Liver segmentation in MRI: A fully automatic method based on stochastic partitions

Low level image partitioning guided by the gradient watershed hierarchy

Multiscale Morphological Segmentations Based on Watershed, Flooding, and Eikonal PDE

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