Shading from shape, the eikonal equation solved by grey-weighted distance transform

Verbeek, P.W.; Verwer, Ben J. H.

doi:10.1016/0167-8655(90)90102-8

Cited by 67 publications

(48 citation statements)

References 4 publications

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“…As such it is actually known as Dijkstra's algorithm. There are also other faster implementations using queues [13,6]. The above GWDT based on discrete chamfer metrics is shown in [13] and [4] to be a discrete approximate solution of the eikonal PDE ||∇U || = η.…”

Section: Gwdt Based On Chamfer Metricsmentioning

confidence: 99%

“…Computing this minimum weighted distance at all image points from any marker is also equivalent to finding the gray-weighted distance transform (GWDT) of the image. There are several types of discrete algorithms to compute the GWDT which include iterated (sequential or parallel) min-sum differences [13] and hierarchical queues [7]. Instead of elaborating more on discrete GWDT algorithms, we prefer now to proceed to our next formulation of watershed that will be based on a continuous (PDE-based) model.…”

Section: Definition 1 We Call Catchment Basin Cb(m I ) Of a Regionalmentioning

confidence: 99%

“…This discrete GWDT can be computed by running a 2D min-sum difference equation like the one implementing the chamfer distance transform of binary images but with spatially-varying coefficients proportional to the gray image values [13]:…”

Section: Gwdt Based On Chamfer Metricsmentioning

confidence: 99%

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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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Section: Gwdt Based On Chamfer Metricsmentioning

confidence: 99%

Section: Definition 1 We Call Catchment Basin Cb(m I ) Of a Regionalmentioning

confidence: 99%

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

Meyer

Maragos

1999

Scale-Space Theories in Computer Vision

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“…Alternatively, a wavefront from object points can be started that propa-gates outwardly at each step, while recording the number of steps as the minimum distance (cf. [17,[87][88][89][90]). However, unlike for example FEED [20], the computational load of Porikli's algorithm does not depend on the number of object points, which makes it constant in performance.…”

Section: Patent Applicationsmentioning

confidence: 99%

Distance Transforms: Academics Versus Industry

Broek

Schouten²

2011

CSENG

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Abstract:In image and video analysis, distance transformations (DT) are frequently used. They provide a distance image (DI) of background pixels to the nearest object pixel. DT touches upon the core of many applications; consequently, not only science but also industry has conducted a significant body of work in this field. However, in a vast majority of the cases this has not been published in major scientific outlets but has been filed as a patent application. This article provides a brief introduction into DT, including a specification of a few of the most prominent algorithms in the field. Next, a few interesting algorithms from the last decade are discussed. A benchmark including eight DT algorithms (i.e., city block, Danielsson's algorithm, chamfer 3-4, hexadecagonal region growing, a recent claimed true Euclidean DT, and three exact Euclidean DT) has been executed, which illustrates the intriguing complexity of DT in terms of precision and computational complexity. Subsequently, a selection of key patent applications are discussed that have emerged in this field, including their scientific merit and areas of application. Finally, this article's findings are summarized and discussed, with an emphasis on both the common ground of scientific articles and patent applications as well as the added value they can have to each other.

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“…Actually, this traversability can be expressed by the minimal cost to go from a minimum to its adjacent along all possible paths. The examination of this traversability points to the problem of the wavefront arrival time which can be solved by the grey-weighted distance transform [27] (see Section 2).…”

Section: Watershed Analysis and Hierarchical Segmentationmentioning

confidence: 99%

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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Shading from shape, the eikonal equation solved by grey-weighted distance transform

Cited by 67 publications

References 4 publications

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

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

Distance Transforms: Academics Versus Industry

Low level image partitioning guided by the gradient watershed hierarchy

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