Skeletonization via Distance Maps and Level Sets

Kimmel, Ron; Shaked, Doron; Kiryati, Nahum; Bruckstein, Alfred M.

doi:10.1006/cviu.1995.1062

Cited by 149 publications

(90 citation statements)

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“…(1)), skeletonization [63], Voronoi tessellations [30,64], Watershed algorithms [65], and MRI data analysis [66]. Next, we will discuss some prominent academic research as reported in the last decade and refer to advances made on existing applications and the introduction of new applications, compared to those just mentioned.…”

Section: On More Than 30 Years Of Researchmentioning

confidence: 99%

“…In the last case, DT are either applied by themselves or as an intermediate method such as: route planning and (robot) navigation [26,28,56,61,70], collision prevention [27], video surveillance [69,71], internal radiation therapy [13], handwriting recognition [62,72], (medical) image segmentation [9][10][11][13][14][15] (see also Fig. (1)), skeletonization [63,73], Voronoi tessellations [30,64], BouligandMinkowsky fractal dimension [74], Watershed algorithms [65], neuromorphometry [73,75], MRI data analysis [76,92], and volume rendering [36,77], to mention but a few.…”

Section: Current and Future Developmentsmentioning

confidence: 99%

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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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Section: On More Than 30 Years Of Researchmentioning

confidence: 99%

Section: Current and Future Developmentsmentioning

confidence: 99%

Distance Transforms: Academics Versus Industry

Broek

Schouten²

2011

CSENG

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“…Skeletonization is a method that provides the thinnest representation of a geometric outline (skeleton) that preserves the topology. Although many skeletonization techniques exist [8][9][10][11] , ARRM approximates rotor disk skeletons by identifying the Voronoi diagram generated using the finite element model surface nodes. The interior segments in the Voronoi diagram provide the rotor disk skeleton.…”

Section: Surface Node Selectionmentioning

confidence: 99%

Adaptive Risk Refinement Methodology for Gas Turbine Engine Rotor Disks

Moody¹,

Millwater²,

Enright³

2008

49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference &Amp;lt;br> 16th AIAA/ASME/AHS Ada

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Probabilistic fracture mechanics is a well-established method for predicting the probability-of-fracture (POF) of gas turbine engine rotor disks subject to low-cycle fatigue.An adaptive risk refinement methodology (ARRM) was developed to automate zone discretization and refinement that are typically associated with this approach. ARRM generates initial meshes using an adaptive nodal selection feature designed to optimize accuracy and efficiency. Adaptive mesh refinement (AMR) is performed until a converged risk solution is obtained. ARRM employs several techniques including skeletonization, constrained Delaunay triangulation (CDT), superparametric interpolation, and adaptive mesh refinement. A numerical example is provided to illustrate the effectiveness of the methodology. Nomenclature Δσ= stress range d s = shifting distance F = fracture of an initial anomaly located in a zone K = number of zones l e = projection path length m = iteration number P[A i ] = probability of having an anomaly in a zone P [B i |A i ] = conditional probability-of-fracture given an anomaly in a zone P[F i ] = probability-of-fracture of an initial anomaly located in a zone P disk = probability-of-fracture in a disk POF = probability-of-fracture

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“…In the literature, different methods have been proposed to compute the medial axis approximately or exactly, for instance methods relying on discrete geometry [5,15,16,7], digital topology [13,25], mathematical morphology [22], computational geometry [3,20], partial differential equations [24], or level-sets [17]. In this work we focus on the discrete medial axis based on the Euclidean metric.…”

Section: Introductionmentioning

confidence: 99%

Scale Filtered Euclidean Medial Axis

Postolski

Couprie

Janaszewski

2013

Discrete Geometry for Computer Imagery

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Abstract. We propose an Euclidean medial axis filtering method which generates subsets of Euclidean medial axis were filtering rate is controlled by one parameter. The method is inspired by Miklos', Giesen's and Pauly's scale axis method which preserves important features of an input object from shape understanding point of view even if they are at different scales. Our method overcomes the most important drawback of scale axis: scale axis is not, in general, a subset of Euclidean medial axis. It is even not necessarily a subset of the original shape. The method and its properties are presented in 2D space but it can be easily extended to any dimension. Experimental verification and comparison with a few previously introduced methods are also included.

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Skeletonization via Distance Maps and Level Sets

Cited by 149 publications

References 0 publications

Distance Transforms: Academics Versus Industry

Distance Transforms: Academics Versus Industry

Adaptive Risk Refinement Methodology for Gas Turbine Engine Rotor Disks

Scale Filtered Euclidean Medial Axis

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