Shape of an arbitrary finite point set in IR2

Worring, Marcel; Smeulders, A.W.M.

doi:10.1007/bf01249894

Cited by 12 publications

(7 citation statements)

References 15 publications

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“…Worring and Smeulders [16] considered the set consistency of a-graph, a variant of the compact region bounded by the a-shape, in 2D. They established that the a-graph of a connected set converges to itself.…”

Section: Consistent Set Estimation and Existing Resultsmentioning

confidence: 98%

An efficient set estimator in high dimensions: consistency and applications to fast data visualization

Chaudhuri

Basu

Tan

et al. 2004

Computer Vision and Image Understanding

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Section: Consistent Set Estimation and Existing Resultsmentioning

confidence: 98%

An efficient set estimator in high dimensions: consistency and applications to fast data visualization

Chaudhuri

Basu

Tan

et al. 2004

Computer Vision and Image Understanding

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“…Straightening the round faces (arcs) of alpha hull by line segments yields the alpha shape. It was proved that the alpha hull is equivalent to the closing of the point set X with a generalized ball of radius 1   and that from the duality of closing and opening the alpha hull is the complement of the opening of c X (complement of X ) with the same ball as the structuring element (Worring and Smelders 1994). Thus by examining boundary facets of the alpha shape of the measured profile, morphological closing and opening envelopes can be derived.…”

Section: Image Processing Based Methods For Planar Surfacesmentioning

confidence: 99%

Morphological filters for functional assessment of roundness profiles

Lou¹,

Jiang²,

Scott³

2014

Meas. Sci. Technol.

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Abstract. Filtration techniques are useful tools of analysing roundness profiles. The 2RC filter and Gaussian filter are commonly used to assess peripheral undulations of the roundness data. However they cannot do every aspect of functional prediction. Morphological filters are employed to characterise roundness profiles for functional assessment. Traditional computation methods for morphological filters are limited to planar surfaces and unable to be extended to roundness measurement. A novel method based on alpha shape theory is developed to break up the confinement. The morphological closing and opening envelopes are obtained by rolling a disk upon the roundness profile from the air and material side of the component respectively. They can be used to identify significant peaks and valleys on the profile respectively, which are vital to the functional performance of component, especially contact phenomenon. A case study is presented that various options of morphological filters and reference circles are applied to a roundness profile, delivering different functional meanings. An in-depth comparison of morphological filters and the Gaussian filter is followed to derive their pros and cons.

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“…There exists a theoretical link between the alpha hull and morphological operations: the alpha hull is equivalent to the closing of the point set X with a generalized ball of radius 1 α − and that from the duality of closing and opening the alpha hull is the complement of the opening of c X (complement of X ) with the same ball as the structuring element [12]. This relationship provides the theoretical basis of using the alpha shape to compute morphological filters.…”

Section: Alpha Shape Algorithmmentioning

confidence: 99%

Algorithms for morphological profile filters and their comparison

Lou

Jiang

Scott

2012

Precision Engineering

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Morphological filters, regarded as the complement of mean-line based filters, are useful in the analysis of surface texture and the prediction of functional performance. The paper first recalls two existing algorithms, the naive algorithm and the motif combination algorithm, originally developed for the traditional envelope filter. With minor extension, they could be used to compute morphological filters. A recent novel approach based on the relationship between the alpha shape and morphological closing and opening operations is presented as well. Afterwards two novel algorithms are developed. By correlating the convex hull and morphological operations, the Graham scan algorithm, original developed for the convex hull is modified to compute the morphological envelopes. The alpha shape method depending on the Delaunay triangulation is costly and redundant for the computation for the alpha shape for a given radius. A recursive algorithm is proposed to solve this problem. A series of observations are presented for searching the contact points. Based on the proposed observations, the algorithm partitions the profile data into small segments and searches the contact points in a recursive manner. The paper proceeds to compare the five distinct algorithms in five aspects: algorithm verification, algorithm analysis, performance evaluation, end effects correction, and areal extension. By looking into these aspects, the merits and shortcomings of these algorithms are evaluated and compared.

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Shape of an arbitrary finite point set in IR2

Cited by 12 publications

References 15 publications

An efficient set estimator in high dimensions: consistency and applications to fast data visualization

An efficient set estimator in high dimensions: consistency and applications to fast data visualization

Morphological filters for functional assessment of roundness profiles

Algorithms for morphological profile filters and their comparison

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