Fast multiscale clustering and manifold identification

Kushnir, Dan; Galun, Meirav; Brandt, Achi

doi:10.1016/j.patcog.2006.04.007

Cited by 71 publications

(65 citation statements)

References 32 publications

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“…This spectral resolution is larger by a factor of 4 than the one usually adopted. This is done here by a fast multiscale clustering algorithm [12], which is based on the Segmentation by Weighted Aggregation (SWA) algorithm [13], motivated by Algebraic Multigrid (AMG) [14]. The algorithm assigns data points into clusters starting at the finest resolution level, the grid spacing.…”

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confidence: 99%

Geometry of Intensive Scalar Dissipation Events in Turbulence

2006

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Maxima of the scalar dissipation rate in turbulence appear in form of sheets and correspond to the potentially most intensive scalar mixing events. Their cross-section extension determines a locally varying diffusion scale of the mixing process and extends the classical Batchelor picture of one mean diffusion scale. The distribution of the local diffusion scales is analysed for different Reynolds and Schmidt numbers with a fast multiscale technique applied to very high-resolution simulation data. The scales take always values across the whole Batchelor range and beyond. Furthermore, their distribution is traced back to the distribution of the contractive short-time Lyapunov exponent of the flow. When a scalar concentration field θ(x, t) is transported in a turbulent flow very large scalar gradients are generated which can be associated with potentially intensive mixing [1]. Frequently, such large-amplitude gradient regions exist across scales that are finer than the smallest turbulent eddies, a case which is known as the Batchelor regime of scalar mixing [2]. Their cross-section is usually estimated by a single mean diffusion scale, the Batchelor scale η B , that equilibrates advection by flow and scalar diffusion. However, scalar gradients are known to fluctuate strongly in turbulent mixing. These fluctuations are caused by the fluctuating scalar amplitudes and by the varying spatial sections across which the scalar differences are built up. Both aspects will cause the strong spatial variability of potentially intensive mixing regions. Thus, a whole range of local diffusion scales l d , which quantifies exactly this variability, will exist around the mean diffusion scale η B . Their distribution is interesting for several reasons. It can enter mixing efficiency measures [3]. The scales prescribe the extension of chemically reactive layers in which the combustion of fuel takes place [4] or the variations of the fluorescence signal as used for the measurement of zooplankton patchiness in the ocean [5].In this Letter, we want to calculate this local diffusion scale distribution p(l d ). It arises from the competition of two dynamic processes. On one hand, the scale distribution will be affected by molecular diffusion that causes a diminishing of existing steep gradients as well as the completion of their formation by reconnection [6,7]. On the other hand, the scales will be determined by the statistics of the local advection flow patterns that pile up scalar differences. While the strongest scalar gradients were related to instantaneous velocity gradients in Ref.[8], we will go one step further in the second part of the Letter and relate the local diffusion scale distribution to the distribution of Lagrangian contraction rates of the flow, as given by the smallest of the three finite-time Lyapunov exponents along Lagrangian trajectories. The Lagrangian approach incorporates the temporal evolution of the persistent flow patterns that eventually generate the strongest scalar gradients or the finest local dissipation...

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Section: Fig 1: (Color Online)mentioning

confidence: 99%

Geometry of Intensive Scalar Dissipation Events in Turbulence

2006

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“…[34]). Our approach is governed by the philosophy of visual data mining: the user should be able to interact rabidly with graphs summarizing his data with the aim of extracting high-level semantics.…”

Section: Discussionmentioning

confidence: 99%

Beyond FCM: Graph-theoretic post-processing algorithms for learning and representing the data structure

Laskaris

Zafeiriou

2008

Pattern Recognition

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“…This segmentation technique was originally developed for 2D image processing [49]. The method creates a hierarchy of scales from groupings of data, starting with individual data points at the finest scale and iteratively coarsening to combine groups.…”

Section: Fast Multiscale Clustering (Fmc)mentioning

confidence: 99%

“…While this Mahalanobis distance lacks physical significance, it can be scaled at the aggregation step to give sense to closeness and farness, depending on the nature of the data set. The scaling parameter, CMaha, determines the sensitivity of the segmentation [49]. FMC requires several other user-defined values, but fixed values for the rest have been effective for all data sets examined.…”

Section: Fast Multiscale Clustering (Fmc)mentioning

confidence: 99%

Uncovering the true nature of deformation microstructures using 3D analysis methods

Ferry

Quadir

Afrin

et al. 2015

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. Three-dimensional electron backscatter diffraction (3D EBSD) has emerged as a powerful technique for generating 3D crystallographic information in reasonably large volumes of a microstructure. The technique uses a focused ion beam (FIB) as a high precision serial sectioning device for generating consecutive ion milled surfaces of a material, with each milled surface subsequently mapped by EBSD. The successive EBSD maps are combined using a suitable post-processing method to generate a crystallographic volume of the microstructure. The first part of this paper shows the usefulness of 3D EBSD for understanding the origin of various structural features associated with the plastic deformation of metals. The second part describes a new method for automatically identifying the various types of low and high angle boundaries found in deformed and annealed metals, particularly those associated with grains exhibiting subtle and gradual variations in orientation. We have adapted a 2D image segmentation technique, fast multiscale clustering, to 3D EBSD data using a novel variance function to accommodate quaternion data. This adaptation is capable of segmenting based on subtle and gradual variation as well as on sharp boundaries within the data. We demonstrate the excellent capabilities of this technique with application to 3D EBSD data sets generated from a range of cold rolled and annealed metals described in the paper.

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Fast multiscale clustering and manifold identification

Cited by 71 publications

References 32 publications

Geometry of Intensive Scalar Dissipation Events in Turbulence

Geometry of Intensive Scalar Dissipation Events in Turbulence

Beyond FCM: Graph-theoretic post-processing algorithms for learning and representing the data structure

Uncovering the true nature of deformation microstructures using 3D analysis methods

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