An Approximate Distribution for the Normalized Cut

Nadarajah, Saralees

doi:10.1007/s10851-008-0089-y

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…In order to obtain higher-discrimination features of the point sets, and assign a semantic label to the laser point well, the initial point sets are further divided so that a point set only contains one ground object or part of a ground object. As a normalized cut [42] can effectively segment the point sets, it is introduced to segment the initial point sets to further obtain content-sensitive multilevel point clusters. Firstly, a point set is divided into two parts by normalized cut, until the number of points in the set is less than a predefined threshold δ.…”

Section: Construction Of Multilevel Point Clustersmentioning

confidence: 99%

Content-Sensitive Multilevel Point Cluster Construction for ALS Point Cloud Classification

Zhang

Zhong

et al. 2019

Remote Sensing

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Airborne laser scanning (ALS) point cloud classification is a challenge due to factors including complex scene structure, various densities, surface morphology, and the number of ground objects. A point cloud classification method is presented in this paper, based on content-sensitive multilevel objects (point clusters) in consideration of the density distribution of ground objects. The space projection method is first used to convert the three-dimensional point cloud into a two-dimensional (2D) image. The image is then mapped to the 2D manifold space, and restricted centroidal Voronoi tessellation is built for initial segmentation of content-sensitive point clusters. Thus, the segmentation results take the entity content (density distribution) into account, and the initial classification unit is adapted to the density of ground objects. The normalized cut is then used to segment the initial point clusters to construct content-sensitive multilevel point clusters. Following this, the point-based hierarchical features of each point cluster are extracted, and the multilevel point-cluster feature is constructed by sparse coding and latent Dirichlet allocation models. Finally, the hierarchical classification framework is created based on multilevel point-cluster features, and the AdaBoost classifiers in each level are trained. The recognition results of different levels are combined to effectively improve the classification accuracy of the ALS point cloud in the test process. Two scenes are used to experimentally test the method, and it is compared with three other state-of-the-art techniques.

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Section: Construction Of Multilevel Point Clustersmentioning

confidence: 99%

Content-Sensitive Multilevel Point Cluster Construction for ALS Point Cloud Classification

Zhang

Zhong

et al. 2019

Remote Sensing

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“…The normalized cut introduced by Shi and Malik [14] is useful in several areas. This measure is of interest not only for image segmentation but also for network theories and statistics [1,13,12,6,15].…”

Section: Introductionmentioning

confidence: 99%

Bipartition of graphs based on the normalized cut and spectral methods

Perera,

Mizoguchi

2012

Preprint

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In the first part of this paper, we survey results that are associated with three types of Laplacian matrices:difference, normalized, and signless. We derive eigenvalue and eigenvector formulaes for paths and cycles using circulant matrices and present an alternative proof for finding eigenvalues of the adjacency matrix of paths and cycles using Chebyshev polynomials. Even though each results is separately well known, we unite them, and provide uniform proofs in a simple manner. The main objective of this study is to solve the problem of finding graphs, on which spectral clustering methods and normalized cuts produce different partitions. First, we derive a formula for a minimum normalized cut for graph classes such as paths, cycles, complete graphs, double-trees, cycle cross paths, and some complex graphs like lollipop graph LP n,m , roach type graph R n,k , and weighted path P n,k . Next, we provide characteristic polynomials of the normalized Laplacian matrices L(P n,k ) and L(R n,k ). Then, we present counter example graphs based on R n,k , on which spectral methods and normalized cuts produce different clusters.

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