Graph theoretical clustering based on limited neighbourhood sets

Urquhart, R.B.

doi:10.1016/0031-3203(82)90069-3

Cited by 166 publications

(65 citation statements)

References 27 publications

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“…Proximity graphs have been applied to clustering as well. Urquhart et al [32] use the Gabriel graph and the Relative Neighbor graph to improve hierarchical clustering, noting that these graphs result in natural clusters that can be separated depending on the local graph density [32]. Carreira and Zemel apply an ensemble of minimum spanning trees to form neighborhood graphs that are more resilient to noise and varying densities [4].…”

Section: Related Workmentioning

confidence: 99%

Locally-scaled spectral clustering using empty region graphs

Correa

Lindström

2012

Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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This paper introduces a new method for estimating the local neighborhood and scale of data points to improve the robustness of spectral clustering algorithms. We employ a subset of empty region graphs -the β -skeleton -and non-linear diffusion to define a locallyadapted affinity matrix, which, as we demonstrate, provides higher quality clustering than conventional approaches based on k nearest neighbors or global scale parameters. Moreover, we show that the clustering quality is far less sensitive to the choice of β and other algorithm parameters, and to transformations such as geometric distortion and random perturbation. We summarize the results of an empirical study that applies our method to a number of 2D synthetic data sets, consisting of clusters of arbitrary shape and scale, and to real multi-dimensional classification examples from benchmarks, including image segmentation.

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Section: Related Workmentioning

confidence: 99%

Locally-scaled spectral clustering using empty region graphs

Correa

Lindström

2012

Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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“…To overcome the problem of fixed threshold, Urquhar [25] determined the normalized weight of an edge using the smallest weight incident on the vertices touching that edge. Other methods [20,21] use an adaptive criterion that depends on local properties rather than global ones.…”

Section: Related Studymentioning

confidence: 99%

A comparative study of some methods for color medical images segmentation

Stănescu

Burdescu

Brezovan

2011

EURASIP J. Adv. Signal Process.

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The aim of this article is to study the problem of color medical images segmentation. The images represent pathologies of the digestive tract such as ulcer, polyps, esophagites, colitis, or ulcerous tumors, gathered with the help of an endoscope. This article presents the results of an objective and quantitative study of three segmentation algorithms. Two of them are well known: the color set back-projection algorithm and the local variation algorithm. The third method chosen is our original visual feature-based algorithm. It uses a graph constructed on a hexagonal structure containing half of the image pixels in order to determine a forest of maximum spanning trees for connected component representing visual objects. This third method is a superior one taking into consideration the obtained results and temporal complexity. These three methods were successfully used in generic color images segmentation. In order to evaluate these segmentation algorithms, we used error measuring methods that quantify the consistency between them. These measures allow a principled comparison between segmentation results on different images, with differing numbers of regions generated by different algorithms with different parameters.

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“…In [1] one determined the normalized weight of an edge by using the smallest weight incident on the vertices touching that edge. Other methods for planar images [2], [3] use an adaptive criterion that depends on local properties rather than global ones.…”

Section: Iintroduction and Related Workmentioning

confidence: 99%

Efficient Volumetric Segmentation Method

Burdescu¹,

Stănescu²,

Brezovan³

et al. 2014

Annals of Computer Science and Information Systems

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--In this paper we extend our previous work for planar images by adding a new step in the volumetric segmentation algorithm that allows us to determine regions closer to it. There are huge of papers for planar images and segmentation methods and most of them are graph-based for planar images and very few papers for volumetric segmentation methods. However, even if image segmentation is a heavily researched field, extending the algorithms to spatial has been proven not to be an easy task. A true volumetric segmentation remains a difficult problem to tackle due to the complex nature of the topology of spatial objects, the huge amount of data to be processed and the complexity of the algorithms that scale with the new added dimension. The problem of partitioning images into homogenous regions or semantic entities is a basic problem for identifying relevant objects. Visual segmentation is related to some semantic concepts because certain parts of a scene are pre-attentively distinctive and have a greater significance than other parts. A number of approaches to segmentation are based on finding compact regions in some feature space. A recent technique using feature space regions first transforms the data by smoothing it in a way that preserves boundaries between regions. The key to the whole own algorithm of volumetric segmentation is the honeycomb cells. The pre-processing module is used mainly to blur the initial RGB spatial image in order to reduce the image store and to make algorithms to be efficient. Then the volumetric segmentation module creates virtual cells of prisms with tree-hexagonal structure defined on the set of the image voxels of the input spatial image and a volumetric grid graph having tree-hexagons as cells of vertices. Early graph-based methods use fixed thresholds and local measures in finding a volumetric segmentation.Index terms-Volumetric Segmentation; Graph-based segmentation; Color segmentation; Syntactic segmentation I.INTRODUCTION AND RELATED WORKSHERE is a wide range of computational vision problems for planar images that could use of segmented images. The problem of partitioning images into homogenous regions or semantic entities is a basic problem for identifying relevant objects. Higher-level problems such as object recognition and image indexing can also make use of segmentation results in matching, to address problems such as figure-ground separation and recognition by parts. In both intermediate level and higher-level vision problems, contour detection of objects in real images is a fundamental problem. However the problems of planar image segmentation and grouping remain great challenges for computer vision. As a consequence we consider that a spatial segmentation method can detect visual objects from images if it can detect at least the most objects. We develop a visual feature-based method which uses a virtual spatial graph constructed on cells of prisms with treehexagonal structure containing half of the image voxels in order to determine a forest of spanning trees fo...

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Graph theoretical clustering based on limited neighbourhood sets

Cited by 166 publications

References 27 publications

Locally-scaled spectral clustering using empty region graphs

Locally-scaled spectral clustering using empty region graphs

A comparative study of some methods for color medical images segmentation

Efficient Volumetric Segmentation Method

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