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Book ChapterDOI

Uncertainty-Based Spatial Data Clustering Algorithms for Image Segmentation

01 Jan 2016-pp 209-227
TL;DR: This chapter focuses on discussing some of the spatial data clustering algorithms developed so far and their applications mainly in the area of image segmentation.
Abstract: Data clustering has been an integral and important part of data mining . It has wide applications in database anonymization, decision making, image processing and pattern recognition, medical diagnosis, and geographical information systems, only to name a few. Data in real-life scenario are having imprecision inherent in them. So, early crisp clustering techniques are very less efficient. Several imprecision-based models have been proposed over the years. Of late, it has been established that the hybrid models obtained as combination of these imprecise models are far more efficient than the individual ones. Several clustering algorithms have been put forth using these hybrid models. It is also found that conventional fuzzy clustering algorithms fail in incorporating the spatial information. This chapter focuses on discussing some of the spatial data clustering algorithms developed so far and their applications mainly in the area of image segmentation.
References
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Book
01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

52,705 citations

Journal ArticleDOI
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.

13,376 citations

Proceedings ArticleDOI
20 Jun 2005
TL;DR: A new measure, the method noise, is proposed, to evaluate and compare the performance of digital image denoising methods, and a new algorithm, the nonlocal means (NL-means), based on a nonlocal averaging of all pixels in the image is proposed.
Abstract: We propose a new measure, the method noise, to evaluate and compare the performance of digital image denoising methods. We first compute and analyze this method noise for a wide class of denoising algorithms, namely the local smoothing filters. Second, we propose a new algorithm, the nonlocal means (NL-means), based on a nonlocal averaging of all pixels in the image. Finally, we present some experiments comparing the NL-means algorithm and the local smoothing filters.

6,804 citations

Journal ArticleDOI
TL;DR: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster which can be used to infer the appropriateness of data partitions.
Abstract: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster. The measure can be used to infer the appropriateness of data partitions and can therefore be used to compare relative appropriateness of various divisions of the data. The measure does not depend on either the number of clusters analyzed nor the method of partitioning of the data and can be used to guide a cluster seeking algorithm.

6,757 citations

Journal ArticleDOI
TL;DR: It is argued that both notions of a rough set and a fuzzy set aim to different purposes, and it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems.
Abstract: The notion of a rough set introduced by Pawlak has often been compared to that of a fuzzy set, sometimes with a view to prove that one is more general, or, more useful than the other. In this paper we argue that both notions aim to different purposes. Seen this way, it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems. First, one may think of deriving the upper and lower approximations of a fuzzy set, when a reference scale is coarsened by means of an equivalence relation. We then come close to Caianiello's C-calculus. Shafer's concept of coarsened belief functions also belongs to the same line of thought. Another idea is to turn the equivalence relation into a fuzzy similarity relation, for the modeling of coarseness, as already proposed by Farinas del Cerro and Prade. Instead of using a similarity relation, we can start with fuzzy granules which make a fuzzy partition of the reference scale. The main contribut...

2,452 citations