An efficient algorithm for approximated self-similarity joins in metric spaces

2020 ◽  
Vol 91 ◽  
pp. 101510 ◽  
Author(s):  
Sebastián Ferrada ◽  
Benjamin Bustos ◽  
Nora Reyes
Fractals ◽  
2017 ◽  
Vol 25 (02) ◽  
pp. 1750021
Author(s):  
R. K. ASWATHY ◽  
SUNIL MATHEW

Self-similarity is a common tendency in nature and physics. It is wide spread in geo-physical phenomena like diffusion and iteration. Physically, an object is self-similar if it is invariant under a set of scaling transformation. This paper gives a brief outline of the analytical and set theoretical properties of different types of weak self-similar sets. It is proved that weak sub self-similar sets are closed under finite union. Weak sub self-similar property of the topological boundary of a weak self-similar set is also discussed. The denseness of non-weak super self-similar sets in the set of all non-empty compact subsets of a separable complete metric space is established. It is proved that the power of weak self-similar sets are weak super self-similar in the product metric and weak self-similarity is preserved under isometry. A characterization of weak super self-similar sets using weak sub contractions is also presented. Exact weak sub and super self-similar sets are introduced in this paper and some necessary and sufficient conditions in terms of weak condensation IFS are presented. A condition for a set to be both exact weak super and sub self-similar is obtained and the denseness of exact weak super self similar sets in the set of all weak self-similar sets is discussed.


2012 ◽  
Vol 5 (12) ◽  
pp. 1922-1925 ◽  
Author(s):  
Yasin N. Silva ◽  
Spencer Pearson

2013 ◽  
Vol 25 (8) ◽  
pp. 1916-1929 ◽  
Author(s):  
Wei Wang ◽  
Jianbin Qin ◽  
Chuan Xiao ◽  
Xuemin Lin ◽  
Heng Tao Shen

2008 ◽  
Vol 100 (7) ◽  
Author(s):  
M. Ángeles Serrano ◽  
Dmitri Krioukov ◽  
Marián Boguñá

Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.


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