MEASURING THE FRACTAL DIMENSION OF SIGNALS - MORPHOLOGICAL COVERS AND ITERATIVE OPTIMIZATION

MARAGOS, P; SUN, FK

dc.contributor.author	MARAGOS, P	en
dc.contributor.author	SUN, FK	en
dc.date.accessioned	2014-03-01T01:09:27Z
dc.date.available	2014-03-01T01:09:27Z
dc.date.issued	1993	en
dc.identifier.issn	1053-587X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/10993
dc.subject	Computational Complexity	en
dc.subject	Discrete Time	en
dc.subject	Fractal Dimension	en
dc.subject	fractional brownian motion	en
dc.subject	General Methods	en
dc.subject	Geometric Structure	en
dc.subject	Morphological Operation	en
dc.subject	Multiple Scales	en
dc.subject	Optimal Method	en
dc.subject	Time Series Data	en
dc.subject.classification	Engineering, Electrical & Electronic	en
dc.subject.other	TEXTURE	en
dc.title	MEASURING THE FRACTAL DIMENSION OF SIGNALS - MORPHOLOGICAL COVERS AND ITERATIVE OPTIMIZATION	en
heal.type	journalArticle	en
heal.identifier.primary	10.1109/TSP.1993.193131	en
heal.identifier.secondary	http://dx.doi.org/10.1109/TSP.1993.193131	en
heal.language	English	en
heal.publicationDate	1993	en
heal.abstract	Fractals can model many classes of time-series data. The fractal dimension is an important characteristic of fractals that contains information about their geometrical structure at multiple scales. The covering methods are a class of efficient approaches to measure the fractal dimension of an arbitrary fractal signal by creating multiscale covers around the signal's graph. In this paper we develop a general method that uses multiscale morphological operations with varying structuring elements to unify and extend the theory and digital implementations of covering methods. It is theoretically established that, for the fractal dimension computation, covering one-dimensional signals with planar sets is equivalent to morphologically transforming the signal by one-dimensional functions, which reduces the computational complexity from quadratic in the signal's length to linear. Then a morphological covering algorithm is developed and applied to discrete-time signals synthesized from Weierstrass functions, fractal interpolation functions, and fractional Brownian motion. Further, for deterministic parametric fractals depending on a single parameter related to their dimension, we develop an optimization method that starts from an initial estimate and iteratively converges to the true fractal dimension by searching in the parameter space and minimizing a distance between the original signal and all such signals from the same class. Experimental results are also provided to demonstrate the good performance of the developed methods.	en
heal.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC	en
heal.journalName	IEEE TRANSACTIONS ON SIGNAL PROCESSING	en
dc.identifier.doi	10.1109/TSP.1993.193131	en
dc.identifier.isi	ISI:A1993KG14800010	en
dc.identifier.volume	41	en
dc.identifier.issue	1	en
dc.identifier.spage	108	en
dc.identifier.epage	121	en