Surface Laplacian and fractal brain mapping

Sebastián, María Victoria; Navascués, M. A.; Valdizán, J R

doi:10.1016/j.cam.2005.04.053

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…2 shows the plot between the reproduction of dimension values calculated from this algorithm and known fractal dimension values. The fractal dimension estimated with 14 channels for this method when the synthetic signal is contaminated with white noise, yielding a signal to noise ratio (SNR) of 10 db [3]. Fig.…”

Section: Resultsmentioning

confidence: 99%

“…The reliability of the algorithm was tested with synthetic signal ranged from 1.001 to 1.099 using Weierstrass functions with known FD [3]. The Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Here we have used cluster analysis to find groups of electrode sites with similar and minimal distance (or nearest neighbour) of its fractal dimensions. There are large numbers of clustering algorithms used by the researchers [3]. Among them, we have used the effective clustering algorithm known as "K-means algorithm" for grouping the electrode sites.…”

Section: Estimation Of Critical Brain Sitesmentioning

confidence: 99%

“…The fractal dimension estimated from using autocorrelation is related to box-dimension of the signal. The short term analysis of EEG signals and their dimension analysis will provide the measure of rate of the complexity [3]. The aim of the paper is to calculate the fractal dimension of the brain activity and applying clustering techniques to locate the critical cortical site.…”

Section: Introductionmentioning

confidence: 99%

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Detection of Critical Brain Sites Using Fractal Analysis

Uthayakumar

Paramanathan

2006

2006 International Conference on Advanced Computing and Communications

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Epilepsy is a neurological disorder involving recurrent abnormal discharges of neurons that produce epileptic seizures, affecting the human brain. Locating the exact seizure portion in the brain is very important for predicting the reoccurrence of epileptic seizure. Many techniques have been usedfor seizure prediction, but they are computationally expensive. In this paper we propose the Nonlinear Mathematical technique (simple to calculate) from the theory of chaos, fractals and clustering methods to locate the brain sites by analyzing the Electroencephalogram signals.

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Section: Resultsmentioning

confidence: 99%

“…The reliability of the algorithm was tested with synthetic signal ranged from 1.001 to 1.099 using Weierstrass functions with known FD [3]. The Fig.…”

Section: Resultsmentioning

confidence: 99%

Section: Estimation Of Critical Brain Sitesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Detection of Critical Brain Sites Using Fractal Analysis

Uthayakumar

Paramanathan

2006

2006 International Conference on Advanced Computing and Communications

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“…In Ref. 3, we worked a simplified theoretical model of electric potential and we found that the errors committed were increased with the order of differentiability of the functions used (spline surfaces solving an integral optimization problem 4 ). This fact convinced us to undertake (with this work) the construction of maps with the tools of the fractal methodology which, in general, provide non-smooth geometric elements.…”

Section: Introductionmentioning

confidence: 99%

Fitting Fractal Surfaces on Non-Rectangular Grids

Navascués

Sebastián

2008

Fractals

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In a complex society, the visualization and interpretation of large amounts of data acquires an increasing importance. This can be done at once by means of two-or three-dimensional maps. To approach this problem, we undertake the construction of several variable fractal functions. In the first place, we introduce real fractal functions defined as perturbations of the classical ones. These basic mappings allow us to compute multidimensional approximations of experimental variables by means of linear combinations of products of fractal functions of Legendre type. The paper proposes a method of non-smooth representation for a large number of three-dimensional data on non-uniform grids. The procedures described are applied in the last part of the paper to the implementation of fitting maps for brain electrical activity.

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