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sfkurtosis

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NAME

sfkurtosis - Computes an index of kurtosis of spherical functions.

SYNOPSIS

sfkurtosis -inputmodel <sh|rbf|maxent> [options]

DESCRIPTION

Computes the kurtosis of any input spherical function. The kurtosis of a function f is
the fourth root of int(f(x) - F)^4/int(f^4(x)), where F = int(f(x)) and the integrals are all over the unit sphere, normalized by the anisotropy of f (see sfanis(1)). The program approximates the integrals by summing over a set of around 8000 points evenly distributed on the sphere. To decrease computation time, the size of the point set can be reduced using the -pointset option.

EXAMPLES

Here are some examples using synthetic data.

Create a synthetic data set:

datasynth -testfunc 3 -snr 16 -voxels 4 -schemefile test/bmx7.scheme > T3_BMX7.Bfloat

Fit the spherical harmonics with maximum order 2 and compute the kurtosis:

shfit -order 2 -schemefile test/bmx7.scheme < T3_BMX7.Bfloat | sfkurtosis -inputmodel sh -order 2 | double2txt

1.150778E00
1.151699E00
1.152421E00
1.138931E00

Try with maximum order 4: shfit -order 4 -schemefile test/bmx7.scheme < T3_BMX7.Bfloat | sfkurtosis -inputmodel sh -order 4 | double2txt

1.156047E00
1.176902E00
1.202380E00
1.149478E00

Repeat using PASMRI: mesd -filter PAS 1.4 -schemefile test/bmx7.scheme < T3_BMX7.Bfloat | sfkurtosis -inputmodel maxent -filter PAS 1.4 -mepointset 54 | double2txt 9.980777E-01 9.980698E-01 9.905318E-01 9.991480E-01

OPTIONS

-inputmodel <sh|rbf|maxent|dt>

Tells the program what type of functions are input. Currently supported options are:

sh - Spherical harmonic series. (Must specify -order.)

maxent - Maximum entropy representations output by mesd. (Must specify -filter and -mepointset.)

rbf - Sums of radial basis functions. (Must specify rbf parameters, eg -rbfsigma, and -rbfpointset.)

-pointset <|1|2|3|4|5|6|7>

Choose the point set used for the numerical integration. The point sets have sizes:

0 - 1082
1 - 1922
2 - 4322
3 - 8672
4 - 15872
5 - 32672
6 - 72032
7 - 78032

The default is point set 3.

BUGS

AUTHOR

Danny Alexander <camino@cs.ucl.ac.uk>

This document was created by man2html, using the manual pages.
Time: 02:07:11 GMT, December 04, 2017

Sfkurtosis