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mfrstats

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NAME

mfrstats - Computes statistics of populations of multiple fibre directions.

SYNOPSIS

mfrstats -voxels <num voxels> [options]

DESCRIPTION

Reads in the output of sfpeaks and computes statistics of the distribution of peak directions and shape properties in the results. Used mostly with simulations for performance analysis or calibration.

The output is:

- number of trials (voxels in input),
- fraction of successful trials (see below)
- mean mean(SF)
- std mean(SF)
- mean std(SF)
- std std(SF)
- for each direction
   - mean direction (x, y, z),
   - mean dyadic eigenvalues (l1, l2, l3),
   - mean SF value,
   - std SF value,
   - mean SF largest Hessian eigenvalue
   - std SF largest Hessian eigenvalue
   - mean SF smallest Hessian eigenvalue
   - std SF smallest Hessian eigenvalue

Note that the order in which the multiple fibre reconstructions output multiple directions is arbitrary, so we need to cluster the directions into those which correspond. This program uses a minor generalization of the simple iterative algorithm described in Alexander and Barker, NeuroImage 27 2005 to associate corresponding directions from each trial.

A trial is considered successful if the sfpeaks consistency flag is one and the number of peaks is greater than or equal to the expected number, which is provided by the user with the -expect option. Statistics are computed only over successful trials.

The dyadic of a direction n is the 3x3 matrix n n^T. The mean dyadic is the average the the dyadics for corresponding directions over all trials. The first eigenvalue kappa_1 of the mean dyadic indicates the concentration of the population of directions; the closer kappa_1 is to one the greater the concentration. Another common concentration statistic, used for example in Alexander and Barker, NeuroImage 27 2005, is gamma = -log(1-kappa_1).

EXAMPLES

Here are some examples using synthetic data with q-ball.

qballmx -schemefile test/bmx7.scheme > /tmp/BMX7_QBMX.Bdouble

datasynth -voxels 20 -testfunc 1 -schemefile test/bmx7.scheme -snr 16 | linrecon - test/bmx7.scheme /tmp/BMX7_QBMX.Bdouble -normalize | sfpeaks -inputmodel rbf -rbfpointset 246 -density 100 | mfrstats -expect 1 -voxels 20 | double2txt

Outputs the following:

2.000000E01    Number of trials

1.000000E00    Fraction of successful trials (with the right number of peaks)

2.581409E00    Mean of the mean ODFs

6.621930E-02   Std of the mean ODFs

3.656060E-01   Mean of the std ODFs

2.705766E-02   Std of the std ODFs

9.997683E-01   |

-1.486494E-02  | Mean principal direction is along x.

-1.556928E-02  |

9.990123E-01   :

6.524040E-04   : Mean dyadic eigenvalues.  ppa_1 is 0.9990123

3.352620E-04   :

4.249405E00    Mean value at peak

1.190887E-01   Std value at peak

-7.553887E00   Mean largest Hessian eigenvalue at peak

1.252532E00    Std largest Hessian eigenvalue at peak

-9.320753E00   Mean smallest Hessian eigenvalue at peak

1.072040E00    Std smallest Hessian eigenvalue at peak

0.000000E00
:              The rest of the output is zero, as each ODF has only one peak

0.000000E00

The following is a simple investigation of how the direction concentration varies with noise level. This time we use a test function with two directions, which q-ball finds harder to reconstruct. Note how shredder pulls out the tenth number from each output, which is the first eigenvalue of the mean dyadic, kappa_1. As expected, kappa_1 and thus the direction concentration, increases with SNR.

for snr in 4 8 12 16 20 24 28 32; do echo SNR is $snr kappa1 is; datasynth -voxels 20 -testfunc 3 -schemefile test/bmx7.scheme -snr $snr | linrecon - test/bmx7.scheme /tmp/BMX7_QBMX.Bdouble -normalize | sfpeaks -inputmodel rbf -rbfpointset 246 -density 100 | mfrstats -expect 2 -voxels 20 | shredder $((8*9)) 8 10000 | double2txt; done

SNR is 4 kappa1 is
7.979403E-01
SNR is 8 kappa1 is
9.448329E-01
SNR is 12 kappa1 is
9.734752E-01
SNR is 16 kappa1 is
9.878569E-01
SNR is 20 kappa1 is
9.943226E-01
SNR is 24 kappa1 is
9.964570E-01
SNR is 28 kappa1 is
9.975895E-01
SNR is 32 kappa1 is
9.982465E-01

Similar examples using PASMRI. For PASMRI, we stick with the default density of 1000 in sfpeaks, since the functions are spikier so peaks are harder to find.

datasynth -voxels 20 -testfunc 1 -schemefile test/bmx7.scheme -snr 16 | mesd -schemefile test/bmx7.scheme -filter PAS 1.4 | sfpeaks -inputmodel maxent -mepointset 54 | mfrstats -expect 1 -voxels 20 | double2txt

Outputs the following:

2.000000E01    Number of trials

1.000000E00    Fraction of successful trials (with the right number of peaks)

9.735838E-18   Mean of the mean PASs

4.243754E-17   Std of the mean PASs

1.871073E-31   Mean of the std PASs

8.155818E-31   Std of the std PASs

9.999753E-01   |

-7.003564E-03  | Mean principal direction is along x.

6.280887E-04   |

9.989441E-01   :

6.807674E-04   : Mean dyadic eigenvalues.  ppa_1 is 0.9989441

3.750962E-04   :

1.940459E-15   Mean value at peak

8.458267E-15   Std value at peak

-3.890602E-13  Mean largest Hessian eigenvalue at peak

1.695874E-12   Std largest Hessian eigenvalue at peak

-3.843908E-13  Mean smallest Hessian eigenvalue at peak

1.675521E-12   Std smallest Hessian eigenvalue at peak

0.000000E00
:              The rest of the output is zero, as each ODF has only one peak

0.000000E00

How the direction concentration varies with noise level for PAS:

for snr in 4 8 12 16 20 24 28 32; do echo SNR is $snr kappa1 is; datasynth -voxels 20 -testfunc 3 -schemefile test/bmx7.scheme -snr $snr | mesd -schemefile test/bmx7.scheme -filter PAS 1.4 | sfpeaks -inputmodel maxent -mepointset 54 | mfrstats -expect 2 -voxels 20 | shredder $((8*9)) 8 10000 | double2txt; done

SNR is 4 kappa1 is
8.640165E-01
SNR is 8 kappa1 is
9.704359E-01
SNR is 12 kappa1 is
9.928484E-01
SNR is 16 kappa1 is
9.942860E-01
SNR is 20 kappa1 is
9.977806E-01
SNR is 24 kappa1 is
9.975917E-01
SNR is 28 kappa1 is
9.989544E-01
SNR is 32 kappa1 is
9.992704E-01

OPTIONS

Standard IO options, as listed in modelfit(1).
-voxels <number of voxels>: The number of voxels in the input data. Defaults to one, so must be specified.
-expect <num. directions>: Specify the expected number of directions. By default the expected number is set to -1, so all trials are successful unless sfpeaks failed.
-numpds <index>: The number of principal directions per voxel in the input (ie, output of sfpeaks(1)). The default is 3, as in sfpeaks(1).

AUTHORS

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

BUGS

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Time: 02:07:11 GMT, December 04, 2017

Mfrstats