Rettig, Oliver

06-13-2008, 01:15 AM

Hallo,

>VICON software (Workstation or Nexus) comes with a Woltring filtering

routine, with predefined parameters (in the

>DynamicPluginGait pipeline of Nexus: of MSE=10). Unfortunately I could

not find any information on the properties

>of the Woltring filter and on the effect of different MSE values. Who

can help me with that?

We are using Vicon Workstation and not Nexus but I think the filtering

should be similar.

It is same years ago I was engaged with the woltring filter and I got

some help from Ton van den Bogert.

>On isbweb.org I found a rather vague statement on the equivalence of

Woltring and Butterworth filtering (for

>certain kinds of data) - what is the relationship, in particular, is

there a direct translation between the MSE-

>parameter for Woltring and the cut-off frequency for the Butterworth?

You are correct, the smoothing splines of the Woltring filter are

equivalent to a butterworth your apply twice to your time series

(starting from the first frame to the last and a second time from the

last to the first frame).

Ton van den Bogert has sent me the following formulars and

explainations:

----------------

The corresponding transfer function is H(w) = [1 + (w/wo)^2M]^-1, where

w is the frequency, wo = (p*T)^(-0.5/M) the filter's cut-off

frequency, p the smoothing parameter, T the sampling interval, and 2M

the order of the spline. If T is expressed in seconds, the

frequencies are expressed in radians/second.

The equation for the transfer function has the property H(w0)= 0.5.

This is because it is a double Butterworth filter (applied twice).

Cut-off frequency is usually defined as the frequency at which

H=1/sqrt(2), and this is why Tony Reina and I have an extra factor in

the equation.

You can easily verify the correctness of your spline smoothing by

processing a sine wave signal at the cut-off frequency. If it comes out

as a sine wave with its amplitude reduced by a factor 1.41 (=sqrt(2)),

you have used the correct VAL.

-----------------

>Do you have recommendations on choosing MSE for the Woltring filter -

in this specific case for kinematic walking

>data sampled at 200 Hz?

My experience is that it is better to use fix cut off frequencies than

to use the automatic estimation algorithm suggested in the original work

of Woltring. For same patients I got strange results by the automatic

algorithm and for our work in clinical routine it is more important to

have stable results.

We are sampling with 120Hz and I use my own Java implementation of the

Woltring filter (not the code shipted with the vicon system, but I can

reproduce their values). So it is possible to choose the paramters

different to the segments the markers are placed on. The velocities of

the markers on the feet and lower-arms are higher that e.g. the pelvis.

So I use higher cut off frequencies for the distal segment markers. E.g.

7Hz for the pelvis and 12Hz for the feet. I am also interested which

values other groups are using or if there are some recommentations

because I have not systematically optimized the cut off frequencies.

Oliver

>VICON software (Workstation or Nexus) comes with a Woltring filtering

routine, with predefined parameters (in the

>DynamicPluginGait pipeline of Nexus: of MSE=10). Unfortunately I could

not find any information on the properties

>of the Woltring filter and on the effect of different MSE values. Who

can help me with that?

We are using Vicon Workstation and not Nexus but I think the filtering

should be similar.

It is same years ago I was engaged with the woltring filter and I got

some help from Ton van den Bogert.

>On isbweb.org I found a rather vague statement on the equivalence of

Woltring and Butterworth filtering (for

>certain kinds of data) - what is the relationship, in particular, is

there a direct translation between the MSE-

>parameter for Woltring and the cut-off frequency for the Butterworth?

You are correct, the smoothing splines of the Woltring filter are

equivalent to a butterworth your apply twice to your time series

(starting from the first frame to the last and a second time from the

last to the first frame).

Ton van den Bogert has sent me the following formulars and

explainations:

----------------

The corresponding transfer function is H(w) = [1 + (w/wo)^2M]^-1, where

w is the frequency, wo = (p*T)^(-0.5/M) the filter's cut-off

frequency, p the smoothing parameter, T the sampling interval, and 2M

the order of the spline. If T is expressed in seconds, the

frequencies are expressed in radians/second.

The equation for the transfer function has the property H(w0)= 0.5.

This is because it is a double Butterworth filter (applied twice).

Cut-off frequency is usually defined as the frequency at which

H=1/sqrt(2), and this is why Tony Reina and I have an extra factor in

the equation.

You can easily verify the correctness of your spline smoothing by

processing a sine wave signal at the cut-off frequency. If it comes out

as a sine wave with its amplitude reduced by a factor 1.41 (=sqrt(2)),

you have used the correct VAL.

-----------------

>Do you have recommendations on choosing MSE for the Woltring filter -

in this specific case for kinematic walking

>data sampled at 200 Hz?

My experience is that it is better to use fix cut off frequencies than

to use the automatic estimation algorithm suggested in the original work

of Woltring. For same patients I got strange results by the automatic

algorithm and for our work in clinical routine it is more important to

have stable results.

We are sampling with 120Hz and I use my own Java implementation of the

Woltring filter (not the code shipted with the vicon system, but I can

reproduce their values). So it is possible to choose the paramters

different to the segments the markers are placed on. The velocities of

the markers on the feet and lower-arms are higher that e.g. the pelvis.

So I use higher cut off frequencies for the distal segment markers. E.g.

7Hz for the pelvis and 12Hz for the feet. I am also interested which

values other groups are using or if there are some recommentations

because I have not systematically optimized the cut off frequencies.

Oliver