View Full Version : Re: Summary - Curve Normalisation

Ingram Murray
02-25-1999, 08:40 PM
Dear subscribers,
Many thanks to all who replied to my question on curve normalisation,
which though not ideal, seems to be a necessary step in the
summarising of motion data.
Several different approaches are available for carrying out this

An extensive set of Fortran routines for the process described by A.
Kneip and Th. Gasser (1992) and K. Wang and Th. Gasser (1996),
(1997) can be downloaded from:
and appear to be very useful.

The Matlab 'interpft' function can be used to perform

Andre Rodacki suggested the use of an Excel macro.

The "SPLUS" software can also be used to implement normalisation

As well as the the reference given by Drew Harrison for Rice J.A.,
Silverman B.W., (1991), the paper:

Leurgans,S.E., Moyeed,R.A.,Silverman B.W (1993) Canonical
correlation analysis when the data are curves. Journal of the Royal
Statistical Society, Bath. Vol 55 (3) pp. 725-740.

May also be of relevance when dealing with curve data sets.

My original message was:
>Dear subscribers,
> I am interested in the techniques used by the biomechanical
>community for 'normalising' or 'registering' the curves obtained,
>of joint angle, force or moment variation during human motion
>analysis studies.
> The aim of this process is to overcome the offsets between
>structurally similar curves due to differences in, for instance, the
>speed of performance of the movements between subjects.
> This then allows 'average' curves to be calculated without
>removing real properties of these curves.
> Methods for this process are described in:
>A. Kneip and Th. Gasser (1992). Statistical tools to analyze data
representing a sample of curves. Annals of Statistics 20 1266-1305.
>K. Wang and Th. Gasser (1997). Alignment of curves by dynamic
>time warping. Annals of Statistics 25, 1251-1276.
>K. Wang and Th. Gasser (1996). Asymptotic and Bootstrap
>confidence bounds for structural average of curves.
>submitted to Annals of Statistics.
>and I am also aware of the use of polynomial expansions and splines
>or Fourier analysis for the normalising of data to one hundred
>percentage points.
>I was wondering if subscribers could express their opinions on the
>merits or otherwise of such techniques, or suggest alternatives. I
>will submit a summary of any replies I receive.

The replies I received follow:

From: Drew Harrison *
Dear Ingram,
The points you raised about normalisation of curves are important.
These are issues, I'm sure many of us have encountered in analysing
our experimental data. A good solution appears to be to use of splines
(usually cubic splines) fitted to the data set of each subject and
re-sample the for a prescribed number of points. Perhaps a Matlab
routine could be made available to all subscribers to do this task -
maybe someone has done this already and would be prepared to share?
The other (more) important issue you raise is related to the
difficulties of analysing data that are curves. Usually our
experiments focus on testing hypotheses based on data taken from
curves (e.g. range of movement of knee joint during the gait cycle).
But, it is more difficult I think, to test the hypotheses that two or
more sets of mean curves may be significantly different. Perhaps the
work of Rice and Silverman is relevant here. Since much biomechanics
research is based on curve data sets maybe there should be more
emphasis on finding adequate solutions to this.

Rice J.A., Silverman B.W., (1991) Estimating the mean and covariance
structure nonparametrically when the data are curves. Journal of the
Royal Statistical Society, Bath. Vol 53 (1) pp. 233-243.

From: Vladimir Zatsiorsky
Professor of Kinesiology, The Pennsylvania State University
Dear Ingram:
Look at the paper by Kanatani-Fujimoto, K., Lazareva,
B.V., Zatsiorsky, V.M. Local proportional scaling of time-series
data. Motor Control, v.1, #1, pp. 20-43. Best.

From: Noel Lythgo
School of Human Movement,Australian Catholic University - Christ
Campus, Melbourne, Australia
Dear Ingram,
I am interested in the replies that you receive. I am sure that they
would include the procedure of ensemble averaging (normalising data to
a 100% cycle for each participant). If not not let me know and i will
forward information.

From: "Calame, Christian"
Product Manager Biomechanics, Kistler Instrumente
Dear Sir
Maybe I am a little biased and also I am not a researcher but we see
too many of our customers doing terrible things with normalizations
like you explain. For example they "overlay" force-time curves of
different walking speeds and "squeeze" them into the same timescale by
normalizing them to 100% contact time. This can not be correct since
different walking speeds result in entirely different dynamics - which
of course can still be seen in the magnitude of the force. However
after a little bit of averaging these differences are all gone and
"the curves look real nice and like in the literature".
As I told you - maybe I am a little biased;-)

From: Rodacki@aol.com
Dear Ingran:
We (biomechanicists) normaly use the time scale to reduce the number
of data points to a 100% of the movement. This is one of the more
usual procedures. in this case, you will need to interpolate the
number of points with respect to time and thus obtain 100 points.
Therefore, the problems of different speeds of the movement. I have
build a macro to run in the excel 7.0 (Office 97) that performs linear
interpolation. if you have interest to try this macro I can send it in
attachment with some instructions to make it run properly. Other
softwares are also suitable to perform splines and other methods of
data interpolation (or extrapolation).

Thanks once again.

Ingram Murray
Room G32
Stephenson Building
University of Newcastle upon Tyne
Newcastle upon Tyne

Tel: 0191 222 6000 ext.6193
Fax: 0191 222 8600
email: i.a.murray@ncl.ac.uk
www: http://www.ncl.ac.uk/crest/IMpers

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