Re: Big problems using Bill Atkinssons new Eye-1 profiles
Re: Big problems using Bill Atkinssons new Eye-1 profiles
- Subject: Re: Big problems using Bill Atkinssons new Eye-1 profiles
- From: Graeme Gill <email@hidden>
- Date: Wed, 08 Feb 2006 01:24:27 +1100
edmund ronald wrote:
Based on my experience writing interpolation software for my Ph.D, I
would say that that too many data points may create overfitting, with
the interpolation surface moving around wierdly and and folding over
itself. Or what could be called a "hegehog" profile. Few data points
should rather create a smooth but inaccurate profile.
I'm not really sure what you mean by "overfitting" in this context.
Generally fitting to real world data may be under constrained or
over constrained. A good model and fitting method will cope with
either situation. In fitting multi-dimensional color values, the
overall problem is often under constrained (because we've got 33^3
or 17^4 parameters, and a lot less measured points), but can be
locally over constrained (where two readings are very close in
device space, but differ in CIE space). Typically under constraint
is solved by applying some behavioural constraint such as smoothness,
and over constraint is solved by weighting the contributions from
nearby samples.
Real world readings contain noise or random factors. A good
fit will take this into account as well, aiming for something
like a maximum likelihood fit. Typically this is equivalent to
filtering the data with some form of smoothing filter,
the degree of smoothing depending on the estimated statistics
of the reading errors. Inadequate filtering or smoothing will
result in the excessive reproduction by the model of the random
artefacts of the particular set of readings used. Such a fit is not
a maximum likelihood one though.
So in and of itself, using more readings should not cause any problems,
in fact it adds information, reducing uncertainty. A poor fitting
method (one that doesn't allow for the error statistics of the readings)
may show more artefacts as the number of samples is increased.
Graeme Gill.
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