Thread Subject: Curve fitting a 3D data set

I'm pretty new in the Matlab-world. How do I make curve fitting on a
3D data set (x, y, z)? Do I need a special toolbox for it?

Thanx for your help :)
Sanne

Sanne Christensen wrote:

> I'm pretty new in the Matlab-world. How do I make curve fitting on a
> 3D data set (x, y, z)? Do I need a special toolbox for it?
>
> Thanx for your help :)
> Sanne

The other day I came across:

http://www.mathworks.nl/matlabcentral/fileexchange/loadFile.do?objectId=6232&objectType=FILE

It seems to do something related.

Also see:

http://www.mathworks.com/access/helpdesk/help/toolbox/curvefit/curvefit.shtml

--
Roy Schestowitz
http://schestowitz.com

My understanding to you question is that you have a known form of function
with some unknown parameters. And you have bunch of 3D data. You want to fit
those data to get the parameters??

If so, the optimization toolbox can help you out. If you can provide more
details, I would be happy to give it a try.

Rentian

"Sanne Christensen" <sc_trold@hotmail.com> wrote in message
news:eef3579.-1@webx.raydaftYaTP...
> I'm pretty new in the Matlab-world. How do I make curve fitting on a
> 3D data set (x, y, z)? Do I need a special toolbox for it?
>
> Thanx for your help :)
> Sanne

That is exactly what I am trying to do. My data should fit to
something like a poly of second order (parabola) and I could only
find functions (polyfit) which could do it in 2D

Teddy Hsung wrote:
>
>
> My understanding to you question is that you have a known form of
> function
> with some unknown parameters. And you have bunch of 3D data. You
> want to fit
> those data to get the parameters??
>
> If so, the optimization toolbox can help you out. If you can
> provide more
> details, I would be happy to give it a try.
>
> Rentian
>
> "Sanne Christensen" <sc_trold@hotmail.com> wrote in message
> news:eef3579.-1@webx.raydaftYaTP...
>> I'm pretty new in the Matlab-world. How do I make curve fitting
> on a
>> 3D data set (x, y, z)? Do I need a special toolbox for it?
>>
>> Thanx for your help :)
>> Sanne
>
>
>

In article <eef3579.2@webx.raydaftYaTP>,
 Sanne <sc_trold@hotmail.com> writes:
 >That is exactly what I am trying to do. My data should fit to
 >something like a poly of second order (parabola) and I could only
 >find functions (polyfit) which could do it in 2D
 >
 >Teddy Hsung wrote:
 >>
 >>
 >> My understanding to you question is that you have a known form of
 >> function
 >> with some unknown parameters. And you have bunch of 3D data. You
 >> want to fit
 >> those data to get the parameters??
 >>
 >> If so, the optimization toolbox can help you out. If you can
 >> provide more
 >> details, I would be happy to give it a try.
 >>
 >> Rentian
 >>
 >> "Sanne Christensen" <sc_trold@hotmail.com> wrote in message
 >> news:eef3579.-1@webx.raydaftYaTP...
 >>> I'm pretty new in the Matlab-world. How do I make curve fitting
 >> on a
 >>> 3D data set (x, y, z)? Do I need a special toolbox for it?
 >>>
  >>> Thanx for your help :)
 >>> Sanne
 >>
 >>
 >>

as long as only a polynomial model is to used, \ alone will do the job for you
otherwise you will need lsqcurvefit from the optimization toolbox.
but ... (x,y,z) -data: and "curvefitting" you mean indeed a curve?
not a surface? and then: which model do you have for that curve?
parametric : (a+b*t+c*t^2 ; d+e*t+f*t^2; g+h*t+i*t^2) with
t the curve parameter (how to get this?) or implicit:
(intersection of two surfaces)
 a(i)+b(i)*x+c(i)*y+d(i)*x^2+e(i)*x*y+f(i)*y^2=0 i=1,2
 plus some normalization constraints?
hth
peter


 

I guess his problem can be formulated like this:

z1 = f(x1, y1, p1,p2...)
z2 = f(x2, y2, p1,p2...)
.
.
.
zn = f(xn, yn, p1,p2...)

where f is a known form of function. p1,p2... are the parameters that he
wants to estimate.

\ (slash) function probably won't work because his function is highly
possible a nonlinear function.

p=LSQCURVEFIT(f,p0,XYDATA,ZDATA) should be able to solve this problem.

where, p is a vector [p1, p2..]', p0 is initial guess of p.

XYDATA is a matrix [x1,y1
                    x2,y2
                    .....
                    xn,yn]

ZDATA is a vector [z1, z2...zn]'

Please let us know how it works

Rentian


"Peter Spellucci" <spellucci@fb04373.mathematik.tu-darmstadt.de> wrote in
message news:cnl2d2$cd5$1@fb04373.mathematik.tu-darmstadt.de...
>
> In article <eef3579.2@webx.raydaftYaTP>,
> Sanne <sc_trold@hotmail.com> writes:
> >That is exactly what I am trying to do. My data should fit to
> >something like a poly of second order (parabola) and I could only
> >find functions (polyfit) which could do it in 2D
> >
> >Teddy Hsung wrote:
> >>
> >>
> >> My understanding to you question is that you have a known form of
> >> function
> >> with some unknown parameters. And you have bunch of 3D data. You
> >> want to fit
> >> those data to get the parameters??
> >>
> >> If so, the optimization toolbox can help you out. If you can
> >> provide more
> >> details, I would be happy to give it a try.
> >>
> >> Rentian
> >>
> >> "Sanne Christensen" <sc_trold@hotmail.com> wrote in message
> >> news:eef3579.-1@webx.raydaftYaTP...
> >>> I'm pretty new in the Matlab-world. How do I make curve fitting
> >> on a
> >>> 3D data set (x, y, z)? Do I need a special toolbox for it?
> >>>
> >>> Thanx for your help :)
> >>> Sanne
> >>
> >>
> >>
>
> as long as only a polynomial model is to used, \ alone will do the job for
> you
> otherwise you will need lsqcurvefit from the optimization toolbox.
> but ... (x,y,z) -data: and "curvefitting" you mean indeed a curve?
> not a surface? and then: which model do you have for that curve?
> parametric : (a+b*t+c*t^2 ; d+e*t+f*t^2; g+h*t+i*t^2) with
> t the curve parameter (how to get this?) or implicit:
> (intersection of two surfaces)
> a(i)+b(i)*x+c(i)*y+d(i)*x^2+e(i)*x*y+f(i)*y^2=0 i=1,2
> plus some normalization constraints?
> hth
> peter
>
>
>

MATLAB provides an easy way to calculate least-squares fits of linear
functions:

    Coefficients = Inputs \ Outputs;

...where 'Inputs' and 'Outputs' are data arrays holding the
independent and dependent variables, respectively, with variables in
columns and observations in rows.

Adding a constant term simply requires a column of ones in the
'Inputs' matrix:

    Coefficients = [ones(size(Inputs,1),1) Inputs] \ Outputs;

This process is readily extended to functions which are nonlinear, but
linear in their inputs by performing whatever transformations are
necessary on the input data before performing the fit. For instance,
if the model were to include squares and cubes of the input variables
(but no interactions), one could try:

    Coefficients = [ones(size(Inputs,1),1) Inputs Inputs.^2 Inputs.^3]
\ Outputs;

Cross-terms are more work, but it should be straightforward at this
point.


-Will Dwinnell
http://will.dwinnell.com


Sanne <sc_trold@hotmail.com> wrote in message news:<eef3579.2@webx.raydaftYaTP>...
> That is exactly what I am trying to do. My data should fit to
> something like a poly of second order (parabola) and I could only
> find functions (polyfit) which could do it in 2D
>
> Teddy Hsung wrote:
> >
> >
> > My understanding to you question is that you have a known form of
> > function
> > with some unknown parameters. And you have bunch of 3D data. You
> > want to fit
> > those data to get the parameters??
> >
> > If so, the optimization toolbox can help you out. If you can
> > provide more
> > details, I would be happy to give it a try.
> >
> > Rentian
> >
> > "Sanne Christensen" <sc_trold@hotmail.com> wrote in message
> > news:eef3579.-1@webx.raydaftYaTP...
> >> I'm pretty new in the Matlab-world. How do I make curve fitting
> on a
> >> 3D data set (x, y, z)? Do I need a special toolbox for it?
> >>
> >> Thanx for your help :)
> >> Sanne
> >
> >
> >

I still have some more pre-processing of my CT-scanned images to do
before I start on the curve fitting part, but thank you for all your
help :)

Teddy Hsung wrote:
>
>
> I guess his problem can be formulated like this:
>
> z1 = f(x1, y1, p1,p2...)
> z2 = f(x2, y2, p1,p2...)
> .
> .
> .
> zn = f(xn, yn, p1,p2...)
>
> where f is a known form of function. p1,p2... are the parameters
> that he
> wants to estimate.
>
> \ (slash) function probably won't work because his function is
> highly
> possible a nonlinear function.
>
> p=LSQCURVEFIT(f,p0,XYDATA,ZDATA) should be able to solve this
> problem.
>
> where, p is a vector [p1, p2..]', p0 is initial guess of p.
>
> XYDATA is a matrix [x1,y1
> x2,y2
> .....
> xn,yn]
>
> ZDATA is a vector [z1, z2...zn]'
>
> Please let us know how it works
>
> Rentian
>
>
> "Peter Spellucci"
<spellucci@fb04373.mathematik.tu-darmstadt.de>
> wrote in
> message news:cnl2d2$cd5$1@fb04373.mathematik.tu-darmstadt.de...
>>
>> In article <eef3579.2@webx.raydaftYaTP>,
>> Sanne <sc_trold@hotmail.com> writes:
>> >That is exactly what I am trying to do. My data should fit
to
>> >something like a poly of second order (parabola) and I
could
> only
>> >find functions (polyfit) which could do it in 2D
>> >
>> >Teddy Hsung wrote:
>> >>
>> >>
>> >> My understanding to you question is that you have a
known form
> of
>> >> function
>> >> with some unknown parameters. And you have bunch of 3D
data.
> You
>> >> want to fit
>> >> those data to get the parameters??
>> >>
>> >> If so, the optimization toolbox can help you out. If
you can
>> >> provide more
>> >> details, I would be happy to give it a try.
>> >>
>> >> Rentian
>> >>
>> >> "Sanne Christensen" <sc_trold@hotmail.com> wrote
in message
>> >> news:eef3579.-1@webx.raydaftYaTP...
>> >>> I'm pretty new in the Matlab-world. How do I make
curve
> fitting
>> >> on a
>> >>> 3D data set (x, y, z)? Do I need a special toolbox
for it?
>> >>>
>> >>> Thanx for your help :)
>> >>> Sanne
>> >>
>> >>
>> >>
>>
>> as long as only a polynomial model is to used, \ alone will do
> the job for
>> you
>> otherwise you will need lsqcurvefit from the optimization
> toolbox.
>> but ... (x,y,z) -data: and "curvefitting" you mean indeed a
> curve?
>> not a surface? and then: which model do you have for that
curve?
>> parametric : (a+b*t+c*t^2 ; d+e*t+f*t^2; g+h*t+i*t^2) with
>> t the curve parameter (how to get this?) or implicit:
>> (intersection of two surfaces)
>> a(i)+b(i)*x+c(i)*y+d(i)*x^2+e(i)*x*y+f(i)*y^2=0 i=1,2
>> plus some normalization constraints?
>> hth
>> peter
>>
>>
>>
>
>
>

Yes - I do mean a curve (when my programme is done it has to
represent a rib of a pig) :) I have looked at the lsqcurvefit, but it
seems that it also only utilises 2D data sets? (or have I missed
something? ;o))

/Sanne

Peter Spellucci wrote:
>
>
>
> In article <eef3579.2@webx.raydaftYaTP>,
> Sanne <sc_trold@hotmail.com> writes:
> >That is exactly what I am trying to do. My data should fit to
> >something like a poly of second order (parabola) and I could
only
> >find functions (polyfit) which could do it in 2D
> >
> >Teddy Hsung wrote:
> >>
> >>
> >> My understanding to you question is that you have a known
form
> of
> >> function
> >> with some unknown parameters. And you have bunch of 3D
data.
> You
> >> want to fit
> >> those data to get the parameters??
> >>
> >> If so, the optimization toolbox can help you out. If you
can
> >> provide more
> >> details, I would be happy to give it a try.
> >>
> >> Rentian
> >>
> >> "Sanne Christensen" <sc_trold@hotmail.com> wrote in
message
> >> news:eef3579.-1@webx.raydaftYaTP...
> >>> I'm pretty new in the Matlab-world. How do I make
curve
> fitting
> >> on a
> >>> 3D data set (x, y, z)? Do I need a special toolbox for
it?
> >>>
> >>> Thanx for your help :)
> >>> Sanne
> >>
> >>
> >>
>
> as long as only a polynomial model is to used, \ alone will do the
> job for you
> otherwise you will need lsqcurvefit from the optimization toolbox.
> but ... (x,y,z) -data: and "curvefitting" you mean indeed a curve?
> not a surface? and then: which model do you have for that curve?
> parametric : (a+b*t+c*t^2 ; d+e*t+f*t^2; g+h*t+i*t^2) with
> t the curve parameter (how to get this?) or implicit:
> (intersection of two surfaces)
> a(i)+b(i)*x+c(i)*y+d(i)*x^2+e(i)*x*y+f(i)*y^2=0 i=1,2
> plus some normalization constraints?
> hth
> peter
>
>
>
>

In article <eef3579.7@webx.raydaftYaTP>,
 "Sanne Christensen" <sc_trold@hotmail.com> writes:
 >Newsgroups: comp.soft-sys.matlab
 >Subject: Re: Curve fitting a 3D data set
 > Message-ID: <eef3579.7@webx.raydaftYaTP>
 >Date: Wed, 24 Nov 2004 15:47:46 -0500
 >References: <eef3579.-1@webx.raydaftYaTP> <cnjb5n$guv$1@news-int2.gatech.edu> <eef3579.2@webx.raydaftYaTP> <cnl2d2$cd5$1@fb04373.mathematik.tu-darmstadt.de>
 >Lines: 70
 >NNTP-Posting-Host: 83.88.75.69
 >MIME-Version: 1.0
 >Content-Type: text/plain; charset="ISO-8859-1"
 >Content-Transfer-Encoding: 8bit
 >Xref: news.tu-darmstadt.de comp.soft-sys.matlab:244487
 >
 >Yes - I do mean a curve (when my programme is done it has to
 >represent a rib of a pig) :) I have looked at the lsqcurvefit, but it
 >seems that it also only utilises 2D data sets? (or have I missed
 >something? ;o))
 >
 >/Sanne

the name sounds like 2D, but it can do curve fitting in 3D.
hth
peter



 >
 >Peter Spellucci wrote:
 >>
 >>
 >>
 >> In article <eef3579.2@webx.raydaftYaTP>,
 >> Sanne <sc_trold@hotmail.com> writes:
 >> >That is exactly what I am trying to do. My data should fit to
 >> >something like a poly of second order (parabola) and I could
 >only
 >> >find functions (polyfit) which could do it in 2D
 >> >
 >> >Teddy Hsung wrote:
 >> >>
 >> >>
 >> >> My understanding to you question is that you have a known
 >form
 >> of
 >> >> function
 >> >> with some unknown parameters. And you have bunch of 3D
 >data.
 >> You
 >> >> want to fit
 >> >> those data to get the parameters??
 >> >>
 >> >> If so, the optimization toolbox can help you out. If you
 >can
 >> >> provide more
 >> >> details, I would be happy to give it a try.
 >> >>
 >> >> Rentian
 >> >>
 >> >> "Sanne Christensen" <sc_trold@hotmail.com> wrote in
 >message
 >> >> news:eef3579.-1@webx.raydaftYaTP...
 >> >>> I'm pretty new in the Matlab-world. How do I make
 >curve
 >> fitting
 >> >> on a
 >> >>> 3D data set (x, y, z)? Do I need a special toolbox for
 >it?
 >> >>>
 >> >>> Thanx for your help :)
 >> >>> Sanne
 >> >>
 >> >>
 >> >>
 >>
 >> as long as only a polynomial model is to used, \ alone will do the
 >> job for you
 >> otherwise you will need lsqcurvefit from the optimization toolbox.
 >> but ... (x,y,z) -data: and "curvefitting" you mean indeed a curve?
 >> not a surface? and then: which model do you have for that curve?
 >> parametric : (a+b*t+c*t^2 ; d+e*t+f*t^2; g+h*t+i*t^2) with
 >> t the curve parameter (how to get this?) or implicit:
 >> (intersection of two surfaces)
 >> a(i)+b(i)*x+c(i)*y+d(i)*x^2+e(i)*x*y+f(i)*y^2=0 i=1,2
 >> plus some normalization constraints?
 >> hth
 > > peter
 >>
 >>
 >>
 >>

Sanne Christensen wrote:
>
>
> I'm pretty new in the Matlab-world. How do I make curve fitting on
> a
> 3D data set (x, y, z)? Do I need a special toolbox for it?
>
> Thanx for your help :)
> Sanne

Dear Sanne,
I think we're working on the same problem.
I got a set of 3D points in Cartesian coordinates and I want to find
the equation of the paraboloid that describes these points. It would
be an antenna. If I have some interesting news about it I'll tell
you, hoping you'll do the same!

Paolo

Hi Paolo

I've scipped using the lsqcurve with x, y, z - it just wouldn't work
for me. Instead I'm using polyfit (I could also use lsqcurve) on x, y
and x, z respectively so I get two curves in a 2D coordinate system.
Then i project one of the curves onto the other and this way I get my
final curve in a 3D coordinate system. I've heard that there are ways
to do it in 3D in Matlab, but I have a deadline coming up and
therefore I don't have time to figure out how to do it :)

/Sanne

Paolo Benetti wrote:
>
>
> Sanne Christensen wrote:
>>
>>
>> I'm pretty new in the Matlab-world. How do I make curve fitting
> on
>> a
>> 3D data set (x, y, z)? Do I need a special toolbox for it?
>>
>> Thanx for your help :)
>> Sanne
>
> Dear Sanne,
> I think we're working on the same problem.
> I got a set of 3D points in Cartesian coordinates and I want to
> find
> the equation of the paraboloid that describes these points. It
> would
> be an antenna. If I have some interesting news about it I'll tell
> you, hoping you'll do the same!
>
> Paolo

try the following:

%suppose my data is a 512x512 double array.

%first define a linear grid
x=linspace(-1,1,512);
[x,z]=meshgrid(x,x);
x=x(:);z=z(:);

A=[x.^2,z.^2,x,z,ones(length(x),1)];
C=data(:)'/A';
% C gives coefficients for 3D parabola

% data, corrected for parabola:
delta=data(:) - (C*A')';
datacorr=reshape(delta,512,512);

%do some plotting:
figure;imagesc(data-datacorr);

-Manfred.

Sanne Christensen wrote:
>
>
> Hi Paolo
>
> I've scipped using the lsqcurve with x, y, z - it just wouldn't
> work
> for me. Instead I'm using polyfit (I could also use lsqcurve) on x,
> y
> and x, z respectively so I get two curves in a 2D coordinate
> system.
> Then i project one of the curves onto the other and this way I get
> my
> final curve in a 3D coordinate system. I've heard that there are
> ways
> to do it in 3D in Matlab, but I have a deadline coming up and
> therefore I don't have time to figure out how to do it :)
>
> /Sanne
>
> Paolo Benetti wrote:
>>
>>
>> Sanne Christensen wrote:
>>>
>>>
>>> I'm pretty new in the Matlab-world. How do I make curve
> fitting
>> on
>>> a
>>> 3D data set (x, y, z)? Do I need a special toolbox for it?
>>>
>>> Thanx for your help :)
>>> Sanne
>>
>> Dear Sanne,
>> I think we're working on the same problem.
>> I got a set of 3D points in Cartesian coordinates and I want to
>> find
>> the equation of the paraboloid that describes these points. It
>> would
>> be an antenna. If I have some interesting news about it I'll
tell
>> you, hoping you'll do the same!
>>
>> Paolo

I've been trying to implement this method but I'm having
some problems. I think I've written the function I'm
fitting to incorrectly. I'm trying to do a global fit to a
data set that I have previously fit by non-globally. This
is the error I get:

??? Error using ==> optim/private/lsqncommon at 131
Function value and YDATA sizes are incommensurate.

my function call is as such:
[x,resnorm,residual,exitflag,output,lambda,jacobian] =
lsqcurvefit(@globfun,x_init,Time_Tot',cleanex.data',lb,ub);

where @globfun is:
function F = globfun(xy,xydata)
F(1) =
xy(2)*(exp(xy(1)*xydata(1))-exp(-(xy(2)+xy(3))*xydata(1)))/(xy(2)+xy(3)-xy(1))
F(2) =
xy(4)*(exp(xy(1)*xydata(2))-exp(-(xy(4)+xy(5))*xydata(2)))/(xy(4)+xy(5)-xy(1))
F(3) =
xy(6)*(exp(xy(1)*xydata(3))-exp(-(xy(6)+xy(7))*xydata(3)))/(xy(6)+xy(7)-xy(1))
...

Time_Tot and cleanex.data are both m by n matrices
Before my error I get the following cycle:
F = 0.7506
F = 0.7506 0.0248
F = 0.7506 0.0248 0.3464
...

Where in the non-global (2D) case I would get a series of
column vectors that would approach cleanex.data(:,i) with
each cycle. Why is it iterating through the individual
functions instead of fitting the system?


"Teddy Hsung" <gtg101p@mail.gatech.edu> wrote in message
<cnl63d$bbt$1@news-int2.gatech.edu>...
> I guess his problem can be formulated like this:
>
> z1 = f(x1, y1, p1,p2...)
> z2 = f(x2, y2, p1,p2...)
> .
> .
> .
> zn = f(xn, yn, p1,p2...)
>
> where f is a known form of function. p1,p2... are the
parameters that he
> wants to estimate.
>
> \ (slash) function probably won't work because his
function is highly
> possible a nonlinear function.
>
> p=LSQCURVEFIT(f,p0,XYDATA,ZDATA) should be able to solve
this problem.
>
> where, p is a vector [p1, p2..]', p0 is initial guess of p.
>
> XYDATA is a matrix [x1,y1
> x2,y2
> .....
> xn,yn]
>
> ZDATA is a vector [z1, z2...zn]'
>
> Please let us know how it works
>
> Rentian
>
>