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From: E W on 5 Aug 2010 07:25
I am trying to find all local maxima of an n-dimensional function (which is numerically in the form of a matrix). Does anyone know of a fast method for this? Thanks in advance.
From: Bruno Luong on 5 Aug 2010 07:42
"E W" <donotsent(a)donotsend.de> wrote in message <i3e72l$mn3$1(a)fred.mathworks.com>...
> I am trying to find all local maxima of an n-dimensional function (which is numerically in the form of a matrix). Does anyone know of a fast method for this? Thanks in advance.

You can use my FEX submission
http://www.mathworks.com/matlabcentral/fileexchange/24705-minmax-filter

% Data, 2d here but should work for nd as well
>> A = peaks;
% Return linear index of the local minima
>> find(A==minmaxfilt(A,3,'min','same'))

ans =

1
49
664
1286
1302
2401

% Bruno
From: Alan Weiss on 5 Aug 2010 07:47
On 8/5/2010 7:25 AM, E W wrote:
> I am trying to find all local maxima of an n-dimensional function (which
> is numerically in the form of a matrix). Does anyone know of a fast
> method for this? Thanks in advance.

I am not sure what you mean "which is numerically in the form of a
matrix." Is your function a real-valued function of an n-dimensional
point? Or is it a matrix-valued function? If it is matrix-valued, what
does local maximum mean?

If your function is real-valued, then perhaps you can use MultiStart
from the Global Optimization Toolbox, with a regular or perturbed array
of initial values:
http://www.mathworks.com/access/helpdesk/help/toolbox/gads/bsc5_cj.html#bseat0r

For an example:
http://www.mathworks.com/access/helpdesk/help/toolbox/gads/bsc9noc.html#bseyhh5

Of course, to get local maxima instead of minima, take the negative of
your objective function:
http://www.mathworks.com/access/helpdesk/help/toolbox/gads/brdvu8r.html#brdvvgw

Alan Weiss
MATLAB mathematical toolbox documentation
From: ImageAnalyst on 5 Aug 2010 09:43
If you have the Image Processing Toolbox, use imregionalmax:

http://www.mathworks.com/access/helpdesk/help/toolbox/images/imregionalmax.html
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