Description This is a very simple function to find the local maximum in any dimensional array. As simple as it is it still gives nice results.
I use the imdilate() function as a maximum operation and then compare the data to the result.
The function receives three parameters:
the data, a vector defining the minimum distance between peaks in each of the data dimensions. and a flag either to exclude equal points or not.
use examples:
a = cumsum(randn(1000,1));
peaks = localMaximum(a,[100]);
figure; plot(a); hold on; plot(peaks,a(peaks),'ro');
[x y] = meshgrid(-6:0.1:6,-6:0.1:6);
a = sinc(x).*sinc(y);
lMaxInd = localmaximum(a,[20 20]);
lMinInd = localMaximum(-a,[20 20]);
figure; mesh(x,y,a); hold on;
plot3(x(lMaxInd),y(lMaxInd),a(lMaxInd),'k*','markersize',10,'linewidth',1.5);
plot3(x(lMinInd),y(lMinInd),a(lMinInd),'g*','markersize',10','linewidth',1.5);
legend('sinc(x)sinc(y)','peaks','valleys','location','best')
P.S
- It is recommended to run (if possible) a LPF on the data before searching for the peaks
Required Products Image Processing Toolbox
MATLAB release MATLAB 7.0.4 (R14SP2)
function varargout = localMaximum(x,minDist, exculdeEqualPoints)
% function varargout = localMaximum(x,minDist, exculdeEqualPoints)
%
% This function returns the indexessubscripts of local maximum in
the data x.
% x can be a vector or a matrix of any dimension
%
% minDist is the minimum distance between two peaks (local maxima)
% minDist should be a vector in which each argument corresponds to
it's
% relevant dimension OR a number which is the minimum distance for
all
% dimensions
%
% exculdeEqualPoints - is a boolean definning either to recognize
points with the same value as peaks or not
% x = [1
2
3 4
4
4 4
4
4 3
3
3 2
1];
% will the program return all the '4' as peaks or
not - defined by the 'exculdeEqualPoints'
% localMaximum(x,3)
% ans =
% 4
5
6 7
8
9 11
12
%
% localMaximum(x,3,true)
% ans =
% 4
7
12
%
%
% Example:
% a = randn(100,30,10);
% minDist = [10 3 5];
% peaks = localMaximum(a,minDist);
%
% To recieve the subscript instead of the index use:
% [xIn yIn zIn] = localMaximum(a,minDist);
%
% To find local minimum call the function with minus the variable:
% valleys = localMaximum(-a,minDist);
if nargin < 3
exculdeEqualPoints = false;
if nargin < 2
minDist =
size(x)/10;
end
end
if isempty(minDist)
minDist = size(x)/10;
end
dimX = length ( size(x) );
if length(minDist) ~= dimX
% In case minimum distance isn't defined for all
of x dimensions
% I use the first value as the default for all
of the dimensions
minDist = minDist( ones(dimX,1) );
end
% validity checks
minDist = ceil(minDist);
minDist = max( [minDist(:)' ;
ones(1,length(minDist))] );
minDist = min( [minDist ;
size(x)] );
%
---------------------------------------------------------------------
if exculdeEqualPoints
% this section comes to solve the problem of a
plato
% without this code, points with the same hight
will be recognized as peaks
y = sort(x(:));
dY = diff(y);
% finding the minimum step in the data
minimumDiff = min( dY(dY ~= 0) );
adding noise which won't
affect the peaks
x = x + rand(size(x))*minimumDiff;
end
%
---------------------------------------------------------------------
se = ones(minDist);
X = imdilate(x,se);
f = find(x == X);
if nargout
[varargout{1:nargout}] = ind2sub( size(x), f );
else
varargout{1} = f;
end
http://www.mathworks.com/matlabcentral/fileexchange/14498-local-maxima-minima
