Find a local max and local min of a surface with noise

I got the matrix above How can I find de MAXIMUM & MINIMUM locals and put the X,Y coodinate into a vector X and a vector Y and when i plot X vs Y o got the dots representating the maximum and minumum values with different color for max and min ps. remember to consider the noise

        A=[0.5000   -0.2668   -0.4606   -0.0866   -0.1433   -0.2063    0.0020   -0.0684    0.0824    0.0618;    -0.0700   -0.1001   -0.6211       -2.0000   -0.6901   -0.5352   -0.5370    0.6527   -0.4742   -0.2398;       -0.0159    0.1090    0.0902   -0.3513   -0.5579   -0.2559   -0.1088    0.2090   -0.1592    0.0290;    0.3378    0.3437    0.4101    0.4995    0.3286    0.1963    0.0434    0.1998    0.2853    0.3430;    0.3673    0.3320    0.2836    0.3189    0.3596    0.1729    0.0493    0.2758    0.2314    0.3171;   -0.7621   -0.5151   -0.3759   -0.1816    0.1758    0.0306   -0.4316    0.1782   -3.0051   -1.9493;   -0.0107   -0.1784        -0.0642   -0.1268   -0.0137    0.0840   -0.1945    0.0944   -0.1449          -0.0296;    0.2212    0.1060    0.0321    3.0020    0.1965   -0.0060    0.0472    0.1958    0.1850    0.3266;    0.1410    0.2704    0.1225   0.2163    0.0337    0.1676    0.1012    0.1511    0.1105    0.3585;   0.1301    0.2741    0.0495    0.0251    0.1299    0.2433    0.0284   0.0727    0.1462    0.1443 ;]

[Oleg Komarov]

What have you done so far?

[Rafael Freire]

I'm not doing the right way.

i made a isocut in the max an min values using this function that 1 create

function [modecut1,modecut_1]=modecut(X,i);

tic;

modecut1 = X;

modecut_1 = X;

modeX = mode ( mode(X) );

modecut_1 (modecut_1 >= modeX * i & modecut_1 <= -modeX * i ) = 0;

modecut_1 (modecut_1 > 0 ) = 256;

modecut_1 (modecut_1 < 0 ) = -256;

Than i use bwlabel an calculate the centroids of the points.

but one problem of that is when i have 2 max nearby for this way i will consider one max only, so i'm loosing important information.

Answer 1

[Rafael Freire]

I use a function extrema2 to do that and works here is the link http://www.mathworks.com/matlabcentral/fileexchange/12275-extrema-m-extrema2-m/content/extrema/extrema2.m and the code I use

 z=crop;
 [zmax,imax,zmin,imin] = extrema2(z,1);
 [m,n]=size(crop);
 y=1:m;
 x=1:n;
 [x,y]=meshgrid(x,y);
 crop(crop<=10)=nan
 figure

 hold on  
      plot3(x(imax),y(imax),zmax,'bo',x(imin),y(imin),zmin,'ro')
       for i = 1:length(zmax)
       text(x(imax(i)),y(imax(i)),zmax(i),['  ' num2str(zmax(i))])
       end
       for i = 1:length(zmin)
        text(x(imin(i)),y(imin(i)),zmin(i),['  ' num2str(zmin(i))])
       end
      hold off 

 hold on
  surf(crop)

Answer 2

[bym]

I am not sure I understand your question but is

imagesc(A)

what you are looking for?

[Rafael Freire]

I'm looking for a values (linear indexing) of the points where is the max of the curves, but I have a lot of maximuns and minimuns in my surface...

This function that you pass helps me in another part of my work.

Thanks anyway

Answer 3

[Walter Roberson]

On a discrete surface, every point is both a local max and local min -- at least until you define your neighborhood. If you want noise to be taken in to account, you also have to define either a noise detection function (if you want to ignore points with noise) or a smoothing function.

You also need to define the behaviour you want for saddle-points, that are local min in one direction but local max in another.

You might want to use gradient() perhaps.

[Rafael Freire]

I'am very new in this business I only work with matlab since february(2011) and I don´t know the right term to design the functions and the technical language , I think I'm made mistakes sorry for that.

I tried to use the gradient and then I plot a quiver graph, it's was clearly visible the "valleys"(min) or "montains"(max) in my 2D surface but after that i stucked.

You sad in one of my questions to use the isocut, but when you have peaks very close to each other they compute as only one, and then i lost precious information. In one of my cases, I got a region of 10x10 points that has a 5 max but 3 of them is really close to each other. I can do it by hand but i have almos 500 surfaces to do that.....so..its impossible done by hand...

Anyway i appreciate the attention and kindness

Best regards

[Walter Roberson]

I suggested isosurface as a possibility in the situation where all the peaks were the same height, not in the situation where the peaks are different heights.

I think you should post a couple of images, one of them with the raw values, and the other of them marked to show where you consider the peaks to be; the sample image should include examples of the noise you mentioned and the marked-up image should show an example of a peak that should be ignored or moved because it is considered to be noise or artificially enhanced by noise.

[Rafael Freire]

How i can post images here?

[Walter Roberson]

Post the images on a service such as tinypic or imageshack and post the URL here.