How to filter out the noisy portion of contourf plot?

The code below shows a ´contourf´ plot

load('impdta.mat')
[C,h] = contourf(x1,y1,ua, 'ShowText','on',FaceAlpha=0.3,EdgeAlpha=0.2,EdgeColor='k',LevelStep=10);
clabel(C,h,'FontSize',7,'Color',[0.6 0.6 0.6])
axis equal

In the above contour plot, the left side of the contour shows a smooth trend. I want to use this contour plot to interpolate to a value (say 60), which in current situation gives multiple 'lines' (marked in red). Is there a way the cluttered contours can be filtered out? An idea could be to use limits of x from zero to 600, but there are multiple plots in which this noncluttered area changes location and the limits cannot be simply applied. I would like to filter out the cluttered portion and left with the smooth contour lines only so that when I interpolate the value, only distinct contours can be extracted. I would appreciate if a solution can be attained.

hold on
contourf(x1,y1,ua, [60 60], 'ShowText','on',FaceAlpha=0,EdgeAlpha=0.5,EdgeColor='r');

Answer 1

[Star Strider]

By inspection, the longest part of the contour is likely the one you want to keep. It is relatively straightforward to find this because of the say the contour matrices are created. When I did thtat and plottted it, there was a gap on the left end that did not yield itself easily to any sort of analytic approach, so I just set up a find call with the appropriate conditions to retrieve those indices.

It may not be the most elegant approach, however it has the virtue of working.

Try this —

load('impdta.mat')
[C1,h1] = contourf(x1,y1,ua, 'ShowText','on',FaceAlpha=0.3,EdgeAlpha=0.2,EdgeColor='k',LevelStep=10);
clabel(C1,h1,'FontSize',7,'Color',[0.6 0.6 0.6])
axis equal
hold on
C2 = contour(x1,y1,ua, [60 60], 'ShowText','on',FaceAlpha=0,EdgeAlpha=0.5,EdgeColor='r', LineWidth=2);

idx1 = find(C2(1,:)==60);                                       % Extact Longest Contour
Len1 = C2(2,idx1);
[maxLen1,lenidx1] = max(Len1);
xv1 = C2(1,idx1(lenidx1)+1:C2(2,idx1(lenidx1)));
yv1 = C2(2,idx1(lenidx1)+1:C2(2,idx1(lenidx1)));

idx2 = find(C2(1,:)<=min(xv1) & C2(2,:)>=max(yv1));             % Search For The Indices of the Rest Of It
xv2 = C2(1,idx2);
yv2 = C2(2,idx2);

figure
[C1,h1] = contourf(x1,y1,ua, 'ShowText','on',FaceAlpha=0.3,EdgeAlpha=0.2,EdgeColor='k',LevelStep=10);
clabel(C1,h1,'FontSize',7,'Color',[0.6 0.6 0.6])
axis equal
hold on
plot(xv1, yv1, '-r', LineWidth=2)
plot(xv2, yv2, '-r', LineWidth=2)
hold off

EDIT — (19 Aug 2024 at 14:44)

Plotting that contour on the surface —

whos('0file','impdta.mat')
Fua = scatteredInterpolant(x1(:), y1(:), ua(:));
xc = [xv1 xv2];
yc = [yv1 yv2];
zc = Fua(xc(:), yc(:));

figure
surfc(x1, y1, ua)
colormap(turbo)
hold on
plot3(xc, yc, zc+7, '-r', LineWidth=2)
hold off

I beleive this is what you want. If you want something else, please be specific.

.

[Muha]

Well, this solution works. Thank you for your response. I will try the other suggested approach as I want to have economical fitting. If I cannot find a solution within a day, I will proceed with your simple approach. Again, thank you for your intuitive idea. Cheers Star!

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.

[Muha]

I have worked on the other solutions discussed. One thing that worked was that I simply put limits from -100 to 100. It is simple solution so far and works reasonably

[c12,h12] = contourf(x1,y1,ua,[-100:10:100], 'ShowText','on',FaceAlpha=0.6,EdgeAlpha=0.5,EdgeColor='k',LevelStep=10);

This step when added on your idea works as I have thought it should. There is a bit more tinkering I am working which I think will be managed as it develops.

Thank you for all the guidance.

[Star Strider]

As always, my pleasure!

[Muha]

I don't know whether I should start a new thread or not, but i will write it here any way. I stepped back a bit from these plots and took a few steps back. So, I have x-grid data, y-grid data and the actual contour values, referred to as x1, y1 and ua, respectively.

load('gdata.mat')
figure
hold on
[c12,h12] = contourf(x1,y1,ua, 'ShowText','on',FaceAlpha=0.6,EdgeAlpha=0.5,EdgeColor='k',LevelStep=10);
clabel(c12,h12,'FontSize',6,'Color','k',fontname='Times New Roman')
axis equal; grid on;
xlim([0 1350])
ylim([0 300])
plot([50 300],[20 280],'o-r')
hold off

At this point, I have added another factor. To simplify things, the red line shows the distance between two sensors. So, these contours should ideally be a magnetic field sort of field between these two sensors. However, this is conducted experimentally, the material defects cause the contour to become irregular. One may ask why it starts at around 150mm horizontal and 10mm vertical, the answer is that this is the area of interest for which the data were obtained. Now that we have familiarized ourselves with the situation. I would show another graph for another pair of sensors.

load('gdata2.mat')
figure
hold on
[c12,h12] = contourf(x1,y1,ua, 'ShowText','on',FaceAlpha=0.6,EdgeAlpha=0.5,EdgeColor='k',LevelStep=10);
clabel(c12,h12,'FontSize',6,'Color','k',fontname='Times New Roman')
axis equal; grid on;
xlim([0 1350])
ylim([0 300])
plot([300 550],[280 20],'o-r')

It can be seen in both grahs that it sort of creates a field between these points which seems to be strong within the supposedly circular area (shape), as shown below. I would like to keep the contours within this circle and simply discard the rest data.

load('gdata2.mat')
figure
hold on
[c12,h12] = contourf(x1,y1,ua, 'ShowText','on',FaceAlpha=0.6,EdgeAlpha=0.5,EdgeColor='k',LevelStep=10);
clabel(c12,h12,'FontSize',6,'Color','k',fontname='Times New Roman')
axis equal; grid on;
% xlim([0 1350])
% ylim([0 300])
plot([300 550],[280 20],'o-r')
    r = sqrt((300-550)^2+(280-20)^2);r = r/2;
    x = 300+r*(550-300)/(2*r); y = 20+r*(280-20)/(2*r); 
    fplot(@(t) r*sin(t)+x, @(t) r*cos(t)+y);
    hold off

Now contourf plot just displays the contour. When I want to interpolate the contour later on, it considers the complete meshgrid which means some filtering is required before interpolating certain contour line. Therefore, my plan is to just keep the data within the circle and make the outside data as nan (maybe nan is not picked for contourf) or some value which is significantly larger such that it does not fall in the contour range (something like 10000).

Is it possible to modify the values of ´ua´ that only the values within circle are effective, rest is first replaced by nan, and then those nan values are replaced by some extreme high vaues, or it just disappears. It cannot be zero.

I have tried the other solution you proposed, it was successful mostly but in some cases, the lines were mistakenly picked in strange zones.

ps: well I found some similar question here.

https://se.mathworks.com/matlabcentral/answers/525898-constraints-on-meshgrid-remove-points-outside-function

I am looking into it.

[Star Strider]

What you want to do is not absolutely impossible, however since your data are discrete, the result looks a bit strange. Isolate the area-of-interest with the inpolygon function, and go from there.

Try tthis —

load('gdata2.mat')
whos('-file','gdata2')

  Name       Size            Bytes  Class     Attributes

  ua        10x37             2960  double              
  x1        10x37             2960  double              
  y1        10x37             2960  double              

figure
hold on
[c12,h12] = contourf(x1,y1,ua, 'ShowText','on',FaceAlpha=0.6,EdgeAlpha=0.5,EdgeColor='k',LevelStep=10);
clabel(c12,h12,'FontSize',6,'Color','k',fontname='Times New Roman')
axis equal; grid on;
% xlim([0 1350])
% ylim([0 300])
plot([300 550],[280 20],'o-r')
    r = sqrt((300-550)^2+(280-20)^2);r = r/2;
    x = 300+r*(550-300)/(2*r); y = 20+r*(280-20)/(2*r); 
    fplot(@(t) r*sin(t)+x, @(t) r*cos(t)+y);
hold off

t = linspace(0, 2*pi, 500);                                     % Create The Circle
xv = r*sin(t)+x;
yv = r*cos(t)+y;

% disp(x1)
% disp(y1)

[in,on] = inpolygon(x1, y1,  xv, yv);                           % Logical Matrix Of Elements Inside Circle

innan = +in;                                                    % Convert From Logical To Numeric
innan(~in) = NaN;                                               % Assign 'NaN' Values

x1nan = x1 .* innan;                                            % Multiply To Convert Appropriate Elements In The Matrices To 'NaN'
y1nan = y1 .* innan;
uanan = ua .* innan;

figure                                                          % Recalculate The 'contourf' Plot With The NEw MAtrices
hold on
[c12,h12] = contourf(x1nan,y1nan,uanan, 'ShowText','on',FaceAlpha=0.6,EdgeAlpha=0.5,EdgeColor='k',LevelStep=10);
clabel(c12,h12,'FontSize',6,'Color','k',fontname='Times New Roman')
axis equal; grid on;
% xlim([0 1350])
% ylim([0 300])
plot([300 550],[280 20],'o-r')
    r = sqrt((300-550)^2+(280-20)^2);r = r/2;
    x = 300+r*(550-300)/(2*r); y = 20+r*(280-20)/(2*r); 
    fplot(@(t) r*sin(t)+x, @(t) r*cos(t)+y);
hold off

It miight be possible to make it look more ‘normal’, however that would most likely require interpolating it to a much finer grid (probably at least 10 times as many elements in each dimension) in order to fill out the blank spaces on the edges (there would still be some). Use the same procedure that I do here on the interpolated grids. The interp2 function would likely be easiest to use for the interpolation.

.

[Muha]

This is exactly what I wanted to achieve. It works well.

I will definitely interpolate to a finer grid before running this code (may add to more computation time). But I will try to see the improvement with interpolated grid. Thanks

Thank you for significant contribution to my research.

[Star Strider]

As always, my pleasure!

Answer 2

[John D'Errico]

One basic rule that always applies to things like this. You DON'T want to smooth contours after you have found them. You can't try to get rid of bumpy, messy contours. The result, even if you managed to do so, would be further artifacts. It is just a bad idea.

Instead, your goal should be to smooth the original data as a smooth, well-behaved surface. Only then do you want to generate the contours. The result will be far better behaved contours, and a better result.

So smooth your data, FIRST. There are many ways you can achieve that goal. But before we even think about that, let me look at your data. ALWAYS PLOT ALL DATA. Plot everything.

load impdta.mat
surf(x1,y1,ua)
xlabel x1
ylabel y1
zlabel ua

In this case, of course, the data in one half of that surface is wildly more noisy than the data in the other half. Contours in the part where x is greater than around say 750 (column 20 was at x=750) are meaningless, and any amount of smoothing will probably not help. Your data is just random noise in that part, and contours would be meaningless there, even if you did smooth the data. As such, honestly I'd just truncate that half of your data for the purposes of making contours. If I take the first 20 columns of each array, we see some trash in one corner, but it is not too excessive.

surf(x1(:,1:20),y1(:,1:20),ua(:,1:20))
xlabel x1
ylabel y1
zlabel ua

I might be willing to smooth that half, and only then compute the contours. It also looks like you have some missing data along two edges.

Now, re-reading your question, I see you have decided that a simple limit applied on x will not work. Such is life. The complex solution you hope exists, and want to magically work will not work, so you are going to need to do something that is possible to do, even if it is not as easy as you wish.

I might suggest looking at the local noise in your surface. In any region where the noise is too high, above some tolerance, I would just delete all data in that area. That is, replace it with a NaNs before you compute the contours. How can you compute the local noise? One approach might be to look at the local residual variance, AFTER you subtract off a locally planar fit. So at any node in the array, take the 8 nearest neighbors, and fit a plane through them. There will be problems around the edges of course, and you don't show much data.

[Image Analyst]

I agree with you but I'm wondering two things.

1. The main problem, as he sees it, is that some contour lines (like for 60) are apparently "broken" (have gaps in them). Why is that? Is it merely a problem of the surface contour becoming so steep there that multiple contours overlap there and only one can be displayed? Or is it a problem of just not showing it because of subsampling for display (like maybe enlarging the diagram might show them)?
2. Why does muha want smoothing in the first place? Why would he want a less accurate, smoother contour plot? What's wrong with more accurate contours that follow the data?

[Muha]

Dear @John D'Errico thank you for your detailed analysis on the problem. These data are gathered experimentally as a grid was plotted and the response was collected from each node in the grid. It can be analogous to a situation where as the signal becomes weak, the noise becomes more. As it is experimental data, no smoothing has been or can be carried out. And, currently, the signal strength cannot be characterized so that we can simply discard the low strength data. I do not intend to smooth the data. However, I just want to discard the noisy data. As you have suggested, I will use the approach you have advised using local residual variance. I will get back to you if there is any success.

@Image Analyst there was no resampling carried out. These data are collected as a difference in signal arrival. In some cases the signals were distinct and clear, in others there could have been errors. I have explained in response to @John D'Errico why the noise is there. I would not go for smoothing. Probably I phrased it in a way that it sounded like that. I intend to keep the smooth lines contour only and discard the jaggedy contours. Their suggestiuon of approaching using the residual variance sounds like a good approach which I am looking into right now.

Again, thank you, these comments gave me some idea to proceed further. Cheers. I will get back in case of success.

Answer 3

[Image Analyst]

So it sounds like you want to remove local outliers and noise but do not want to touch/smooth data points that you consider to be "good". So you want denoising. I have some ideas around that if you can consider your data as a grid so that we can treat it as an image. But I don't have time now. I'll give a longer, more thorough answer later today. Please be patient. In the meantime, see this excellent overview of image denoising methods by Prof. Milanfar.

Modern tour of image filtering denoising

K-LLD - Professor Peyman Milanfar

[Image Analyst]

From your reply to @Star Strider it appears you don't want to denoise your data, but just want the longest contour line, so I won't give anymore denoising information.