Finding local maxima on a slightly noisy data

Question

Math Enthusiast 2018-12-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/434247-finding-local-maxima-on-a-slightly-noisy-data

评论： Akira Agata 2018-12-11

Trajectory.PNG

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Hi,

I have my plot,as shown in "Trajectory.png" file.

My X-Axis data is just:

Xdata = [1:100];

My Y-Axis data is as follows:

0
0
09222708159463
44546159330348e-07
09222611499462
13686837721616e-13
19629985182991
307031063055145
889191608677226
13686837721616e-13
13686837721616e-13
0
13686837721616e-13
13686837721616e-13
0
13686837721616e-13
02297834274279
0388633487946145
06185167072739
13686837721616e-13
361256176978336
609935965840200
219116803722684
752088093054083
13686837721616e-13
0
13686837721615e-13
13686837721617e-13
13686837721616e-13
7332583247782
877119357353
09424951365800
947857561548907
15967343285703
85842059479906
90599054430073
03340833244700
74611749440277
25454771605403
405678614930056
32781000899039
540378086763468
98803176650120
37173336776097
03332435894425
19689864919353
11301835089563
88897972952186
5756563901977
01603701789582
78266388299620
608273922686689
879773039416162
900317534766668
807217040648508
326548725644831
207175108036568
495172539519853
520077384058685
173410667917717
0642667898143524
131548850902771
161997164449503
0413293955654355
490113271390482
08274572574879
838386694466136
10542735760100e-15
0980279964920274
49459508834199
19798004219773
394520279605238
10542735760100e-15
10542735760101e-15
10542735760100e-15
47973128457182
718756197167734
382866238818068
58339794004342
10894362431230
0407985149444
6536822408392
40103735780748
22280189553396
99971342894857
71371333131814
99983968601066
57127665277943
68150302624610
257865115144954
0303588377283994
26389973299037
16741322335018
41971109494362
91582002185642
52274280044650
35828014515571
146871341252485
06696816496338
06293020725324

I want to find my local maxima for this plot.

In the plot,we can see that, there is a lot of noise.Due to this noise,When I try to find local maxima,with this function,I get around 16 points, instead of 3.

I am using the following code for finding local maxima:

[Maxima,MaxIdx] = findpeaks(K);

Here,K is Y-Axis data.(N x 1 data)

I would be really glad,if someone can explain,the procedure to remove the noise,so that finally,when we call the function to find Maxima,it gives us 3 values(i.e. at xvalues 31,50 and 82) instead of 16 values.

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Answer 1

Jim Riggs 2018-12-6

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The peaks are very distinct. Why not just select a threshold value (say, 20) and only use peaks that are above the threshold?

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Math Enthusiast 2018-12-6

@Jim: That seems sensible.I think,I will proceed like that.

Could you also answer this.I basically have a 2D Trajectory,consisting of different lines and arcs.I am trying to find out breakpoints (the points, where each a curve C1 transforms into curve C2).

For example,if we have four lines (something like rectangle),I am following this method:

1) Find the curvature radius for all the points and plot it.

2) Then,I get the graph,like the one,I have attached in my query.The peaks having value more than threshold are basically the breakpoints.

It seems to work in case of Lines,but not sure,if this is the right approach,when I have a trajectory comprising of lines and arcs.Could you please explain if I need to use some kind of filter to find the correct peaks in this case.I mean, inorder to find the breakpoints,where a line is getting changed to arc.

Thanks

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Answer 2

Akira Agata 2018-12-6

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https://ww2.mathworks.cn/matlabcentral/answers/434247-finding-local-maxima-on-a-slightly-noisy-data#answer_350962

在 MATLAB Online 中打开

I think one possible way would be setting 'MinPeakProminence' option in findpeaks function, like:

findpeaks(yourData,'MinPeakProminence',30)

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Math Enthusiast 2018-12-10

@ImageAnalyst: Well, if you look at his code,he is also using, a threshold of "30".

So,obviously, I would have to find my threshold value properly.

Akira Agata 2018-12-11

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>Image Analyst-san and Math Enthusiast-san,

Thank you for your comments!

Yes, I have explicitly set a threshold to "30" in my previous code. If you want to automatically find a threshold value, you need to define the peak(s) you want.

For example, if you define "the peak(s)" as a peak with a prominence of more than three scaled median absolute deviations (MAD) away from the median value, the code will be like this:

[~,~,th] = isoutlier(yourData);
findpeaks(yourData,'MinPeakProminence',th)

Since the threshold becomes ~4.8 in this definition, findpeaks finds 4 peaks, as shown below.

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