Solved

Locating local maxima of arbitrary curve

Posted on 2008-10-15
4
806 Views
Last Modified: 2013-11-13
I need to locate the local maxima across a histogram. That is, I need to locate the 'hills' in the histogram graph. Is the best way to do this to calculate the first derivative across the curve until it is under some low (near zero) threshold value? The graph can be quite noisy so I'm not sure what the best way to do this is. Also, what size window should be used to calculate the derivative across the points of the arbitrary curve?

Thanks in advance
0
Comment
Question by:corey_mcm
  • 3
4 Comments
 
LVL 84

Expert Comment

by:ozo
ID: 22728342
If the function is continuously differentiable the local maxima will be where the derivative is 0 and the second derivative is negative
0
 
LVL 84

Expert Comment

by:ozo
ID: 22728356
If the function is discrete, than anywhere f(n-1) <  f(n) > f(n+1) is a local maximum
0
 
LVL 5

Author Comment

by:corey_mcm
ID: 22728399
I'm generating a critically smoothed gaussian kernel of the histogram.. Is the safe to use the following (where 'value' is the histogram array):

To calculate the first order derivative:

dOne (int x) {
    return value[i+1] - value[i];
}

To calculate the second order derivative:

dTwo (int x) {
    return dOne(x+1) - dOne(x);
}
0
 
LVL 84

Accepted Solution

by:
ozo earned 500 total points
ID: 22728461
That's one way to do it.
A local maximum would then be where dOne goes from positive to negative
0

Featured Post

Free Tool: Site Down Detector

Helpful to verify reports of your own downtime, or to double check a downed website you are trying to access.

One of a set of tools we are providing to everyone as a way of saying thank you for being a part of the community.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

In this post we will learn different types of Android Layout and some basics of an Android App.
In this post we will learn how to connect and configure Android Device (Smartphone etc.) with Android Studio. After that we will run a simple Hello World Program.
Viewers will learn about arithmetic and Boolean expressions in Java and the logical operators used to create Boolean expressions. We will cover the symbols used for arithmetic expressions and define each logical operator and how to use them in Boole…

733 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question