How can I increase the automatic detection of a small local feature as part of a probability density function?

09 September 2014 4 9K Report

I have an interesting challenge to detect a very small local feature as part of a 1-D probability density function. The task is very straightforward for a human being, but it appears to be quite cumbersome to perform this automatically, which is my aim (Actually, I could detect in 60% of the cases, but that is very low for my application).

I have attached an example: the left hand side is where there is nothing to detect, and the right hand side is where there is a little peak (I am interest in) as indicated by the arrow.

Many thanks!

Hossein Soleimani

what do you mean by feature? is you curve the probability distribution function?

if you have the curve, it is easy to detect any local max...!!!!

Marcus Neuer

Dear Tünde,

such a feature can be detected with automatisms quite reliable. There are different paths that depend on the time you may want to invest. First, in the branch of spectroscopic analysis, you will find a diversity of publications devoted to peak searching and peak detection. Most of them typically rely on using derivatives to find the extrema. Try to search for "Mariscotti" Peak search and you can find several sophisticated techniques derived from Mariscotti´s original works, that will help you to reduce noise and volatility in your curve.

For your purpose, another, easier and perhaps more pragmatic approach also using above ideas would be to directly calculate the second derivative of your PDFs. In the second derivative, constant and slowly varying parts of your curve will be eliminated and the peaks will appear as "W" shaped objects. Tackling and triggering on the tip of this "W" is typically easier than to find the peak in the original curve. You can do this by defining a region of interest (ROI) within the second derivative or use a correlation based approach. In that way, you can try to find publications dealing with so-called template matching or pattern matching.

With best regards,

Marcus

Aleksandar Dimitriev

Are you trying to find local maxima in the PDF? Then it's trivial to find them using gradient descent, or any of a hundred other algorithms.

Anshul Joshi

Matlab has peak detection (http://www.mathworks.com/help/signal/examples/peak-analysis.html). You can detect multiple peaks in your 1D function.

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