Locating point where slope becomes most steep

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A on 19 Jun 2012
Commented: GOPEE Ajit Kumar on 25 Feb 2017
Hello, I am trying to extract data from this graph, generated from the image to the right of it:
As you can tell from the graph, the slope starts to decrease most rapidly at about 1000 pixels.
My code will ask for a restriction zone, so it is not a problem to only investigate between say 800 pixels and 1100 pixels. However, I am not sure how to locate the point where the slope begins to decrease most rapidly.
Thank you for your help!
Image Analyst
Image Analyst on 20 Jun 2012
Do you really need the x location of the steep part? Or can you just threshold the y values to find it? For example, maybe you can get the x like this: x= find(signal > 0.3, 1, 'last') so you find the x location where the signal exceed some threshold, like 0.3.
What if you had a steep part that was in the range y = [0.2 to 0.5] but you had a steeper one somewhere down in the range of y= [0 to 0.2]? Are you sure you'd want the lower amplitude signal just because it's steeper?

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Answers (2)

the cyclist
the cyclist on 19 Jun 2012
As Ryan comments, you "just take the derivative", but that is a gross simplification. Taking the numerical derivative of noisy discrete data is a tricky business.
I would suggest taking a look at the following FEX submission, and carefully reading the description:

Ayodele Oladeji
Ayodele Oladeji on 12 Jan 2015
Edited: Ayodele Oladeji on 12 Jan 2015
Perform the following steps
  • Use a low pass filter to smoothen the data points (smooth function could be helpful)
  • Find the gradient of all points on the data and calculate the slope= (( diff(y_data)/diff(x_data))
  • Depending on what you define as "most rapidly", you can apply the function find to your slope data and track index as follows: find(slope >= steep_threshold).
I hope that was helpful
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GOPEE Ajit Kumar
GOPEE Ajit Kumar on 25 Feb 2017
ok but how do you calculate the gradient of all points on the data if I have curve in a binary image and that I do not know the equation of the curve? Thanks

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