# Curavture/Slope Filtering

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Ian Bunker on 14 May 2021
Commented: Star Strider on 17 May 2021
I am currently making a program to process some data, part of this process is removing graphs that are sloped, such as the one below:
And retaining graphs that have curvature such as the one below:
I don't come from a strong applied mathematics background, one idea was to take a partial derivative and compare to a set threshold, the curvature formula is another possibility. Does anyone have any experience with this type of problem you would be willing to share?

Star Strider on 14 May 2021
One approach could be to look for changes in the slope (using the gradient function here) with respect to the number of elements in the vector, and reject those with the number of slope changes below a certain threshold.
To illustrate —
changefcn = @(y) numel(y) - nnz(gradient(y)<0);
x = linspace(0, 1); % Use The Same Independent Variable For simplicity
Curve1 = 1./(1+x);
Changes1 = changefcn(Curve1)
Changes1 = 0
figure
plot(x, Curve1)
text(mean(xlim),mean(ylim), sprintf('Changes = %2d',Changes1))
Curve2 = sin(15*pi*x)*0.1 - x;
Changes2 = changefcn(Curve2)
Changes2 = 44
figure
plot(x, Curve2)
text(mean(xlim),mean(ylim), sprintf('Changes = %2d',Changes2))
.
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Star Strider on 17 May 2021
As always, my pleasure!