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Curavture/Slope Filtering

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Ian Bunker
Ian Bunker 2021년 5월 14일
댓글: Star Strider 2021년 5월 17일
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?

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Star Strider
Star Strider 2021년 5월 14일
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
Star Strider 2021년 5월 17일
As always, my pleasure!

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