Curavture/Slope Filtering

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?

Answer 1

[Star Strider]

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))

.

[Ian Bunker]

This is a really versatile way of accomplishing this task, it also preserves the data more than a lengthy mathematical operation with multiple error ranges. Thanks!

[Star Strider]

As always, my pleasure!