MATLAB: Decreasing point on curve

Question

Hello,

What could determine the point where the curve start decreasing? how to best specify this point?

Thank you.

Answer 1

Hi,

I think the best way to do so has already been described here and here:

basically there are two ways described there:

1- triangle thresholding

2- local maxima of curvature

i prefer the first one as i think it directly answer your question (the second one is for more spesific tasks)

% here is a small code to help you start
% Lets say your data are defined in (x,y) values
% then do the following
time = x;% here you should enter your data name

data = y;% here you should enter your data name
% Basically it draws a line from the peak to the tail and then draws 
% perpendicular lines from that hypotenuse line to the curve. 
% The longest (smollest) perpendicular line from the hypotenuse to the curve 
% indicates the "corner" of the curve. Maybe that will work for you. (this discribtion was taken from the reference before)
% Two endpoints on the curve "data"
x = [time(1) time(end)];
y = [data(1) data(end)];
% The slope of the line connecting the two endpoints
m = ( y(2) - y(1) )/( x(2) - x(1) );
pm= - 1 / m;
figure();hold all
hP = plot(time,data,'b',x,y,'g',x(1),y(1), 'ro');grid on
yl = ( (m * time) + (m^2 * data) - (m * x(1)) + y(1) )/(1+m^2);
xl = T1 - m*(yl - data);
d2 = (xl - time).^2 + (yl - data).^2;
perpDist = d2;
[val_max, idx_max] = max(perpDist);
[val_min, idx_min] = min(perpDist(2:end-1));
[val_maxL, idx_maxL] = max(perpDist(1:idx_min));
plot(time,data,'b',time(idx_max),data(idx_max),'ro',time(idx_min),data(idx_min),'ro',time(idx_maxL),data(idx_maxL),'ro');grid on;hold all; plot(time,perpDist); hold off

I hope this answer your question (how accurate the point will depend on your massy data)