How to calculate the area dissimilarity between two curves?
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I have two smoothed curves 'f' and 'g'.
f = [4.66356058704069;4.76003678995220;4.85195856216057;4.93937125386862;5.02241091568476;5.10134964882580;5.17664095531976;5.24896508820865;5.31927440175128;5.38883870162610;5.45908891231901;5.53146074451118;5.60723836246689;5.68739805142138;5.77245188496874;5.86229139244967;5.95603122633945;6.05185282963574;6.14684810324653;6.23686307337801;6.31713266653654;6.38291548453061;6.43012857947280;6.45598222878181;6.45961471018444;6.44272707671764;6.41021793173056;6.37081820388660;6.33483553209117;6.31189865041951;6.30870177304451;6.32932410300064;6.37554934094787;6.44718519393563;6.54238288416678;6.65795665776154;6.78970329352158;6.93272161169404;7.08173198273553;7.23139583607635;7.37663516888456;7.51295205483015;7.63674815284922;7.74522475322546;7.83628282367168;7.90842305541129;7.96064590925989;7.99235166170680;8.00324045099670;7.99321232321114]
and
g= [3.42595434180783;3.52889117917543;3.63122045210296;3.73294216049285;3.83405630405245;3.93456288219636;4.03446189394889;4.13375333784643;4.23243721183987;4.33051351319701;4.42798223853624;4.52484338386025;4.62109694458974;4.71674291559714;4.81178129124035;4.90621206539645;5.00003523149543;5.09325078264601;5.18585871176133;5.27785901168476;5.36925167531561;5.46003669573492;5.55021406633123;5.63978378092629;5.72874583375865;5.81710021946721;5.90484693307479;5.9919859699717;6.07851732589953;6.16444099693433;6.24975697947062;6.33446527020481;6.41856586611880;6.50205876447018;6.58494396278248;6.66722145883533;6.74889125065473;6.82995333650325;6.91040771487023;6.99025438446208;7.06949334419241;7.14812459317236;7.22614813069081;7.30356395619462;7.38037206926889;7.45657246961725;7.53216515704210;7.60715013142487;7.68152739270630;7.75529694086660]
'f' is produced by smoothing
x_f =[1.36; 1.26; 1.15; 1.07; 1.04; 0.975; 0.919; 0.902; 0.85]
y_f =[8.166216269;7.843848638;7.365180126;7.170119543;7.192934221;6.956545443;6.459904454;6.257667588;5.379897354]
And 'g' is produced by smoothing
x_g = [1.43;1.33;1.25;1.18;1.11;1.05;1;0.952;0.909;0.87;0.833]
y_g =[9.193091461;8.14221752;7.560356469;7.320262202;7.209229304;7.139303413;7.064348687;6.618999297;6.065270152;5.49321781;4.925745302]
I want to find the area dissimilarity between them. I am using this Equation
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/197436/image.png)
where D is the intersection between domains of two functions. The curves(f and g) needs to be rescaled before computing these dissimilarity. Dividing 'f' and 'g' by the maximum value of f. So the maximum value is 1.
Can you please help me, how can i implement this in MATLAB?
回答(1 个)
KSSV
2018-10-9
If D is the area you can calculate it using :
x_f =[1.36; 1.26; 1.15; 1.07; 1.04; 0.975; 0.919; 0.902; 0.85] ;
y_f =[8.166216269;7.843848638;7.365180126;7.170119543;7.192934221;6.956545443;6.459904454;6.257667588;5.379897354] ;
x_g = [1.43;1.33;1.25;1.18;1.11;1.05;1;0.952;0.909;0.87;0.833] ;
y_g =[9.193091461;8.14221752;7.560356469;7.320262202;7.209229304;7.139303413;7.064348687;6.618999297;6.065270152;5.49321781;4.925745302] ;
% Smoothe the curves
N = 1000 ;
xi_f = linspace(min(x_f),max(x_f),N)';
yi_f = interp1(x_f,y_f,xi_f) ;
f = [xi_f yi_f] ;
xi_g = linspace(min(x_g),max(x_g),N)';
yi_g = interp1(x_g,y_g,xi_g) ;
g = [xi_g yi_g] ;
P = InterX(f',g') ;
P(:,1) = [] ;
%%Get interscetion area
x0 = min(P(1,:)) ; x1 = max(P(1,:)) ;
f0 = f ; g0 = g ;
f(f(:,1)<x0,:) = [] ;f(f(:,1)>x1,:) = [] ;
g(g(:,1)<x0,:) = [] ;g(g(:,1)>x1,:) = [] ;
d = abs(trapz(f(:,1),f(:,2))-trapz(g(:,1),g(:,2))) ;
plot(f(:,1),f(:,2),'r')
hold on
plot(g(:,1),g(:,2),'b')
plot(P(1,:),P(2,:),'*k')
Get the function InterX from the link: https://in.mathworks.com/matlabcentral/fileexchange/22441-curve-intersections
3 个评论
KSSV
2018-10-9
The above code worked fine for me......let them be not same...doesn't matter....did you get any error?
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