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Frechet Distance Calculator

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Estimate the similarity between curves in space using the scalar Frechet Distance.

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Description

Tristan Ursell
Frechet Distance between two curves
May 2013

 f = frechet(X1,Y1,X2,Y2)
 f = frechet(X1,Y1,X2,Y2,res)

 (X1,Y1) are the x and y coordinates of the first curve (column vector).
 (X2,Y2) are the x and y coordinates of the second curve (column vector).

 The lengths of the two curves do not have to be the same.

 'res' is an optional parameter to set the resolution of 'f', the time to
 compute scales linearly with 'res'. 'res' must be positive, and if 'res'
 is larger than the largest distance between any two points on the curve
 the function will throw a warning. If 'res' is unspecified, the function
 will select a reasonable value, given the inputs.

 This function estimates the Frechet Distance, which is a measure of the
 dissimilarity between two curves in space (in this case in 2D). It is a
 scalar value that is symmetric with respect to the two curves (i.e.
 switching X1->X2 and Y1->Y2 does not change the value). Roughly
 speaking, this distance metric is the minimum length of a line that
 connects a point on each curve, and allows one to traverse both curves
 from start to finish. (wiki: Frechet Distance)

 The function requires column input vectors, and the function 'bwlabel'
 from the image processing toolbox.

EXAMPLE: compare three curves to find out which two are most similar

%curve 1
t1=0:1:50;
X1=(2*cos(t1/5)+3-t1.^2/200)/2;
Y1=2*sin(t1/5)+3;

%curve 2
X2=(2*cos(t1/4)+2-t1.^2/200)/2;
Y2=2*sin(t1/5)+3;

%curve 3
X3=(2*cos(t1/4)+2-t1.^2/200)/2;
Y3=2*sin(t1/4+2)+3;

f12=frechet(X1',Y1',X2',Y2');
f13=frechet(X1',Y1',X3',Y3');
f23=frechet(X2',Y2',X3',Y3');
f11=frechet(X1',Y1',X1',Y1');
f22=frechet(X2',Y2',X2',Y2');
f33=frechet(X3',Y3',X3',Y3');

figure;
subplot(2,1,1)
hold on
plot(X1,Y1,'r','linewidth',2)
plot(X2,Y2,'g','linewidth',2)
plot(X3,Y3,'b','linewidth',2)
legend('curve 1','curve 2','curve 3','location','eastoutside')
xlabel('X')
ylabel('Y')
axis equal tight
box on
title(['three space curves to compare'])

subplot(2,1,2)
imagesc([[f11,f12,f13];[f12,f22,f23];[f13,f23,f33]])
xlabel('curve')
ylabel('curve')
cb1=colorbar('peer',gca);
set(get(cb1,'Ylabel'),'String','Frechet Distance')
axis equal tight

Required Products Image Processing Toolbox
MATLAB release MATLAB 7.14 (R2012a)
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Comments and Ratings (2)
30 Jan 2014 Venkat R

Nice submission. Has great potential application.

05 Aug 2013 you  

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