How to quantify shape similarity between two vectors.

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dipak sanap
dipak sanap 2024-9-9
回答： Image Analyst 2024-9-10
Ran in:
I need to quanitfy how similarity between two spectral profile. I have looked at procrustes distance but it dosent work when spectrum is shifted on x axis. Is there a way to quanitfy this, ideally between 0 (no similairty) and 1 (perfect similarity) ?
x1 = 0:0.1:10;
Y1 = gaussmf(x1,[0.8 5 ]);
Y2 = gaussmf(x1,[0.8 3 ]);
Y3 = gaussmf(x1,[0.4 2 ]);
figure(1)
plot(x1,Y1, 'k','Linewidth',2)
hold on
plot(x1,Y2, 'b','Linewidth',2)
hold on
plot(x1,Y3, 'r','Linewidth',2)
legend(["A","B","C"])
figure(1)
In the toy example, A and B are very similar so that should have a high similairty index but A-C and B-C should have lower similarity.

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回答（3 个）

Torsten
Torsten 2024-9-9
编辑：Torsten 2024-9-9
Shift the curves by their means first so that the means of all objects lie in the origin (0). This will remove translational differences between the objects.
Matt J
Matt J 2024-9-10
编辑：Matt J 2024-9-10
Ran in:
Perhaps you could use correlation-based similarity?
x1 = 0:0.1:10;
Y1 = gaussmf(x1,[0.8 5 ]);
Y2 = gaussmf(x1,[0.8 3 ]);
Y3 = gaussmf(x1,[0.4 2 ]);
corrcoeff(Y2,Y1)
ans = 1.0000
corrcoeff(Y2,Y3)
ans = 0.8944
corrcoeff(Y1,Y3)
ans = 0.8944
function coeff=corrcoeff(u,v)
coeff=max(xcorr(u,v))/norm(u)/norm(v);
end
Image Analyst
Image Analyst 2024-9-10

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