How to quantify shape similarity between two vectors.

Question

dipak sanap 2024-9-9，18:01

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https://ww2.mathworks.cn/matlabcentral/answers/2151384-how-to-quantify-shape-similarity-between-two-vectors

回答： Image Analyst 2024-9-10，16:55

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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Answer 1

Torsten 2024-9-9，18:10

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编辑：Torsten 2024-9-9，18:11

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.

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Answer 2

Matt J 2024-9-10，5:00

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编辑：Matt J 2024-9-10，14:20

在 MATLAB Online 中打开

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