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What distance metric can I use for comparing image features like elongation and solidity of a contour of each image? Except Least Square and without using a support vector machine because i do not know at which class images belong.

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Have you tried using the first two eigenvectors of the contour matrix (or its covariance matrix) as a measure for elongation? – Junuxx Feb 27 '13 at 9:59
up vote 3 down vote accepted

If I understood you correctly, each contour is described by a 2-element feature vector $f = [e, s]$, where $e$ is elongation and $s$ is solidity.

In that case, you might want to try the Mahalanobis distance, which is defined as follows: $$d(f_1, f_2) = \sqrt{(f_2 - f_1)C^{-1}(f_2 - f_1)}$$ where $f_1$ and $f_2$ are the feature vectors that you are comparing, and $C$ is the covariance matrix of your data set.

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