• [cliquer ici pour la version en français]

Di Gesú, V. & Starovoitov, V., 1999, Distance-based functions for image comparison, Pattern Recognition Letters, 20(2), pp. 207–14.

Methodology/Main results

The paper deals with an extension of IDF (Image Distance Function). IDF is another name for Distance Transform. The extension is classicaly obtained by viewing a pixel as a point $(i, j, a_ij)$ in 3D space.

The proposition is compared to other methods. Wilson extension is rejected due to heavy computation times. Retained methods are :

• HG : the classical Hausdorff distance
• AD : averaged distances. Based on local means of IDF difference (as in Baddeley’s expression). Parameter : sliding window size. No given reference.
• GD : global distance. Home-made solution combining distances and gray-level differences. No given reference.
• SD : symmetry based distnace. Seems to be a measure of symmetry with respect to axes. See [Discrete Symmetry Transform, Di Gesù 1996]. Added to reading list.
• C0 : normalized cross correlation ratio
• SE : root MSE

Theses methods are compared with respect to :

• normalization : are the values between 0 and 1?
• consitence : $d = 0$ iff images are identical, $d = 1$ iff one image is uniformly to gray level $G$ and the other uniformly to 0.
• symmetry
• triangulare inequality : ok for AD and CO
• complexity : between $O(N^2)$ and $O(N^4)$

Finally : HG, GD, SD, SE are metrics. AD and CO are similarities (note : the authors don’t define these).

The distances are qualitatively compared on some image exemples. Better results are obtained when local structures comparison is combined with global intensity comparison.

Advantages/Interest

Some interesting considerations for building a “topology” of image distances.

Distadvantages/Criticism

Too much home-made solution. Gray-level extension by mixing spatial and intensity dimensions leading to inhomogenuous expressions.