David W. Jacobs, Daphna Weinshall, et al.
IEEE Transactions on Pattern Analysis and Machine Intelligence
Any notion of "closeness" in pattern matching should have the property that if A is close to B, and B is close to C, then A is close to C. Traditionally, this property is attained because of the triangle inequality (d(A, C) ≤ d(A, B) + d(B, C), where d represents a notion of distance). However, the full power of the triangle inequality is not needed for this property to hold. Instead, a "relaxed triangle inequality" suffices, of the form d(A, C) < c(d(A, B) + d(B, C)), where c is a constant that is not too large. In this paper, we show that one of the measures used for distances between shapes in (an experimental version of) IBM's QBIC1 ("Query by Image Content") system (Niblack et al., 1993) satisfies a relaxed triangle inequality, although it does not satisfy the triangle inequality.
David W. Jacobs, Daphna Weinshall, et al.
IEEE Transactions on Pattern Analysis and Machine Intelligence
Kenneth L. Clarkson, Elad Hazan, et al.
Journal of the ACM
Xiaoxiao Guo, Shiyu Chang, et al.
AAAI 2019
Joseph Y. Halpern
aaai 1996