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
Hironori Takeuchi, Tetsuya Nasukawa, et al.
Transactions of the Japanese Society for Artificial Intelligence
Khalid Abdulla, Andrew Wirth, et al.
ICIAfS 2014
Chen-chia Chang, Wan-hsuan Lin, et al.
ICML 2025