The Distribution Family of Similarity Distances G. J. Burghouts, A. W. M. Smeulders, J. M. Geusebroek In Advances in Neural Information Processing Systems 2007. [bibtex] [pdf] [url]

Assessing similarity between features is a key step in object recognition and scene categorization tasks. We argue that knowledge on the distribution of distances generated by similarity functions is crucial in deciding whether features are similar or not. Intuitively one would expect that similarities between features could arise from any distribution. In this paper, we will derive the contrary, and report the theoretical result that L_p-norms -a class of commonly applied distance metrics- from one feature vector to other vectors are Weibull-distributed if the feature values are correlated and non-identically distributed. Besides these assumptions being realistic for images, we experimentally show them to hold for various popular feature extraction algorithms, for a diverse range of images. This fundamental insight opens new directions in the assessment of feature similarity, with projected improvements in object and scene recognition algorithms.

@InProceedings{BurghoutsNIPS2007,
  author       = "Burghouts, G. J. and Smeulders, A. W. M. and Geusebroek, J. M.",
  title        = "The Distribution Family of Similarity Distances",
  booktitle    = "Advances in Neural Information Processing Systems",
  volume       = "20",
  year         = "2007",
  url          = "https://ivi.fnwi.uva.nl/isis/publications/2007/BurghoutsNIPS2007",
  pdf          = "https://ivi.fnwi.uva.nl/isis/publications/2007/BurghoutsNIPS2007/BurghoutsNIPS2007.pdf",
  has_image    = 1
}