Supermetric search with the four-point property

Richard Connor, Lucia Vadicamo, Franco Alberto Cardillo, Fausto Rabitti

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

10 Citations (Scopus)
97 Downloads (Pure)


Metric indexing research is concerned with the efficient evaluation of queries in metric spaces. In general, a large space of objects is arranged in such a way that, when a further object is presented as a query, those objects most similar to the query can be efficiently found. Most such mechanisms rely upon the triangle inequality property of the metric governing the space. The triangle inequality property is equivalent to a finite embedding property, which states that any three points of the space can be isometrically embedded in two-dimensional Euclidean space. In this paper, we examine a class of semimetric space which is finitely 4-embeddable in three-dimensional Euclidean space. In mathematics this property has been extensively studied and is generally known as the four-point property.
All spaces with the four-point property are metric spaces, but they also have some stronger geometric guarantees. We coin the term supermetric as, in terms of metric search, they are significantly more tractable. We show some stronger geometric guarantees deriving from the four-point property which can be used in indexing to great effect, and show results for two of the SISAP benchmark searches that are substantially better than any previously published.
Original languageEnglish
Title of host publication9th International Conference on Similiarty Search and Applications
Number of pages14
ISBN (Print)9783319467580
Publication statusPublished - 24 Oct 2016
EventSISAP 2016 - 9th International Conference on Similarity Searches and Applications - Tokyo, Japan
Duration: 24 Oct 201626 Oct 2016

Publication series

NameLecture Notes in Computing Science
ISSN (Print)0302-9743


ConferenceSISAP 2016 - 9th International Conference on Similarity Searches and Applications


  • metric search
  • Hilbert embedding
  • four-point property

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