Locality sensitive hashing for efficient similar polygon retrieval

Haim Kaplan, Jay Tenenbaum

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Locality Sensitive Hashing (LSH) is an effective method of indexing a set of items to support efficient nearest neighbors queries in high-dimensional spaces. The basic idea of LSH is that similar items should produce hash collisions with higher probability than dissimilar items. We study LSH for (not necessarily convex) polygons, and use it to give efficient data structures for similar shape retrieval. Arkin et al. [2] represent polygons by their "turning function"- a function which follows the angle between the polygon's tangent and the x-axis while traversing the perimeter of the polygon. They define the distance between polygons to be variations of the Lp (for p = 1,2) distance between their turning functions. This metric is invariant under translation, rotation and scaling (and the selection of the initial point on the perimeter) and therefore models well the intuitive notion of shape resemblance. We develop and analyze LSH near neighbor data structures for several variations of the Lp distance for functions (for p = 1,2). By applying our schemes to the turning functions of a collection of polygons we obtain efficient near neighbor LSH-based structures for polygons. To tune our structures to turning functions of polygons, we prove some new properties of these turning functions that may be of independent interest. As part of our analysis, we address the following problem which is of independent interest. Find the vertical translation of a function f that is closest in L1 distance to a function g. We prove tight bounds on the approximation guarantee obtained by the translation which is equal to the difference between the averages of g and f.

Original languageEnglish
Title of host publication38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021
EditorsMarkus Blaser, Benjamin Monmege
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771801
DOIs
StatePublished - 1 Mar 2021
Event38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021 - Virtual, Saarbrucken, Germany
Duration: 16 Mar 202119 Mar 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume187
ISSN (Print)1868-8969

Conference

Conference38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021
Country/TerritoryGermany
CityVirtual, Saarbrucken
Period16/03/2119/03/21

Keywords

  • Locality sensitive hashing
  • Lp distance
  • Nearest neighbors
  • Polygons
  • Similarity search
  • Turning function

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