Locality Sensitive Hashing (LSH) is an effective method of indexing a set of items to support efficient nearest neighbors queries in high-dimensionalspaces . The basic idea of LSH is that similar items should produce hashcollisions with higher probability than dissimilar items . Arkin et al. representpolygons by their “turning function” – a function which follows the angle between the polygon’s tangent and the $ x $-axis while traversing the perimeter . They define the distance between polygons to be variations of the $ L_p $ (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 notionof shape resemblance . We prove some new properties of these turning functions that may be of independent interest. To tune ourstructures to turning functions of polygons, we prove someNew properties of the turning functions, we use it to give LSH structures for similar data structures for polygons. To learn more about LSH data structures, we develop and analyze LSH near neighbor data structures to LSH Data Structures for LSH- Structures, we also develop LSH

Author(s) : Haim Kaplan, Jay Tenenbaum

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Keywords : lsh - structures - turning - data - functions -

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