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Unformatted text preview: 1. Euclidean Distance : standard distance concept D e ( p,q ) = r ( xs ) 2 + ( yt ) 2 2. CityBlock Distance : move along 4neighbors (right angles) D 4 ( p,q ) =  xs  +  yt  measure number of 4neighbor movements 3. Chessboard Distance : like the movements along a chessboard D 8 ( p,q ) = max { xs  ,  yt } measure number of 8neighbor movements CMPEN/EE455 Lect 5 9 The distance measures above are called metrics , because they satisfy the following three properties of a metric: 1. Positive deniteness: a. D ( p,q ) b. D ( p,q ) = 0 p q 2. Symmetry: D ( p,q ) = D ( q,p ) 3. Triangle inequality: D ( p,q ) D ( p,z ) + D ( z,q ) CMPEN/EE455 Lect 5 10 The digital disks with r = 1 for the three distance metrics are: circle, diamond (rhombus), and square....
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 Fall '08
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