# l5 - 1 Euclidean Distance standard distance concept D e p,q...

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1 CMPEN/EE455 Lecture 5 Topics today: 1. (G&W 2.5) More on pixel connectivity; binary images 2. (G&W 2.5.3) Distance metrics: distance between pixels

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CMPEN/EE455 – Lect 5 2 BINARY IMAGE: 1’s (255’s?): foreground (objects of interest) 0’s: background
CMPEN/EE455 – Lect 5 3 the famous LENNA image: gray scale image

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CMPEN/EE455 – Lect 5 4 threshold LENNA: binary-valued image (all 1’s and 0’s)
CMPEN/EE455 – Lect 5 5 same as previous page (threshold LENNA): but adjust DISPLAY values, so we can see something!

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CMPEN/EE455 – Lect 5 6 Keep only two biggest components in thresholded LENNA no labels used
CMPEN/EE455 – Lect 5 7 Keep only two biggest components in thresholded LENNA Labels (diﬀerent gray levels) used to distinguish two components

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CMPEN/EE455 – Lect 5 8 Distance Metrics: The distance between 2 pixels can be deﬁned in several ways. Let p = ( x,y ) and q = ( s,t ) be two pixels.

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Unformatted text preview: 1. Euclidean Distance : standard distance concept D e ( p,q ) = r ( x-s ) 2 + ( y-t ) 2 2. City-Block Distance : move along 4-neighbors (right angles) D 4 ( p,q ) = | x-s | + | y-t |- measure number of 4-neighbor movements 3. Chessboard Distance : like the movements along a chessboard D 8 ( p,q ) = max {| x-s | , | y-t |}- measure number of 8-neighbor 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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## This note was uploaded on 09/24/2009 for the course EE 455 taught by Professor Staff during the Fall '08 term at Penn State.

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l5 - 1 Euclidean Distance standard distance concept D e p,q...

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