02 - Pixel Connectivity

02 - Pixel Connectivity - 4/28/2008 Pixel Relationships...

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4/28/2008 1 Pixel Relationships 84 () D Np N p N p = N D ( p ) 1 copyright 2002©H. R. Myler A pixel has four horizontal and vertical neighbors and four diagonal neighbors Some of the neighbors may fall outside the image if p is on the border of the image m-Connectivity 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 0 1 4-connected 8-connected m-connected 0 1 0 0 0 1 V – set of intensity values used to define connectivity. In binary images, V = {1} – refers to connectivity of pixels with value 1. 2 copyright 2002©H. R. Myler Two pixels, p and q, with values from V are m-connected if: (i) q is in N 4 (p) or (ii) q is in N D (p) and N 4 (p) N 4 (q) is empty.
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4/28/2008 2 A (digital) path (or curve) from pixel p with coordinates (x,y) to pixel q with coordinates (s,t) is a sequence of distinct pixels with coordinates 00 11 ( , ), ( , ),. ..( , ) nn x yx y x y where () ( ) ( ) xy xya n dxy s t ( ,)( , )( , )( , ) = = and pixels (, ) ( , ) ii i i x y and x y + + are connected for 1 in In this case, n is the length of the path. If (, )(, ) x y = the path is a closed path. We can define 4-, 8-, or m-paths depending on type of 3 copyright 2002©H. R. Myler connectivity specified: path between top right and bottom right pixels are 8—paths and m-path (previous slide) If S is a subset of pixels in am image, two pixels p and q are said to be connected in S if there is a path between them consisting entirely of pixels in S. For any p in S the set of pixels that are connected to it in For any in S, the set of pixels that are connected to it in S is called a connected component of S. if it only has one connected component, then set S is called a connected set .
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02 - Pixel Connectivity - 4/28/2008 Pixel Relationships...

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