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What is a seam (seam carving)

I am reading an article about cutting a seam to resize an image.

Down to page 3, where they mathematically define a seam, I need help explaining it.

The document says the seam is an 8-connected pixel path. How can this be 8-connected if the pixel cannot be on the same line? Shouldn't it be 3-linked?

http://www.seamcarving.com/arik/imret.pdf 20 mb PDF

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An 8-linked pixel path means that all 8 neighbors o around pixel x :

 ooo oxo ooo (1)

Count when determining if a pixel is connected. therefore x in

 xoo oxo oox (2)

are 8-connected. on the contrary, only 4 of these 4 neighbors look o :

  o oxo o (3)

according to this scheme, x in fig. 2 is not considered connected.

(there are no 3-related in computer graphics (what I know))

as said, the definition of a vertical seam:

the vertical seam is an 8-connected pixel path in the image from top to bottom, containing one and only one pixel in each line of the image

it seems to me pretty easy to understand. this is:

 x x x

- vertical seam (because there is only one pixel in the line):

 x x x

this is; this is:

 x xx x

no (because the line has two pixels).

hope this helps.

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It will not be connected 3, it will be connected 6, but since nothing is called 6 connected path, it is called 8-connected

("6" refers to 6 potential neighbors of a given pixel - 3 on the line above and 3 on the next line :)

 xxx o xxx
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