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Monotonically iincreasing, not strictly increasing.
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In [[image processing]] and [[image recognition]], '''pixel connectivity''' is the way in which [[pixels]] in 2- or 3-dimensional images relate to their neighbors.
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==Types of connectivity==
===2-dimensional===
====4-connected====
4-Connected pixels are neighbors to every pixel that touches one of their edges. These pixels are connected horizontally and vertically, or diagonally. In terms of pixel coordinates, every pixel that has the coordinates
 
: <math>\textstyle(x\pm1, y)</math> or <math>\textstyle(x, y\pm1)</math>
 
is connected to the pixel at <math>\textstyle(x, y)</math>.
 
See also: [[Von Neumann neighborhood]]
 
==== 6-connected ====
6-connected pixels are neighbors to every pixel that touches one of their corners (which includes pixels that touch one of their edges) in a [[Hexagonal tiling|hexagonal]] grid or [[stretcher bond]] rectangular grid.
 
There are several ways to map hexagonal tiles to integer pixel coordinates. With one method, in addition to the 4-connected pixels, the two pixels at coordinates <math>\textstyle(x+1,y+1)</math> and <math>\textstyle(x-1,y-1)</math> are connected to the pixel at <math>\textstyle(x,y)</math>.
 
====8-connected====
8-connected pixels are neighbors to every pixel that touches one of their edges or corners. These pixels are connected horizontally, vertically, and diagonally. In addition to 4-Connected pixels, each pixel with coordinates <math>\textstyle(x\pm1,y\pm1)</math> or <math>\textstyle(x\pm1,y\mp1)</math> is connected to the pixel at <math>\textstyle(x,y)</math>.
 
See also: [[Moore neighborhood]]
 
===3-dimensional===
====6-connected====
6-connected pixels are neighbors to every pixel that touches one of their faces. These pixels are connected along one of the [[Cartesian coordinate system#Cartesian coordinates in three dimensions|primary axes]]. Each pixel with coordinates <math>\textstyle(x\pm1, y, z)</math>, <math>\textstyle(x, y\pm1, z)</math>, or <math>\textstyle(x, y, z\pm1)</math> is connected to the pixel at <math>\textstyle(x, y, z)</math>.
 
====18-connected====
18-connected pixels are neighbors to every pixel that touches one of their faces or edges. These pixels are connected along either one or two of the primary axes. In addition to 6-Connected pixels, each pixel with coordinates <math>\textstyle(x\pm1, y\pm1, z)</math>, <math>\textstyle(x\pm1, y\mp1, z)</math>, <math>\textstyle(x\pm1, y, z\pm1)</math>, <math>\textstyle(x\pm1, y, z\mp1)</math>, <math>\textstyle(x, y\pm1, z\pm1)</math>, or <math>\textstyle(x, y\pm1, z\mp1)</math> is connected to the pixel at <math>\textstyle(x, y, z)</math>.
 
====26-connected====
26-connected pixels are neighbors to every pixel that touches one of their faces, edges, or corners. These pixels are connected along either one, two, or all three of the primary axes. In addition to 18-Connected pixels, each pixel with coordinates <math>\textstyle(x\pm1, y\pm1, z\pm1)</math>, <math>\textstyle(x\pm1, y\pm1, z\mp1)</math>, <math>\textstyle(x\pm1, y\mp1, z\pm1)</math>, <math>\textstyle(x\pm1, y\mp1, z\mp1)</math>, <math>\textstyle(x\mp1, y\pm1, z\pm1)</math>, <math>\textstyle(x\mp1, y\pm1, z\mp1)</math>, <math>\textstyle(x\mp1, y\mp1, z\pm1)</math>, or <math>\textstyle(x\mp1, y\mp1, z\mp1)</math> is connected to the pixel at <math>\textstyle(x, y, z)</math>.
 
== See also ==
* [[Digital topology]]
* [[Grid cell topology]]
 
==References==
 
*{{Citation | author=A. Rosenfeld , A. C. Kak | title=Digital Picture Processing | publisher=Academic Press, Inc.| year=1982 | isbn=0-12-597302-0 }}
*{{Citation
| url = http://www.mathworks.com/access/helpdesk_r13/help/toolbox/images/morph12.html
| title = Mathworks: Pixel Connectivity
| year = 2009
| author =
| journal = IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
| pages = 52–62
| volume = 18
| issue = 1
| doi = 10.1109/TIP.2008.2007067
| isbn =
| format =
| accessdate = 2009-02-16
| pmid = 19095518
| last1 = Cheng
| first1 = CC
| last2 = Peng
| first2 = GJ
| last3 = Hwang
| first3 = WL
}}
*{{Citation
| url = http://homepages.inf.ed.ac.uk/rbf/HIPR2/connect.htm
| title = Pixel Connectivity
| year = 2009
| author =
| journal = IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
| pages = 52–62
| volume = 18
| issue = 1
| doi = 10.1109/TIP.2008.2007067
| isbn =
| format =
| accessdate = 2009-02-16
| pmid = 19095518
| last1 = Cheng
| first1 = CC
| last2 = Peng
| first2 = GJ
| last3 = Hwang
| first3 = WL
}}
 
[[Category:Digital topology]]
[[Category:Graph connectivity]]

Revision as of 06:00, 27 November 2013

In image processing and image recognition, pixel connectivity is the way in which pixels in 2- or 3-dimensional images relate to their neighbors.

Types of connectivity

2-dimensional

4-connected

4-Connected pixels are neighbors to every pixel that touches one of their edges. These pixels are connected horizontally and vertically, or diagonally. In terms of pixel coordinates, every pixel that has the coordinates

(x±1,y) or (x,y±1)

is connected to the pixel at (x,y).

See also: Von Neumann neighborhood

6-connected

6-connected pixels are neighbors to every pixel that touches one of their corners (which includes pixels that touch one of their edges) in a hexagonal grid or stretcher bond rectangular grid.

There are several ways to map hexagonal tiles to integer pixel coordinates. With one method, in addition to the 4-connected pixels, the two pixels at coordinates (x+1,y+1) and (x1,y1) are connected to the pixel at (x,y).

8-connected

8-connected pixels are neighbors to every pixel that touches one of their edges or corners. These pixels are connected horizontally, vertically, and diagonally. In addition to 4-Connected pixels, each pixel with coordinates (x±1,y±1) or (x±1,y1) is connected to the pixel at (x,y).

See also: Moore neighborhood

3-dimensional

6-connected

6-connected pixels are neighbors to every pixel that touches one of their faces. These pixels are connected along one of the primary axes. Each pixel with coordinates (x±1,y,z), (x,y±1,z), or (x,y,z±1) is connected to the pixel at (x,y,z).

18-connected

18-connected pixels are neighbors to every pixel that touches one of their faces or edges. These pixels are connected along either one or two of the primary axes. In addition to 6-Connected pixels, each pixel with coordinates (x±1,y±1,z), (x±1,y1,z), (x±1,y,z±1), (x±1,y,z1), (x,y±1,z±1), or (x,y±1,z1) is connected to the pixel at (x,y,z).

26-connected

26-connected pixels are neighbors to every pixel that touches one of their faces, edges, or corners. These pixels are connected along either one, two, or all three of the primary axes. In addition to 18-Connected pixels, each pixel with coordinates (x±1,y±1,z±1), (x±1,y±1,z1), (x±1,y1,z±1), (x±1,y1,z1), (x1,y±1,z±1), (x1,y±1,z1), (x1,y1,z±1), or (x1,y1,z1) is connected to the pixel at (x,y,z).

See also

References

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  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

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  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

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    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

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