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==Abstract Cell Complex Digital Image Representation==
A digital image may be represented by a 2D Abstract Cell Complex (ACC) by decomposing the image into its ACC dimensional constituents: points (0-cell), cracks/edges (1-cell), and pixels/faces (2-cell).▼
[[File:Digital Image ACC Decomposition.PNG|thumb|A 3x4 digital image decomposed into its Abstract Cell Complex dimensional constituents.]]
▲A digital image may be represented by a 2D Abstract Cell Complex (ACC) by decomposing the image into its ACC dimensional constituents: points (0-cell), cracks/edges (1-cell), and pixels/faces (2-cell).
This decomposition together with a coordinate assignment rule to unambiguously assign coordinates from the image pixels to the dimensional constituents permit certain image analysis operations to be carried out on the image with elegant algorithms such as crack [[Boundary Tracing]], [[Digital Straight Segment]] subdivision, etc. One such rule maps the points, cracks, and faces to the top left coordinate of the pixel. It should be noted that these dimensional constituents require no explicit translation into their own data structures but may be implicitly understood and related to the 2D array which is the usual data structure representation of a digital image. This coordinate assignment rule and the renderings of each cell incident to this image is depicted in the image at right.▼
[[File:Digital Image ACC Coordinate Assignment.PNG|thumb|Digital Image ACC Coordinate Assignment]]
▲This decomposition together with a coordinate assignment rule to unambiguously assign coordinates from the image pixels to the dimensional constituents permit certain image analysis operations to be carried out on the image with elegant algorithms such as crack [[Boundary Tracing]], [[Digital Straight Segment]] subdivision, etc. One such rule maps the points, cracks, and faces to the top left coordinate of the pixel. It should be noted that these dimensional constituents require no explicit translation into their own data structures but may be implicitly understood and related to the 2D array which is the usual data structure representation of a digital image. This coordinate assignment rule and the renderings of each cell incident to this image is depicted in the image at right.
== References ==
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