[Insight-users] Finding Connctedness

[Luis Ibanez]

Hi Ross,

Unfortunately 18 connectedness is not symmetic either...

It may be interesting to refactor the connectedness on the FloodFill
iterator so users could select from the commonly used topologies
(e.g. 26, 6 , 18) or even introduce one of their own.

Probably the best discussion about digital topology on medical images
is the book by Gabor T. Herman:
http://www.cs.gc.cuny.edu/~gherman/

"The Geometry of Digital Spaces"
http://www.birkhauser.com/detail.tpl?ISBN=0817638970

where both the FCC (Face Centred Cubic) and BCC (body centered cubic)
grids are discussed as support for 3D images.

Herman's group has developped algorithms for computer tomography
reconstruction on such grids.

The signal processing community is well aware of the advantages of
hexagonal grids in 2D and FCC/BCC grids in 3D. Those grids provide
better approximations for satisfying the sampling conditions of the
Shannon's theorem. It is also well known that FFT is more efficient
on hexagonal grids.

In spite of this evidence, modern image processing remains stuck
in the rectilinear grid mainly becase of writing nested for() loops
is easy in X and Y (bad FORTRAN heritage...)

Hopefully ITK iterators would help to get rid of this artificial
limitation.


The only way to get object/background symmetry in digital topology
on rectilinear grids is by accepting non-isotropic connectedness.
Which is in fact a hacked way of doing the right FCC or BCC topologies
on a rectilinear grid by distorting space.

Using this approach, a distorted FCC results in a 12-connected grid,
while a distorted BCC results in a 14-connected grid.




   Luis


============================================

Ross Whitaker wrote:

> 
> 
> "Connectedness" can be used for things other than tissue segmentation. 
> For instance, when tracing edges or tracking features, it is sometimes 
> desirable to have a notion of connectedness that is asymmetrical.  There 
> is nothing wrong with providing such functionality, as long as it is 
> documented.  I.e. I don't think we should not get pedagogical about the 
> algorithms we offer.
> 
> Is 18 connectedness symmetric?
> 
> Ross
>