Re: [Vxl-maintainers] Re: Border handling for images

[Harry L. V. <hl...@st...>]

Very nice.

FWIW, here is an obscure boundary condition that I implemented once, 
that reduces attenuation and visual artifacts near the border of an 
image when convolved with a smoothing filter. It makes no assumptions 
about pixel values beyond the border, and does not give more weight to 
border and corner pixels like "geodesic" does. It is equivalent to 
truncating the convolution kernel so that it does not overlap border 
pixels, while renormalizing it to avoid attenuating image intensity.

It can be implemented efficiently by convolving using 
vil_border_constant(0), and then rescaling the resulting image pixels at 
points where the kernel hung off the edge. The scale factor is the ratio 
of the integral of the entire kernel over that integral over the kernel 
which overlaps the image at that point. That value will be a constant 
for most of a row or column.

For example, if the original kernel is the 3x3 array [1 1 1; 1 2 1; 1 1 
1] the normalization factors for each image pixel would be:
 
  10/5 10/7 ... 10/7 10/5
  10/7   1  ...   1  10/7
            ...
  10/7   1  ...   1  10/7
  10/5 10/7 ... 10/7 10/5
 
I think this approach only make sense for positive valued 
(non-differencing) filters though. It's not something to be added to the 
existing framework; though vil_convolve* could recognize 
'vil_border_none' as a special case. I just thought I'd mention it in 
case it's of interest to anyone.

--Harry

Nicolas Burrus wrote:
> Peter,
>
> Actually I've implemented four kinds of border extensions, 
> vil_border_constant, vil_border_geodesic, vil_border_reflect (symmetry 
> w.r.t. the closest edge, I guess this is what you are talking about) 
> and vil_border_periodic (the right edge is linked to the left one and 
> the bottom one to the top one, like a "double" torus). I could not 
> think of other very common ones.
>
> Thanks,
>
> -- 
> Nicolas
>
> On 5/8/06, *Peter Vanroose* <pet...@ya... 
> <mailto:pet...@ya...>> wrote:
>
>     Nicolas,
>
>     I like the idea very much! It's a nice, modular design.
>     I would say, go ahead with it in CVS vxl.
>
>     (I'm thinking of yet another typical border extension method:
>     use reflected values, i.e., the border acts like a mirror.)
>
>     --      Peter.
>
_________________________________________________________
 Harry L. Voorhees, hl...@st..., 978-475-5279
    Stellar Science Ltd. Co., www.stellarscience.com
         "Stellar Scientific Software Solutions"