Thread Subject: Simple symmetry in image

Hi there,

I'm trying to guess a plane of symmetry in a grayscale image.
The plane is expected to be vertical (ie, left/right
symmetry that you would find in, say, an image of a
spray-painted letter 'V').

What technique should I use to determine this plane?
For example, I have tried moving a window of pixels from the
left to right end of the picture, and at each step:
- mirroring the right half of the window
- subtracting this mirrored right half from the window left half
- summing the resulting pixels
The result of this sum gives a measure of symmetry as a
function of horizontal location, however I'm sure there are
more precise and robust ways to get this measure.

Can anyone please enlighten me?
I have the image processing toolbox.

Thanks for any help,
Sven.

In article <fnmf5h$e1k$1@fred.mathworks.com>,
Sven <sven.holcombe@removethis.gmail.com> wrote:

>I'm trying to guess a plane of symmetry in a grayscale image.

>For example, I have tried moving a window of pixels from the
>left to right end of the picture, and at each step:
>- mirroring the right half of the window
>- subtracting this mirrored right half from the window left half
>- summing the resulting pixels
>The result of this sum gives a measure of symmetry as a
>function of horizontal location, however I'm sure there are
>more precise and robust ways to get this measure.

I do not have a better method to suggest at the moment, but
I note that your technique could possibly be optimized a bit
by using cumsum(). If you had C = cumsum() along rows,
and W the window size, and L the location being probed, then
the measure would be

sum( (C(:,L-W+1) - C(:,L-W)) - (C(:,L+W+1) - C(:,L+W)) )

or something close to that.
--
  "There are some ideas so wrong that only a very intelligent person
  could believe in them." -- George Orwell

roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote in
message <fnmgha$jn8$1@canopus.cc.umanitoba.ca>...
> In article <fnmf5h$e1k$1@fred.mathworks.com>,
> Sven <sven.holcombe@removethis.gmail.com> wrote:
>
> >I'm trying to guess a plane of symmetry in a grayscale image.
>
> >For example, I have tried moving a window of pixels from the
> >left to right end of the picture, and at each step:
> >- mirroring the right half of the window
> >- subtracting this mirrored right half from the window
left half
> >- summing the resulting pixels
> >The result of this sum gives a measure of symmetry as a
> >function of horizontal location, however I'm sure there are
> >more precise and robust ways to get this measure.
>
> I do not have a better method to suggest at the moment, but
> I note that your technique could possibly be optimized a bit
> by using cumsum(). If you had C = cumsum() along rows,
> and W the window size, and L the location being probed, then
> the measure would be
>
> sum( (C(:,L-W+1) - C(:,L-W)) - (C(:,L+W+1) - C(:,L+W)) )
>
> or something close to that.

Thanks Walter, the cumsum() method works very well. I have
found that for my images, the symmetry plane becomes more
apparent if I view the columnwise cumsum result, rather than
the original image. So, I am using your method on this
cumsum(originalI) image, and I can then find local absolute
mins in the result. I have to admit that I can't quite
conceptualise how your sum( ... ) line above actually works.
 Why do you only consider adjacent pairs of columns here?

Regardless, thank you very much.
Sven.