[Insight-users] Shape prior level sets: question about MAPCostFunction

[Quan Chen]

I thought it whether it is directed or undirected depends on the
narrow band active region you select.  If you select it around curve
A, then it is like calculate directed distance h(A, B). Curve A can be
very small and close to a bigger curve B and still get a good score. 
If you also select it around curve B, then the above scenario would
yield a big distance difference.


On Wed, 16 Feb 2005 14:39:22 -0800, Zachary Pincus <zpincus at stanford.edu> wrote:
> Quan,
> 
> Thanks for your suggestion!
> 
> I believe that the L-infinity norm of the difference between two signed
> distance functions is very similar to the undirected Hausdorff distance
> between the zero-level curves of those functions. (If we compute the
> difference only where one or the other of the signed distance functions
> is zero and take the L-inf norm [i.e. max] of that, then we would get
> precisely the undirected Hausdorff distance! Evaluating the difference
> between two distance functions at a point where one function is zero is
> simply looking up the minimum distance from one zero-level curve to the
> other at a point; doing this for both curves, and then taking the max
> gives the undirected Hausdorff distance.)
> 
> I had been thinking of moving to the L-inf norm for these calculations;
> this is a very principled reason to do so.
> 
> Thanks,
> Zach
> 
> On Feb 16, 2005, at 2:12 PM, Quan Chen wrote:
> 
> >> I decided that for my work, I would prefer to change the definition of
> >> the inside term from Leventon's work. He states that P(current curve |
> >> estimated shape) is inversely proportional to the volume of the
> >> current
> >> curve outside the estimated shape. This is just one possible model for
> >> that probability. I noticed that both the evolving curve and the
> >> estimated shape are signed distance functions, so they can be directly
> >> compared. As such, I use the L1-norm of the difference between these
> >> functions (in the narrow band active region) as a similarity metric,
> >> and use that as a proxy for the probability. L2 and L-infinity norms
> >> (RMSD and maximum deviation) seem good too. In this way, I encourage
> >> the shape model to "stay near" the evolving curve. This is bad when
> >> the
> >> curve is very small compared to its desired final size, however -- in
> >> these regimes Leventon's initial suggestion is better. I am examining
> >> ways to switch between the two probability definitions based on the
> >> size of the curve.
> >
> > Seems you are using some measure similiar to directed Hausdorff
> > distance, how about use UN-directed Hausdorff distance?
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>