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

[Zachary Pincus]

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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