[vtkusers] Statistical Model with partially available observations (using vtkPCAStatistics and vtkPCAAnalysisFilter)

[Dänzer, Stefan]

Hello David,

answers threaded in below.

_______________________________________________________________________
Dipl. Inform. Stefan Daenzer
Research Associate | Working Group - Scientific Methods

Universität Leipzig | Faculty of Medicine
Innovation Center Computer Assisted Surgery (ICCAS)
Semmelweisstr. 14
D - 04103 Leipzig
Germany

Phone: ++49 (0) 341 / 97 - 1 20 03
Fax: ++49 (0) 341 / 97 - 1 20 09
Email: stefan.daenzer at iccas.de

-----Ursprüngliche Nachricht-----
Von: David Thompson [mailto:dcthomp at sandia.gov] 
Gesendet: Freitag, 19. März 2010 19:18
Cc: 'vtkusers at vtk.org'
Betreff: Re: [vtkusers] Statistical Model with partially available observations (using vtkPCAStatistics and vtkPCAAnalysisFilter)

> I'm a research assistant at the Innovation Center Computer Assisted  
> Surgery (ICCAS) in Leipzig, Germany. I'm working on Active Shape  
> Models and Active Appearance Models at the moment. I've discovered  
> two classes of interest for me in vtk. These are:
> vtkPCAAnalysisFilter (Intended for spatially corresponding points on  
> shape models) and
> vtkPCAStatistics (A more general filter to assess observations and  
> project those observations in the eigenspace of their covariance  
> matrix. This is what I use for creating statistical models of  
> texture, e.g. Active Appearance Models)
>
> I was wondering how these two filters cope with incomplete  
> observations, e.g. missing data components in the observations.

The vtkPCAStatistics filter requires each observation to be complete,  
but...

> Let me illustrate this by an example. If we want to build a  
> statistical model of an object in an image, say an apple in a  
> photograph. Assume we have several photos of apples and their  
> respective segmentations as training data for our model. Further  
> assume some apples are only contained partially in some of the  
> photos. Statistically speaking, those apples represent partial  
> observations. I was wondering how to best incorporate those partial  
> observations in a statistical model which could be built by the two  
> mentioned vtk filters.

... it sounds to me like each of your observations is a measurement of  
*an* apple, not a measurement of *all* apples. Thus a single photo  
might contain several observations (at most one for each distinct  
apple). Each segmented apple is an observation in its own right. In  
that case, your observations are not partial. Or do I not understand  
your situation?

Maybe I was a bit unclear in my example. There is only one apple in each photo.

	David