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

[David Thompson]

Hi Stefan,

 >>> ...
 >>> vtkPCAStatistics ... is what I use for creating statistical  
models of
 >>> texture, e.g. Active Appearance Models) ...
 >>> I was wondering how ... 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.

I see. And after a quick google of AAMs, it looks like a triangulation  
of the landmarks is used to integrate error between each pixel in the  
fit image and the linear approximation provided by the AAM (I could be  
horribly wrong). Assuming you're using the PCA filter to minimize this  
error (again, I could be horribly wrong), I would treat each triangle  
in the triangulation of the AAM landmarks as an independent  
observation of error. You would have to be careful with normalization  
so that frequently obscured triangles weren't ignored. You would also  
need to assume that whatever was obscuring landmarks was not included  
in the error estimate for a given triangle (i.e., only the object  
appears in the convex hull of the landmarks). Without more details on  
exactly how AAM works, I can only guess at how the PCA filters might  
be used.

	David