Automated Statistical Shape Analysis Planning Notes

this page contains rough notes used to define the automated statistical shape analysis. These have been revised and edited to form the formal project proposal

Summary, Meeting of 15 June 2007

We outlined a short sequence of analysis programs (starting with Yongang's work) that we believe will provide a general means to create a 3D shape-based atlas of shapes (e.g. vector geometry objects). The product of the analysis will be an atlas of the input shapes and a set of p-values representing the significance of some statistic that measure the difference of a shape in the original population from the atlas.

Initally, this difference measurement will be Euclidean distance, and the p-value based on a standard t-test. If it all works out, we can later add other mesurements and statistical tests.

We expect it will be used like this:

Researcher:
a) identifies two popluations - a test group , and a control group
b) generates shape ROI of , say, a hippocampus for these,
c) turns these into the input to Yongang's program, which is now (i think) minc OBJ files.
d) calls our analysis with the two groups of OBJ files as input
e) get's the output atlas with the p-values
f) publishes, with the attendant fame and glory.

This differs from what we presently do by a) it's based on shapes
b) it's "true 3d" (does not depend on 2d planar approxmations of UCF contours).
c) it does not depend on the assumption that you can reasonably fit a line to the shape (this is the core assumption of the medial core analysis of the hippocampus that is used now).
d) it will be cross-platform (e.g. Java, and C++ binaries for Sun,Mac,Windows and selected Linux).
e) source code will be available.

We expect to implement this as

• a set of Java programs to create the atlas and statistics (Craig's group provides this)
• a C++ program to the the nonlinear matching (please correct my description) (from Yongang)
• a Pipline to tie it all together - for LONI afilliates to use
• a script (probably PERL) to tie it all together, for -non LONI afilliates
• web pages documenting all the parts, and how they fit together
• A loni software download package containing all the above.

As we are all busy already, we'll need to fit the work to be done into what we are already doing, and so we plan to present a timeline to Dr. Toga of

• now - plan the project
• sep 30 - beta relase of everything to LONI afilliates for a month of testing
• oct 30 - final public release.

Raw Meeting Notes, 15 June 2007

process:
  
   for each shape in a group of shapes (G0):
 1)  Find Atlas (G0)

   a) pick one shape from the group G0.
   b) rigid align other shapes to this one
   c) compute average of (b) and the ref. shape -> AVG0
   d) align all members of G0 to AVG0 -> G1
   e) compute average of G1 -> AVG1
   f) measure change between || AVG1 - AVG0 ||
   g) repeat (d),(e),(f) until (f) < tolerance
   h) final AVG_N is the "AtlasG0"
   
 2) at each point in each control shape (SC) in G0:
    a) find difference vector between SC and Atlas (dilation)
    b) project this vector onto the atlas surface normal at that point
    c) append the magnitude of this projection to a list for this vertex
 3) do (2) except for disease shapes (DC)
 4) calulate a statistical test (T-Test, initally)  comparing the two lists for significance (p-value)
 5) assign this P-value to a copy of the atlas (p<0.05 is probably significant).



This method differs from existing tools because
   * it is completely general (no assumption that a medial line is a good fit)
   * it is totally 3d


Other Statistical Tests:
   * R-rank test ? 
   * distance should be euclidean distance
   * other metrics to measure ...

Questions:
   * is RigidQuaternionTransform equivalent to Yongang's matlab code (his Matlab code is well known, and "optimum").