Currently, there is no widely agreed upon skeletonizing algorithm that can provide a definite single pixel skeleton result as needed in classification and 
other comparisons. The situation is similar to the vectorization process where important parameters are selected subjectively. These low level tasks are 
sequentially rigid and non-reversible. I.e. mistakes made in earlier processing steps will not have a chance to be corrected. Our approach can be applied 
to the results from any skeletonizing algorithm as initial values and generates posterior samples which can be used to  compute posterior mean and 
confidence intervals.

To analyze a circular shape subset of interest from the estimated  skeletons, we present two multivariate flexible models that compare image structures 
and shapes which vary. For each object, the locations and  properties of points, which are sampled along the skeleton, are aligned  automatically by the 
given shape information and set as responses. A multivariate statistic is computed to compare the groups of objects change over time. Within a single 
object, the covariance matrix of sampled points is assumed circulant. The second method assumed a deformed ellipse model for each object skeleton 
with measurement error i.i.d distributed. The posterior mean shapes are used as responses for comparison at different time points.