Statistical Shape Models enables boundary finding in situations where gradient information is either non-existent or counter-intuitive.  They have this distinct advantage over general active contours that deform according to the underlying intensity terrain.  However...
 

...the intended shape must be known a priori and accurate statistics on that shape available.
 
 
 

I.  Developing a Statistical Shape Model
 
 
 

 
 

A.  Find Correspondence

 

B. Resample

Shapes come from non-aligned Medical Image Data (Need to align shapes in order to extract meaningful statistics on the shape).
 

C. Find Mean Shape

D. Align Shapes

I. Generalized Procrustes Analysis

• Rotation
• Scale
• Translation

E.  Compute Shape Basis Vectors

1. Singular Value Decomposition
2. Keep n most significant Basis Vectors

Each shape can be characterized by projecting it onto the basis vectors and storing the resulting n weights (contribution in the direction of the ith basis vector).
 

Shape Space  Is defined by the basis vectors and the standard deviation of the projection weights of all the images in the training set.  Thus, if 10 basis vectors are kept, the Shape Space is defined by 11 vectors.

F.  Model Gray Level Profiles

G.  Course Alignment of Mean Shape to Study

 
H.  Search Image to Match Profile

1. Constrained by Plausible Shape of Shape Model
 

I.  Use Detected Boundary as the second Body Force in Non-Rigid Registration Technique