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• The parameters are
is the curve length from u(0) to u(t)
s|L is the curve length from v(0) to v(s)
a|b modulus operation
GOAL : To find s = {s0 , s1 , … sn-1 } such that the shape ‘V’ (target) from it corresponds well to the template shape.
Problem
• How to represent the shape?
• We use Catmull Rom Splines since
a. They are smooth
b. They interpolate the landmarks.
Problem
• How to represent and initialize the landmarks?
We manually label the landmarks s.t1. The no. of landmarks are same2. The starting pt. is approximately the
same.i.e , we roughly correspond the landmarks
manually.
Goal
• We try to minimize the cost function,
Ø(s) = d(U,V) + λR(s)
d(U,V) -> landmark based shape difference
R(s) -> representation Error
λ -> Regularization Factor
Open Shapes
• For open curves, we
1. Fix the end points
2. Remove segment between the first and last point while calculating R(s).
Multiple Curves
1. ‘L’ is calculated taking all the curves.
2. R(s) is calculated seperately for each curve.
Multiple Shape Correspondence
• We have a set of samples We have to find an average shape to which all the shapes corresponds well.
• We do it by1. Taking average of all the shapes using
procustes analysis2. Slide the shapes w.r.t to the average shape3. Repeat the above process.