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Shape Correspondence through Landmark Sliding. Anup Kedia. Introduction. Shape Landmarks. Contd. Landmark Sliding Shape Correspondence Result. Need. Statistical Shape Analysis Accuracy. Different types of Shapes. Supports closed, open, self-crossing and multiple shapes. Input. - PowerPoint PPT Presentation
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Anup Kedia
Shape Correspondence through Landmark Sliding
Anup Kedia
Introduction
• Shape• Landmarks
Contd..
• Landmark Sliding• Shape Correspondence
• Result
Need
• Statistical Shape Analysis
• Accuracy
Different types of Shapes
• Supports closed, open, self-crossing and multiple shapes.
Input
• Landmarks of template shape
• Landmarks of target shape
• The shape is open or closed
Contd..
• 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.
Contd..
Problem
• If a landmark moves beyond its neighbours?
We add a constraint
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
Contd..
L Thin Plate matrix
λ = 10-3 in our experiments
Experiment
Open Shapes
• For open curves, we
1. Fix the end points
2. Remove segment between the first and last point while calculating R(s).
Experiment for open shapes
Multiple Curves
1. ‘L’ is calculated taking all the curves.
2. R(s) is calculated seperately for each curve.
Experiment for multiple curves
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.
Experiment
Conclusion
• Works for all types of shapes
• It considers both global shape deformation and local geometric features unlike the previous methods.