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.