1. Image Processing and Analysis (ImagePandA) 9 – Shape Christoph Lampert / Chris Wojtan

2. Outline Representation Boundary following Signatures R(theta) Convex deficiency Skeletons Shape Descriptors Boundary Fourier descriptors Statistical Moments Regional Simple: area, permieter, ratio, … Topology (Euler characteristic) E = C-H Statistical Moments Moment Invariants Morphing Blending Morphing Level set methods 2

3. Overview Want to be able to compare and describe shapes and images Need meaningful geometric representations Need metrics which are similar for similar images Boundary description Shape of boundary/border Region description Color/texture/stuff within shape 3

4. Simple metrics Area Perimeter Ratio between Area & Perimeter CS 484, Fall 2012©2012, Selim Aksoy4

5. Boundary following 5

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7. 7

8. Distance vs. Angle signature 8 Invariant to translation, scale, and rotation Assuming: start from centroid, consistently pick starting point

9. Distance vs. Angle signature 9

10. 10 Invariant to translation, scale, and rotation, assuming: start from centroid How would you compute the centroid? consistently pick starting point eg farthest from centroid Parameterize by angle so # of pixels is irrelevant

11. Convex defficiency 11

12. Convex defficiency 12

13. Skeletons 13

14. Moment Invariants 14

15. Moment Invariants 15

16. Moment Invariants 16

17. Moment Invariants 17

18. Moment Invariants 18