1. Image Processing and Analysis (ImagePandA) 10 – Shape and Motion Christoph Lampert / Chris Wojtan

2. Space 2

3. 3 Distance functions

4. 4 Signed Distance functions

5. 5 Medial Axis

6. 6 Signed Distance functions

7. 7 Normals

8. 8 Signed Distance functions

9. 9 Curvature

10. 10 Signed Distance functions

11. 11 Surface Extraction

12. 12 Surface Extraction

13. 13 Surface Extraction

14. 14 Surface Extraction

15. Time 15

16. Blending Images 16

17. 17 t=0 t=1

18. 18

19. 19 t=0t=1 t=0.5

20. 20 t=0t=1 t=0.5

21. Morphing Images 21

22. Distorting Images Typically break up image into triangle mesh Each triangle has a piece of the image Moving vertices distorts the triangle Applies affine transformation to the triangle Applies affine transformation to the image 22

23. Morphing Images Find corresponding features in both images Interpolate feature positions Blend image colors  More sophisticated non-uniform distortions and blends are used in practice 23

24. Distortion 24

25. Distortion 25 Take image data from a pixel location And send it to some generic non-pixel location?

26. 26 Semi-Lagrangian Advection

27. Displacement Field 27

28. Displacement Field 28

29. Displacement Field 29

30. 30 Semi-Lagrangian Advection

31. Advection 31

32. Advection 32

33. Advection 33

34. 34 Semi-Lagrangian Advection

35. 35 Semi-Lagrangian Advection

36. 36 Signed Distance functions

37. The level set method https://www.youtube.com/watch?v=t7yOR882Et0 https://www.youtube.com/watch?v=TeuLhhR7UxM https://www.youtube.com/watch?v=JaBBQDx2BBk#t=61 https://www.youtube.com/watch?v=JaBBQDx2BBk#t=128 37

38. Level set method for segmentation Velocity is gradient of some “energy function” Always go downhill What is our energy function? We want it to penalize undesired segmentations Should tightly wrap around object Add length and curvature to energy Attract towards edges in image Subtract magnitude of image gradient from energy 38

39. Level set method for segmentation 39 LEFT: the initial curve was at the boundary of the image. RIGHT: the initial curve was a closed contour around a point on the inside of the pollen grain. The boundary is identified in white.