1. Chapter 8

2. Documented applications of TRS and affine moment invariants Character/digit/symbol recognition Recognition of aircraft and ship silhouettes (also from non-perpendicular views) Recognition of components on an assembly belt Recognition of biological shapes – algae, fishes, whales,... Landmark recognition in robotics Image registration (medical, satellite, aerial,...) Normalization of database images, retriaval Motion flow estimation Digital watermarking

3. Recognition of circular landmarks Measurement of scoliosis progress during pregnancy

4. The goal: to detect the landmark centers The method: template matching by invariants

5. Recognition of distorted landmarks

6. Landmark clusters in the space of the AMI’s

7. Landsat TMSPOT Satellite image registration

8. Registration algorithm Independent segmentation of both images Extraction of salient regions Calculating AMI’s Finding three most stable pairs in the AMI space Calculating the primal affine transform parameters Transforming the SPOT regions over the Landsat Finding matching regions by minimum distance in the image plane (10 found altogether). Region centroids serve as final control points Calculating the final affine transform parameters by a least-square fit Resampling and transformation of the SPOT image

9. Segmentation

10. Selected regions

11. Matched region pairs

12. Three most stable pairs found in the AMI space (the labels in circles) The other matching regions found by minimum distance in the image plane

13. Registered and superimposed images

14. Optical flow estimation Traditional method A method based on Zernike moments. Note fewer artifacts.

15. Image retrieval Moment invariants can be used as features for content-based image retrieval, particularly in case of simple 2D objects.

16. Digital watermarking by moments The host image The image with an invisible watermark based on rotation invariants.

17. Documented applications of convolution and combined invariants Character/digit/symbol recognition in the presence of camera shake or other blurs Robust image registration (medical, satellite) Camera position estimation through registration Multichannel deconvolution and superresolution Detection of image forgeries Focus/blur measurement

18. Camera position estimation through registration Photo at the initial position (sharp) Photo at the current position, unknown shift and rotation (blurred background because of the object in the foreground)

19. Position estimation algorithm Independent corner detection in both images Extraction of salient corner points Calculating blur-rotation invariants of a circular neighborhood of each extracted corner Matching corners by the invariants (14 matches found) Estimating the relative between-image shift and rotation by a least-square fit

20. Matched corners

21. Multichannel blind deconvolution For MBD, robust registration of the input blurred frames is required.

22. The Poor Fisherman, Paul Gauguin, 1896 MBD of long-exposure images

23. Copy-move forgery (clone of a region from the same image) The cloned region is often intentionally blurred to make its detection difficult Dividing the image into blocks, calculating blur invariants and looking for blocks having the same invariants Presence of identical blocks indicates cloning forgery. “Blind” detection without having the original. Detecting image forgeries

24. original duplicated regions fake

25. Recent world-famous photo of Iranian missiles

26. Duplicated regions indicate that the picture was manipulated

27. Moment-based focus measure Odd-order moments  blur invariants Even-order moments  blur/focus measure If M(g1) > M(g2)  g2 is less blurred (more focused)

28. Usage of a focus measure Global measurement – ordering a set of images, which differ from each other by a degree of blur, according to their quality. Typically in astronomy.

29. Images of different level of blur

30. Sunspots – blurring by atmospheric turbulence

31. Saturn images – intentional out-of-focus blur

32. Usage of a focus measure Global measurement – ordering a set of images, which differ from each other by a degree of blur, according to their quality. Typically in astronomy. The moments perform very well in the above cases because of their robustness to noise.

33. Usage of a focus measure Local measurement – selecting the frame in which a certain small region is sharp/least defocussed. Typically in multifocal image fusion.

34. Multifocus fusion based on a local blur measurement

35. Usage of a focus measure Local measurement – selecting the frame in which a certain small region is sharp/least defocussed. Typically in multifocal image fusion. The moments are worse than wavelets and Laplacian because of their global character.