1. International Workshop on Computer Vision
Computer Vision at IPM
Mehrdad Shahshahani
Institute for Studies in Theoretical Physics and Mathematics
International Workshop on Computer Vision
April 26-30, Tehran,Iran

2. Computer Vision Group Masoud Alipour Somayeh Danafar Ali Farhadi
Hanif Mohammadi
Nima Razavi
Azad Shadman
Lila Taghavi
Ali-Reza Tavakoli

3. Scope of Effort Limited to the Analysis of A Single Image
Object Differentiation
Segmentation
Conspicuously Absent: Use of a Data Bank

4. Methodologies Emphasis on Experimental Methods Statistical Analysis
Higher Order Statistics
SVD Transforms
Application of Methods of Computational Geometry
Memory/Priors

5. Variation of Correlations (cont.)

6. Variation of Correlations (cont.)

7. Variation of Correlations (cont.)

8. Rough Classification of Images

9. Rough Classification of Images (cont.)

10. Detection

11. Detection (cont.)

12. Detection (cont.) General Conclusion
Analysis of local correlations in a single image allows the detection of an extraneous object in a texture environment.

13. Segmentation
Application of analysis of correlations to segmentation of images
Requires more elaborate analysis
Roughly Speaking, two step process:
1. Identification of regions (windows) containing object.
2. Determination of the boundary of the object.

14. Segmentation (cont.)

15. Segmentation (cont.)

16. Segmentation (cont.)

17. Segmentation (cont.) General Conclusion
By analysis of local correlations segmentation can be achieved on the basis of local structure of textures.
Not necessary to make use of memory.
Analysis is based on a single image.
Complexity of algorithm is O(N).

18. A Test Case How can one tell the difference between a cat and a dog?
The question can be viewed from a neurophysiologic or image processing point of view.
Can measures of statistical variability be used in distinguishing between dogs and cats?

19. LPC Surfaces One canonically constructs a surface (LPC surface)
from the analysis of local correlations of an image.

20. LPC Surfaces (cont.)

21. LPC Surfaces (cont.)

22. LPC Surfaces (cont.) LPC surfaces are highly non-differentiable.
Discrete geometry of LPC surfaces.
Curvature of a triangulated surface.

23. Triangulation of a Surface

24. Curvature of a triangulation
Curvature at a vertex v is
6 – number of edges incident on v
General Conclusion: Count the number of triangles to obtain measure of statistical variability of the surface.

25. Counting triangles

26. Counting Triangles
Statistical Variability of textures of cats and dogs reflected in discrete curvature LPC surfaces.
It can be achieved more simply by a judicious method for counting triangles per unit area.
Can tell the difference between a REAL dog and a REAL cat!

27. Singular Value Decomposition
SVD decomposition of sliding windows
S=UDV
Diagonal entries positive and in decreasing order.
Do the diagonal matrices D contain significant information about structural content of an image?

28. SVD (continued)

29. SVD (continued)

30. SVD (continued)

31. SVD (continued)

32. SVD Transforms
From Diagonal entries of SVD decomposition of sliding windows on an image we construct the SVD transform or SVD surface.

33. SVD Transform (cont.)

34. SVD Transform

35. Application of SVD Transforms
1. Detection of objects in a texture background.
2. Detection of fractures or defects.
3. Segmentation of Images.
4. Determination of location of eyes.

36. Detection

37. Detection (continued)

38. Detection (continued)

39. Detection of Fractures

40. Segmentation

41. Segmentation (continued)

42. Effect of change in lighting and blurring on segmentation

43. Segmentation (continued)

44. Segmentation (continued)

45. Segmentation (continued)
Conclusion:
Segmentation via SVD transforms isolates objects on the basis of their local texture structures.
Is not sensitive to changes in lighting, orientation, or similar distortions.

46. Locating the Eyes = - SVD Transform Edge detection with noise removal

47. Robust

48. Analysis of SVD
Understanding the meaning and implications of the SVD decomposition
Substituting the diagonal part D from one image into another.

49. Analysis of SVD (cont.)
ws=4
D woman in U,V Lena

50. Analysis of SVD (cont.)
ws=4
D Lena in U,V woman

51. Analysis of SVD (cont.)
ws=32
D Lena in U,V woman

52. Analysis of SVD
ws=4
D Lena in U,V random

53. Analysis of SVD (cont.)
ws=32
D random in U,V Lena

54. Conclusion Diagonal SVD contains significant information.
Relative importance of D relative to U,V decreases as window size increases.
U, V contain information about correlational structure of image.
For small window sizes U and V behave like high frequencies.

55. Other Research 1. Eye/Iris Printing 2. Shape Matching
3. Robotic Motion