1 / 50

Alireza Tavakoli Targhi att@kth.se

Singular Value Decompositions with applications to 1. Texture differentiation 2. Detection of an extraneous object in a texture environment 3. Segmentation of images 4. Locating eyes in facial images. Alireza Tavakoli Targhi att@kth.se

silas-church
Download Presentation

Alireza Tavakoli Targhi att@kth.se

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Singular Value Decompositions with applications to1. Texture differentiation2. Detection of an extraneous object in a texture environment3. Segmentation of images4. Locating eyes in facial images Alireza Tavakoli Targhi att@kth.se Institute for Studies in Theoretical Physics and Mathematics (IPM), Iranand Royal Institute of Technology (KTH), Sweden International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  2. Introduction We propose new measures for texture classification based on a local version of Singular Value Decomposition (SVD) . The proposed measures classify textures by their roughness and structure. Experimental results show that these measures are suitable for texture clustering and image segmentation and they are robust to changes in local lighting, orientation etc. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  3. Overview of SVD Singular Value Decomposition A=U1*D*U2 Ui Orthogonal Matrix , D Diagonal Matrix with Diagonal Entries in descending order: d1 >d2 > …>=0 International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  4. SVD Curves To find the SVD curve of an arbitrary row of the texture: • Scan a row with overlapping w*w windows Wa , a=1,2,3,….. ; w ≈ 32 • Calculate the SVD Decomposition • Wa =U1,a*Da *U2,a • As windows scan the image we obtain w curves (i) corresponding to diagonal entries d1,a >d2,a>….>dw,a International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  5. Classification Diagonal entries reflect image characteristics . International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  6. The sizes of the first few coefficients are considerably larger than the remaining International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  7. SVD Curve Classifiers We introduce two measures, obtained from SVD curves, which capture some of the perceptual and conceptual features in an image. SVD Curve distance classifier SVD Curve mean classifier International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  8. SVD Curve Mean Classifier • Our experiments show that the smaller coefficients d a,j , i.e., da,j with 23<j<32, are more representative of the structure of the texture and less dependent on inessential features. In practice, we set l = 22 and k = 10. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  9. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  10. SVD-Distance Classifier International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  11. Detection of Extraneous Object: International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  12. Even Small objects International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  13. Interest Point Detector International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  14. The technique identifies the bug even the location of its legs International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  15. Added two coins International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  16. No Differentiation International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  17. SVD Transform • We slide a w*w window across the image. • We identify each window by its upper left corner coordinates (x,y). • Let F be a function of w variables. • The SVD surface is the graph of the function (x,y) → the value of F on D(x,y ). • The SVD transform is the representation of the of the SVD surface as a 2D image. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  18. SVD Transform International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  19. Original Image SVD Transform SVD surface International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  20. Segmentation via SVD Transform International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  21. Segmentation via SVD Transform International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  22. Segmentation via SVD Transform International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  23. Segmentation via SVD Transform International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  24. Segmentation via SVD Transform International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  25. Segmentation via SVD Transform International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  26. Application of Feature Vector IISVD Transform, Segmentation International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  27. Segmentation via SVD Transform International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  28. Sensitivity to Texture International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  29. Sensitivity to Texture The Berkeley Segmentation Data Base. Computer Vision Group. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  30. Segmentation via SVD Transform International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  31. Segmentation via SVD transform The Berkeley Segmentation Data Base. Computer Vision Group. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  32. The Berkeley Segmentation Data Base. Computer Vision Group. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  33. Effect of change of a parameter The Berkeley Segmentation Data Base. Computer Vision Group. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  34. Effect of change of a parameter International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  35. Segmentation (cont.) International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  36. Segmentation (cont.) International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  37. Segmentation (cont.) International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  38. Segmentation (cont.) International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  39. Images show the effect of substituting the diagonal part or the orthogonal parts from the SVD decomposition of an image into that of another image.ws=5 Understanding SVD International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  40. Images show the effect of substituting the diagonal part or the orthogonal parts from the SVD decomposition of Lena into that of a randomly generated image.ws=5 Understanding SVD International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  41. Understanding SVD Images show the effect of substituting the diagonal part or the orthogonal parts from the SVD decomposition of an image into that of another image.ws=32 International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  42. Understanding SVD Images show the effect of substituting the diagonal part or the orthogonal parts from the SVD decomposition of Lena into that of a randomly generated image.ws=32 International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  43. Invariance relative to inversion These images are negatives of each other. Their SVD surfaces are identical. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  44. An SVD Surface International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  45. Detecting cracks and defects International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  46. Detecting cracks and defects International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  47. Detecting cracks and defects International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  48. Detecting cracks and defects International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  49. Theoretical Framework • We do not have a definitive answer why SVD works to the extent that it does. However, on the basis of our experimentations we can assert the following: • 1. The diagonal entries of SVD capture some features of an image which are not encoded by the correlations of nearby pixels in an image. • 2. This may explain why images constructed on the basis local correlations virtually never exhibit features similar to ones in real images. Images constructed on the basis of Markov random fields or similar procedures generally look very random. • 3. As the size of the sliding window increases the importance of the orthogonal parts of SVD decomposition relative to the diagonal part increases. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

  50. Work in Progress • We are in the process of applying SVD for material/surface classification. • The SVD transform can be applied to the test case of differentiating between a dog and a cat. The results are preliminary and require further tests. • SVD transforms are also being tested on movie images. • Our methods are being tested on medical images by IRMA (Image Retrieval in Medical Applications) of Institut fuer Medizinische Informatik Universitaetklinikum der RWTH in Aachen, Germany. International Workshop on Computer Vision April 26-30, 2004 Tehran,Iran

More Related