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  1. Outline ... Feature extraction Feature selection / Dim. reduction Classification ...

  2. Outline ... Feature extraction shape texture Feature selection / Dim. reduction Classification ...

  3. How to extract features? • Eg.: giantin gpp130 ER LAMP Mito Nucleolin TfR Tubulin DNA Actin

  4. How to extract features? • Eg.: giantin gpp130 ER ER area(?) Mit LAMP Mito Nucleolin brightness(?) TfR Tubulin DNA Actin

  5. distance function: Euclidean, on the area, perimeter, and 20 ‘moments’ [QBIC, ’95] Q: other ‘features’ / distance functions? Images - shapes

  6. (A1: turning angle) A2: wavelets A3: morphology: dilations/erosions ... Images - shapes

  7. Wavelets - example http://grail.cs.washington.edu/projects/query/ Wavelets achieve *great* compression: 20 400 16,000 100 # coefficients

  8. Wavelets - intuition • Edges (horizontal; vertical; diagonal)

  9. Wavelets - intuition • Edges (horizontal; vertical; diagonal) • recurse

  10. Wavelets - intuition • Edges (horizontal; vertical; diagonal) • http://www331.jpl.nasa.gov/public/wave.html

  11. Wavelets • Many wavelet basis: • Haar • Daubechies (-4, -6, -20) • Gabor • ...

  12. Daubechies D4 decompsotion Original image Wavelet Transformation

  13. Gabor Function We can extend the function to generate Gabor filters by rotating and dilating

  14. adv Feature Calculation • Preprocessing • Background subtraction and thresholding, • Translation and rotation • Wavelet transformation • The Daubechies 4 wavelet • 10th level decomposition • The average energy of the three high-frequency components

  15. adv Feature Calculation • Preprocessing • 30 Gabor filters were generated using five different scales and six different orientations • Convolve an input image with a Gabor filter • Take the mean and standard deviation of the convolved image • 60 Gabor texture features

  16. Wavelets: • Extremely useful • Excellent compression / feature extraction, for natural images • fast to compute ( O(N) )

  17. (A1: turning angle) A2: wavelets A3: morphology: dilations/erosions ... Images - shapes

  18. Other shape features • Morphology (dilations, erosions, openings, closings) [Korn+, VLDB96] “structuring element” shape (B/W) R=1

  19. Other shape features • Morphology (dilations, erosions, openings, closings) [Korn+, VLDB96] “structuring element” shape R=0.5 R=1 R=2

  20. Other shape features • Morphology (dilations, erosions, openings, closings) [Korn+, VLDB96] “structuring element” shape R=0.5 R=1 R=2

  21. Morphology: closing • fill in small gaps • very similar to ‘alpha contours’

  22. Morphology: closing • fill in small gaps ‘closing’, with R=1

  23. Morphology: opening • ‘closing’, for the complement = • trim small extremities

  24. Morphology: opening • ‘closing’, for the complement = • trim small extremities ‘opening’ with R=1

  25. Morphology • Closing: fills in gaps • Opening: trims extremities • All wrt a structuring element:

  26. Morphology • Features: areas of openings (R=1, 2, …) and closings

  27. Morphology • resulting areas: ‘pattern spectrum’ • translation ( and rotation) independent • As described: on b/w images • can be extended to grayscale ones (eg., by thresholding)

  28. Conclusions • Shape: wavelets; math. morphology • texture: wavelets; Haralick texture features

  29. References • Faloutsos, C., R. Barber, et al. (July 1994). “Efficient and Effective Querying by Image Content.” J. of Intelligent Information Systems 3(3/4): 231-262. • Faloutsos, C. and K.-I. D. Lin (May 1995). FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets. Proc. of ACM-SIGMOD, San Jose, CA. • Faloutsos, C., M. Ranganathan, et al. (May 25-27, 1994). Fast Subsequence Matching in Time-Series Databases. Proc. ACM SIGMOD, Minneapolis, MN.

  30. References • Christos Faloutsos, Searching Multimedia Databases by Content, Kluwer 1996

  31. References • Flickner, M., H. Sawhney, et al. (Sept. 1995). “Query by Image and Video Content: The QBIC System.” IEEE Computer 28(9): 23-32. • Goldin, D. Q. and P. C. Kanellakis (Sept. 19-22, 1995). On Similarity Queries for Time-Series Data: Constraint Specification and Implementation (CP95), Cassis, France.

  32. References • Charles E. Jacobs, Adam Finkelstein, and David H. Salesin. Fast Multiresolution Image Querying SIGGRAPH '95, pages 277-286. ACM, New York, 1995. • Flip Korn, Nikolaos Sidiropoulos, Christos Faloutsos, Eliot Siegel, Zenon Protopapas: Fast Nearest Neighbor Search in Medical Image Databases. VLDB 1996: 215-226

  33. Outline ... Feature extraction Feature selection / Dim. reduction Classification ...

  34. Outline ... Feature selection / Dim. reduction PCA ICA Fractal Dim. reduction variants ...

  35. Feature Reduction • Remove non-discriminative features • Remove redundant features • Benefits : • Speed • Accuracy • Multimedia indexing

  36. SVD - Motivation brightness area

  37. SVD - Motivation brightness area

  38. minimum RMS error SVD – dim. reduction SVD: gives best axis to project brightness v1 area

  39. SVD - Definition • A = ULVT - example: v1

  40. math SVD - Properties THEOREM [Press+92]:always possible to decomposematrix A into A = ULVT , where • U,L,V: unique (*) • U, V: column orthonormal (ie., columns are unit vectors, orthogonal to each other) • UTU = I; VTV = I (I: identity matrix) • L: eigenvalues are positive, and sorted in decreasing order

  41. Outline ... Feature selection / Dim. reduction PCA ICA Fractal Dim. reduction variants ...

  42. ICA • Independent Component Analysis • better than PCA • also known as ‘blind source separation’ • (the `cocktail discussion’ problem)

  43. Intuition behind ICA: “Zernike moment #2” “Zernike moment #1”

  44. Motivating Application 2:Data analysis “Zernike moment #2” PCA “Zernike moment #1”

  45. Motivating Application 2:Data analysis ICA “Zernike moment #2” PCA “Zernike moment #1”

  46. Conclusions for ICA • Better than PCA • Actually, uses PCA as a first step!

  47. Outline ... Feature selection / Dim. reduction PCA ICA Fractal Dim. reduction variants ...

  48. adv Fractal Dimensionality Reduction Calculate the fractal dimensionality of the training data. 2. Forward-Backward select features according to their impact on the fractal dimensionality of the whole data.

  49. adv Dim. reduction Spot and drop attributes with strong (non-)linear correlations Q: how do we do that?

  50. adv Dim. reduction - w/ fractals not informative