1. Presenter: Cheong Hee Park Advisor: Victoria Interrante Texture Classification using Spectral Decomposition

2. Overview Goal: Visualization of multivariate data set in a planar 2D using principal perceptual features of texture. Step1: Classify textures into meaningful categories. Classification by directionality Classification by regularity Structural grouping Step2: Synthesize a series of textures to convey values of multivariate data.

3.  Review of texture analysis and data visualization Discrete Fourier Transform Classification by directionality Classification by regularity Classification by Structure Future work

4. Visualization of Magnetic field using orientation, size and contrast Using Visual Texture for Information Display - Colin Ware and William Knight (1995)

5. Display over a 3D surface using height, density and regularity Building Perceptual Textures to Visualize Multidimensional Datasets (C. Healey, J. Enns, 1998 )

6. Harnessing natural textures for multivariate visualization (Victoria Interrante) farms(percent) in 1992 percent change of farms from 1987 to 1992

8. What is texture? An image composed of uniform or non-uniform repetition of natural or artificial patterns Methods used for texture analysis Autocorrelation Co-occurrence based method Parametric models of texture Gray level run length  Spectral decomposition

9. Principal features of texture Directionality: directional vs non-directional Coarseness: coarse vs fine Contrast: high contrast vs low contrast Regularity: regular vs irregular (periodicity, randomness) Line likeness: line-like vs blob-like Roughness: rough vs smooth

10. Toward a texture naming system: identifying relevant dimensions of texture(A.R.Rao, G.L.Lohse, 1996) Lace - like Directional, Locally-oriented Non-random, Repetitive, non-directional directional Marble-like Random, Non granular, Somewhat repetitive random Random, granular

11. Texture features corresponding to visual perception - Tamura, Mori and Yamawaki psychological measurement of directionality (by human subjects using pair comparison method) computational measurement of directionality (using local vertical and horizontal directional operators)

12. Modeling spatial and temporal textures - Fang Liu Decomposition of texture into three components based on Wold theory: harmonic(periodicity), evanescent(directionality), indeterministic(random). Measured deterministic energy from harmonic and evanescent components, and indeterministic energy from indeterministic component.

13. deterministic indeterministic DFT Used energy measurements for texture modeling and image retrieval

14. Discrete Fourier Transform Given an image y(m,n), DFT IDFT

15. Y(l,k) in a frequency domain represents the response of cosine and sine filters.

16. Hanning window DFT filtering FrequencyFrequency

18. directionality regularity

19. Directionality 0 --------- 17 0 10 Directionality = (K; number of columns) f f

20. 27 textures with highest directionality

21. The 27 middle directional textures

22. 27 textures with lowest directionality

23. directionality

24. Instead of two processes FFT and local window interpolation, apply global sinusoidal filters directly to the texture

25. Directionality from direct filtering

27. - Psychological experiment by Tamura - Ours(by interpolation) - (by direct filtering) - computational experiment by Tamura Q: How can we judge which method is better ?

28. Pattern regularity as a visual key D. Chetverikov using autocorrelation of gray intensities

29. Regularity (A: overlapping area) dominant direction height/2 i Regularity = max f – min f }i

30. Regularity classification

31. Directionality Regularity

32. Directionality Regularity (by direct filtering )

33. Structural grouping Absolute Difference (L1 norm)

35. brick-like net-like

37. granular line-like

38. Future work How to map attributes of multivariate data to texture perceptual dimensions independently? What perceptual features of texture are most orthogonal? -- Minimize interference when they are combined for display of multivariate data. Mapping should be continuous within an attribute and make maximum distinction between attributes.