1. Texture with Moments Longin Jan Latecki CIS Dept. Temple Univ., Philadelphia latecki@temple.edu with some slides from David Kriegman, UCSD

2. Texture examples

3. Wheat Alfalfa Alfalfa Forest Forest Corn Corn Wheat Alfalfa Alfalfa Corn Wheat Soybean Corn Corn Corn Corn Corn Forest Forest Alfalfa Alfalfa Corn Soybean Corn Spatial Resolution = 6 m

4. Texture with invariant moments

5. p, q = 0, 1, 2, …; • = (p + q / 2) +1; p+q = 2, 3, …

6. Seven 2D moment invariants that are invariant to translation, scale, mirroring, and rotation. 1 = 20 + 02 2 = (20 - 02)2 + 4211 3 = (30 - 312)2 + (03 - 321)2 4= (30 + 12)2 + (03 + 21)2 5 = (330 - 312)(30 + 12)[(30 + 12)2 –3(21 + 03)2] + (321 - 03)(21 + 03)  [3(30 + 12)2 – (21 + 03)2] Hu, M. K. (1962) Visual Pattern Recognition by Moment Invariants, IEEE Transactions on Information Theory, Vol IT-8.

7. 6 = (20 - 02)[(30 + 12)2 – (21 + 03)2] + 411(30 + 12)(21 + 03) 7 = (321 - 03)(30 + 12)[(30 + 12)2 - 3(21 + 03)2] + (312 - 30)(21 + 03)  [3(30 + 12)2 – (21 + 30)2]

15. y x

18. Matlab function • invmoments

20. Homework 6:How do the 7 moment classify the six textures?