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

2. Texture examples

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