1. Vision & Recognition

2. From a different direction At different times, particularly if it has been modified in the interval In different light A particular object may have different visual attributes when viewed: Observations

3. Be able to distinguish between different objects with the same appearance Be able to recognize the same object viewed from different directions or in different light Be able to recognize the same object after modification Be able to distinguish between an object and its reflection Objectives

4. Pattern recognition Robot vision Remotely operated devices Security related software Disease Diagnosis Applications

5. 5 The Minimum 3-D Feature Set The Minimum 3-D Feature Set Two cubes of the same color are indistinguishable. Cubes are distinguished by color, color count and color position

6. 6 The Minimum 3-D Feature Set The Minimum 3-D Feature Set 2 sides color ‘A’ 2 sides color ‘B’ Maximum of 2 distinguishable cubes Cubes are distinguished by color, color count and color position

7. 7 The Minimum 3-D Feature Set The Minimum 3-D Feature Set 3 sides color ‘A’ 3 sides color ‘B’ Maximum of 2 distinguishable cubes. 2 colors -> 8 cubes Cubes are distinguished by color, color count and color position

8. 8 The Minimum 3-D Feature Set Like color sides opposite vs. like colored sides adjacent. 3 colors -> 27 cubes Cubes are distinguished by color, color count and color position

9. 9 With 4 color cubes, pattern breaks. We would expect 4 3 = 64 But we only get 42 distinguishable cubes. Why? ---> Rotations ! The Minimum 3-D Feature Set

10. 10 Rotations and Reflections The Eight Queens Problem for (i = 0; i < 8; i++){ ok = 1; pNextPair->column = i; pPairOnTop = pTop; while (ok = 1 && pPairOnTop != NULL){

12. Hidden patterns revealed by tiling solutions

13. Horizontal Shifts One left succeeds, all others fail to find solution

14. Vertical Shifts One up or one down succeeds; all others fail to find a solution

15. Rotation & Mirror Effects Same object viewed from different angles

16. Diagonal shifts & Mirror Effects

17. Additional Mirror Effects

18. How do we determine which patterns are significant?

19. 12 partitions 12 distinct solutions Why not 96 (= 12 x 8) permutations? The answer is that one of our partitions contains only 4 "aliases" because the solution is diagonally symmetric Permutations of the solution vectors

20. Shape detection algorithms Without color… example universe: assembly-line where all parts are uniformly steel-colored

21. Shape detection algorithms Edge detection Using changes in reflectivity

22. Shape detection algorithms Edge detection Edges can intersect with planes, or air Is the background the same object or a different one?

23. Shape data structures Corners have “more information” per point Collection of points and relative distances Collection of lines and intersections Collections of shape primitives

24. Shape data structures Corners can be used to define Collections of edges and intersections Or boundaries of planes

25. Shape data structures Skeletons…AKA Wire-Frames Advantage… easier to morph

26. Shape data structures Volume filling shape primitives advantage: can easily calculate volume as sum of primitives’ volume

27. There are many applications... Volumes of research… And many areas yet unexplored... Vision & Recognition

28. Thank you.