1. 1. Using TDA on ImagesCarmen Cox
2. 2. The IdeaMona Lisa by Leonardo Da Vinci Two Girls Reading by Pablo Picasso
3. 3. The IdeaMona Lisa by Leonardo Da Vinci Two Girls Reading by Pablo Picasso
4. 4. Big Question Can TDA pick up zero- and one-dimensionalpersistence on images?
5. 5. Method Create a simplicial complex out of a grayscaleimage and feed it to rca1mfscm Comparison between persistence diagrams
6. 6. The Dataset: Images Each image is made up of pixels with some valueassociated with each pixel Thus, an image can be thought of as a giant matrix Color images use RGB values between 0 (white)and 255 (black) but I used grayscale instead,where the values are a float between 0 and 1
7. 7. The Dataset: Images
8. 8. The Dataset: Images
9. 9. Creating a Simplex out of an Image0 0.25 0.37 0.70.59
10. 10. Creating a Simplex out of an Imagevertex
11. 11. Creating a Simplex out of an Imageedge
12. 12. Creating a Simplex out of an Image
13. 13. Creating a Simplex out of an Image
14. 14. Creating a Simplex out of an Image
15. 15. Feed into rca1mfscm Vertex input: [index index grayscale value] Edge input, of edge between vertex i and vertex j: [index i index j max grayscale value of i and j] Create N x 3 array, S>> [I J] = rca1mfscm(S,1.2);
16. 16. Some Simple ExamplesZero-dimensional persistence
17. 17. Some Simple ExamplesOne-dimensional persistence
18. 18. Some Simple ExamplesZero-dimensional persistence
19. 19. Some Simple ExamplesOne-dimensional persistence
20. 20. Some Simple ExamplesZero-dimensional persistence
21. 21. Some Simple ExamplesOne-dimensional persistence
22. 22. A More Interesting ExampleZero-dimensional Persistence
23. 23. A More Interesting ExampleOne-Dimensional Persistence
24. 24. Mona Lisa0-D1-D
25. 25. Two Girls Reading0-D1-D
26. 26. Comparison: Zero-DimensionalPersistenceMona Lisa Two Girls Reading
27. 27. Comparison: One-DimensionalPersistenceMona Lisa Two Girls Reading
28. 28. Girl with a Pearl Earring0-D1-D
29. 29. Comparison: Zero-DimensionalPersistenceMona Lisa Girl with a Pearl Earring Two Girls Reading
30. 30. Comparison: One-DimensionalPersistenceMona Lisa Girl with a Pearl Earring Two Girls Reading
31. 31. Future Directions Machine learning Can paintings from different art periods bedistinguished using TDA and machine learning?Can any group of images be distinguished? Color images Addressing problem of size
32. 32. Thank you!