Using tda on images
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Using TDA on Images Carmen Cox
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Transcript of Using tda on images
- 1. Using TDA on ImagesCarmen Cox
- 2. The IdeaMona Lisa by Leonardo Da Vinci Two Girls Reading by Pablo Picasso
- 3. The IdeaMona Lisa by Leonardo Da Vinci Two Girls Reading by Pablo Picasso
- 4. Big Question Can TDA pick up zero- and one-dimensionalpersistence on images?
- 5. Method Create a simplicial complex out of a grayscaleimage and feed it to rca1mfscm Comparison between persistence diagrams
- 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. The Dataset: Images
- 8. The Dataset: Images
- 9. Creating a Simplex out of an Image0 0.25 0.37 0.70.59
- 10. Creating a Simplex out of an Imagevertex
- 11. Creating a Simplex out of an Imageedge
- 12. Creating a Simplex out of an Image
- 13. Creating a Simplex out of an Image
- 14. Creating a Simplex out of an Image
- 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. Some Simple ExamplesZero-dimensional persistence
- 17. Some Simple ExamplesOne-dimensional persistence
- 18. Some Simple ExamplesZero-dimensional persistence
- 19. Some Simple ExamplesOne-dimensional persistence
- 20. Some Simple ExamplesZero-dimensional persistence
- 21. Some Simple ExamplesOne-dimensional persistence
- 22. A More Interesting ExampleZero-dimensional Persistence
- 23. A More Interesting ExampleOne-Dimensional Persistence
- 24. Mona Lisa0-D1-D
- 25. Two Girls Reading0-D1-D
- 26. Comparison: Zero-DimensionalPersistenceMona Lisa Two Girls Reading
- 27. Comparison: One-DimensionalPersistenceMona Lisa Two Girls Reading
- 28. Girl with a Pearl Earring0-D1-D
- 29. Comparison: Zero-DimensionalPersistenceMona Lisa Girl with a Pearl Earring Two Girls Reading
- 30. Comparison: One-DimensionalPersistenceMona Lisa Girl with a Pearl Earring Two Girls Reading
- 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. Thank you!