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Reduksi Dimensi Image dengan Principal Components Analysis (PCA)

Reduksi Dimensi Image dengan Principal Components Analysis (PCA) . Sumber: Trucco & Verri chap. 10 Standford Vision & Modeling. Contoh: problem Pattern Recognition. Rotate coordinate system:. Problem Dimensi tinggi ??. PCA (Principal Component Analysis).

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Reduksi Dimensi Image dengan Principal Components Analysis (PCA)

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  1. Reduksi Dimensi Image dengan Principal Components Analysis (PCA) Sumber: Trucco & Verri chap. 10 Standford Vision & Modeling

  2. Contoh: problem Pattern Recognition

  3. Rotate coordinate system:

  4. Problem Dimensi tinggi ??

  5. PCA (Principal Component Analysis) • Untuk reduksi dimensi data (Dimensional Reduction) !!! • Ekstraksi struktur data dari dataset high dimenson. • Mencari basis signal berdasarkan data statistik objek.

  6. PCA

  7. PCA

  8. Demo dengan Matlab: • Mencari basis signal citra wajah. • Image recognition, face recognition.

  9. PCA

  10. Reduksi dimensi linear: High-dimensional Input Space

  11. Linear Subspace: = + = + 1.7

  12. Linear Subspace:

  13. Principal Components Analysis: m

  14. Contoh: Data: Kirby, Weisser, Dangelmayer 1993

  15. Contoh: Data: New Basis Vectors PCA

  16. Contoh: Data: EigenLips PCA

  17. Contoh: Face Recognition dengan Eigenfaces (Turk+Pentland, ):

  18. Contoh: Face Recognition System (Moghaddam+Pentland):

  19. Contoh: Visual Cortex Hubel

  20. Contoh: Visual Cortex Hubel

  21. Contoh: Receptive Fields Hubel

  22. Contoh: Receptive Fields Hancock et al: The principal components of natural images

  23. Contoh: Receptive Fields Hancock et al: The principal components of natural images

  24. Contoh: Active Appearance Models (AAM): (Cootes et al)

  25. Contoh: Active Appearance Models (AAM): (Cootes et al)

  26. Contoh: Active Appearance Models (AAM): (Cootes et al)

  27. Contoh: 3D Morphable Models (Blanz+Vetter)

  28. Ulasan Constrain - V V E(V) Analytically derived: Affine, Twist/Exponential Map Learned: Linear/non-linear Sub-Spaces

  29. Non-Rigid Constrained Spaces E(S) Constrain S = (p ,…,p ) 1 n

  30. Mixture Models Non-Rigid Constrained Spaces • Linear Subspaces: • Small Basis Set • Principal Components • Analysis Nonlinear Manifolds:

  31. Manifold Learning EM Mixture of Patches Training Data

  32. Mixture of Projections

  33. Contoh: Eigen Tracking (Black and Jepson)

  34. Contoh: Shape Models for tracking:

  35. Feature/Shape Models secara umum: Visual Motion Contours: Blake, Isard, Reynard

  36. Feature/Shape Models secara umum: Visual Motion Contours: Blake, Isard, Reynard

  37. Linear Discriminant Analysis:

  38. Fisher’s linear discriminant:

  39. Contoh: Eigenfaces vs Fisherfaces Glasses or not Glasses ?

  40. Contoh: Eigenfaces vs Fisherfaces Input New Axis Belhumeur, Hespanha, Kriegman 1997

  41. Basis Shape Algorithms lainnya: • ICA (Independent Components Analysis, Bell+Sejnowski) • Maximize Entropy (or spread of output distribution):

  42. Basis Shape Algorithms lainnya: • NMF (non-negative matrix factorization, Lee+Seung) • LNMF (local NMF, Li et al)

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