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Unsupervised Learning of Categories from Sets of Partially Matching Image Features

Unsupervised Learning of Categories from Sets of Partially Matching Image Features. Dominic Rizzo and Giota Stratou. Grauman and Darrell’s Work. Detects categories Pyramid match kernel Graph partitioning Unsupervised or Semi-supervised Prototypical image selection Caltech-4

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Unsupervised Learning of Categories from Sets of Partially Matching Image Features

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  1. Unsupervised Learning of Categories from Sets of Partially Matching Image Features Dominic Rizzo and Giota Stratou

  2. Grauman and Darrell’s Work • Detects categories • Pyramid match kernel • Graph partitioning • Unsupervised or Semi-supervised • Prototypical image selection • Caltech-4 • Subset we implemented • Unsupervised category detection • Pyramid match kernel • Normalized cuts • Subset of Caltech-256 (8)

  3. Algorithm Outline Extract Features Detect Interest Points Truncate Feature Vectors & Lexicographically Sort Calculate Pyramid Match Score Partition Affinity Matrix

  4. Feature Extraction Harris-Affine PCA-SIFT Harris-Affine PCA-SIFT Caltech-256 Image Dataset (Raw Images) Caltech-256 Image Dataset (Feature Vectors) ... Harris-Affine PCA-SIFT The Grid

  5. Pyramid Match Kernel • PMK histograms indirectly calculated • If direct, First histogram ~ 10,000^10 elements • Size decreases by 1/2 each increment • Matlab can’t handle that • Calculate intersections • Histograms are sparse • Compare feature locations directly • Lexicographic sort • Pointer walking • C-MEX function for inner loop • Still the slowest part of the code

  6. Grouping as Graph Partitioning G=(V,E)→ DISJOINT A,B CUT(A,B)= OPTIONAL BIPARTITIONING: min CUT(A,B) NORMALISED CUT:

  7. Grouping as Graph Partitioning (2) G=(V,E) D=diagonal d(i)= W=similarity weights

  8. Recursive Two-Way N-Cut • USE SECOND SMALLER EIGENVECTOR TO PARTITION INTO TWO PARTS • NEED DECISION THRESHOLD • CAN RUN RECURSIVELY FOR MORE CATEGORIES

  9. Simultaneous K-Way Cut with Multiple Eigenvectors • KEEP TOP K EIGENVECTORS • NEED CLUSTERING ALGORITHM (i.e k-MEANS) • min Ncut(A1,A2,…Ak)

  10. Results Example: TWO CATEGORIES: 95 images 100 images Ncut 16 + 179 hit ratio: 111/195=0.5692 false alarm ratio: 79/195=0.4051

  11. Pyramid Match Kernel • Weighted intersection of multi-resolution histograms • Similarity scoring • O(dm log D) • d-dimensional features • m features • Maximal range D • Relatively fast

  12. Affinity Matrix • Fully connected graph of images • N x N matrix • Nodes are images • Edges are affinities • Affinity scores • Computed via pyramid match kernel

  13. Graph Partitioning • Clusters categories of images • Recursively partition • Min-normalized cut • NP-complete • Approximate solution • Eigenvalue problem • K is the image affinity matrix • D = f(K) • x is the partition

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