1. Finding Clusters within a Class to Improve Classification Accuracy Literature Survey Yong Jae Lee 3/6/08

2. Object Recognition Determine which, if any, of a given set of objects appear in a given image or video UT tower Trees Statue

3. Problem Statement A problem of matching models of objects built from a database with object models found in novel images Representation of object model is important Need to learn a model from train set

4. Object: Cars Example: Car images returned from Google

5. Find Clusters

6. Object Representation key paper #1 Scale Invariant Feature Transform (SIFT) [Lowe. 2004] Local features based on the appearance of the object at particular interest points Thresholded image gradients are sampled over 16x16 array of locations Create array of orientation histograms 8 orientations x 4x4 histogram array = 128 dimensions

7. Compute Similarity key paper #2 Proximity Distribution Kernels [Ling et al. 2007] Address the spatial relation between local features Invariant to scale, rotation, translation

8. Clustering key paper #3 Normalized Cuts [Shi et al. 2001] Graph theoretic approach to clustering Measure the goodness of partition by formulating the objective as an eigenvalue problem Maximize the within cluster similarity relative to the across cluster difference # of clusters must be given X1X1 X2X2 X3X3 X4X4 X1X1 K 11 K 12 K 13 K 14 X2X2 K 21 K 22 K 23 K 24 X3X3 K 31 K 32 K 33 K 34 X4X4 K 41 K 42 K 43 K 44

9. Classification key paper #4 Support Vector Machines [Vapnik et al. 1995] Discriminative Classifier based on optimal separating hyperplane Margin of separation: the separation between the hyperplane and the closest data point

10. Infinite possible hyperplanes

11. SVM Learning finds the a hyperplane for which the margin of separation is maximized

12. Questions

13. References H. Ling and S. Soatto, “Proximity Distribution Kernels for Geometric Context in Category Recognition,“ IEEE 11th International Conference on Computer Vision, pp. 1-8, 2007. D. Lowe, “Distinctive Image Features from Scale-Invariant Keypoints," International Journal of Computer Vision, vol. 60, no. 2, pp. 91-110, 2004. J. Shi and J. Malik, “Normalized cuts and image segmentation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 8, pp. 888-905, 2000. C. Cortes and V. Vapnik, “Support-vector networks," Machine Learning, vol. 20, no. 3, pp. 273-297, 1995.

14. PDK φ2φ2 φ1φ1 φ3φ3 φ6φ6 φ5φ5 φ4φ4 φ7φ7 (c 1,1)(c2,4) (c 3,3) (c 4,2) (c 5,2) (c 6,3)(c 7,1) Codebook, V = 4 r # 024 6 H r (2,3) j r i Proximity Distribution H r