Finding Clusters within a Class to Improve Classification

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

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

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

Object: Cars • Example: Car images returned from Google

Find Clusters

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 16 x 16 array of locations • Create array of orientation histograms • 8 orientations x 4 x 4 histogram array = 128 dimensions

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

Clustering key paper #3 • Normalized Cuts [Shi et al. 2001] • Graph theoretic approach to clustering X 1 X 2 X 3 X 4 X 1 K 12 K 13 K 14 X 2 K 21 K 22 K 23 K 24 X 3 K 31 K 32 K 33 K 34 X 4 K 41 K 42 K 43 K 44 • 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

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

• Infinite possible hyperplanes

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

Questions

References • • H. Ling and S. Soatto, “Proximity Distribution Kernels for Geometric Context in Category Recognition, “ IEEE 11 th 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.

PDK r 0 2 4 # 6 Hr(2, 3) Codebook, V = 4 j φ1 φ3 φ6 (c 1, 1) φ2 φ4 φ5 φ7 (c 3, 3) (c 6, 3) (c 2, 4) (c 4, 2) r (c 5, 2) (c 7, 1) i Proximity Distribution Hr