1 E.V. Myasnikov 2007 Digital image collection navigation based on automatic classification methods Samara State Aerospace University RCDL 2007- 2007 .. 2 Navigation in collection of digital images alternative to image retrieval system complement to image retrieval system convenient browsing system Approaches to navigation system construction to construct projection of the whole image collection into 2-D navigation space to cluster image collection into the set of clusters (hierarchy) and then construct 2-D projection of each cluster to construct tree-like structure using an optimization rule 3 Clustering methods Hierarchical clustering (agglomerative) Single link Complete link Average link Nonhierarchical clustering K-means Kohonen neural networks (SOM) Fuzzy clustering 4 Linear Principal component analysis (PCA) Nonlinear Classical Kruskal MDS (multidimensional scaling) Sammon projection Force-Directed Replacement Projection methods Discrete lattice solution Continuous solution 5 Demands to the navigation system Representation of the collection has a form of 2D vectors (as icons, points on the monitor) The set of images having higher level of similarity is displayed when bringing near the region The set of images having lower level of similarity is displayed when moving away from the current region Property of reversibility Operations with the navigation map Scrolling (up, down, left, right) Scaling (up, down) 6 Main phases of proposed approach Feature extraction Cluster hierarchy construction Mapping into 2-D navigation space using restrictions imposed by cluster hierarchy Digital images Navigation space 7 Clustering Phase: Analyzed Methods Hierarchical clustering scheme 1.Adjacency matrix calculation 2.Rank each object among clusters 3.Merge elements with minimal distance between them 4.Elimination of the raw and column of absorbed cluster and matrix recalculation 5.Stopping criterion test and transition to the step 3 Inter-cluster distance single link minimal distance between objects involved in clusters complete link maximal distance between objects involved in clusters Kohonen neural network WTA correction rule: w (t+1) = w (t) + (t)[x(t) - w (t)] d(x(t), w (t)) = min 1 i K d(x(t), w i (t)) Following equation holds true for the winning neuron To construct the hierarchy of clusters Kohonen neural network functions in a recursive order 8 Clustering: Experimental results * Experiment was conducted on samples of size equal to 1000 Number of clusters Average quantization error * Single link Complete link WTA Quantization error: Examples of clusters 9 Mapping Phase: Sammon projection Error d ij - distance between objects i and j in multidimensional space d * ij - distance between objects i and j in two dimensional space y jk - coordinates in 2D space Iterative formula Notation Operational time ~ O[N 3 ] (under the assumption that the number of iterations is of the same order as the number of objects) 10 Construction of initial configuration for Sammon mapping Average error value * Number of iterations Sammon mapping with random initalization Best Sammon mapping over 10 runs with random initialization PCA0.139 Two-phase method (PCA as initial configuration for Sammon mapping) * samples of 100 images from dataset of images were used to conduct the experiment Two-phase method example 11 Methods of speeding-up Sammon projection 1. Triangulation 2. Neural Network 3. Approximation using random sets Chalmers96 adaptation for Sammon projection (CS) Two sets are constructed for each object on each iteration: set of k 1 close objects set of k 2 random objects Operational time ~ O[N 2 ] (under the assumption that the number of iterations is of the same order as the number of objects and k 1 +k 2