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E . V. Myasnikov

RCDL 2007 Интернет-математика 2007. Навигация по коллекциям цифровых изображений на основе методов автоматической классификации. Е.В. Мясников. Самарский государственный аэрокосмический университет. mevg@smr.ru.

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E . V. Myasnikov

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  1. RCDL 2007 Интернет-математика 2007 Навигация по коллекциям цифровых изображений на основе методов автоматической классификации Е.В. Мясников Самарский государственный аэрокосмический университет mevg@smr.ru Digital image collection navigation based onautomatic classification methods E.V. Myasnikov Samara State Aerospace University 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) Nonhierarchical clustering Kohonen neural networks (SOM) K-means Average link Single link Complete link Fuzzy clustering

  4. Projection methods Continuous solution Discrete lattice solution Nonlinear Linear Principal component analysis (PCA) Classical Kruskal MDS (multidimensional scaling) Sammon projection Force-Directed Replacement

  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 Digital images Feature extraction Cluster hierarchy construction Mapping into 2-D navigation space using restrictions imposed by cluster hierarchy Navigation space

  7. Clustering Phase: Analyzed Methods Hierarchical clustering scheme Kohonen neural network • Adjacency matrix calculation • Rank each object among clusters • Merge elements with minimal distance between them • Elimination of the raw and column of absorbed cluster and matrix recalculation • Stopping criterion test and transition to the step 3 Following equation holds true for the winning neuron d(x(t),w(t))= min1 i  Kd(x(t),wi (t)) Inter-cluster distance WTA correction rule: single link minimal distance between objects involved in clusters complete link maximal distance between objects involved in clusters w(t+1) = w(t) + (t)[x(t) - w(t)] To construct the hierarchy of clusters Kohonen neural network functions in a recursive order

  8. Clustering: Experimental results Quantization error: *Experiment was conducted on samples of size equal to 1000 Examples of clusters

  9. Mapping Phase: Sammon projection Notation dij- distance between objectsi andjin multidimensional space d*ij - distance between objectsi andjin two dimensional space yjk - coordinates in 2D space Error Iterative formula Operational time ~ O[N3] (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 Two-phase method example *samples of 100 images from dataset of 10 000 images were used to conduct the experiment

  11. Methods of speeding-up Sammon projection 1. Triangulation 2. Neural Network 3. Approximation using random sets Chalmers’96 adaptation for Sammon projection (CS) Two sets are constructed for each object on each iteration: • set of k1 close objects • set of k2 random objects Operational time ~ O[N2] (under the assumption that the number of iterations is of the same order as the number of objects and k1+k2 << N)

  12. Proposed Methods:Combined Method (CM) Idea: Use hierarchical clustering to build the projection Method description • Build Sammon projection for the top level of the cluster tree • Build Sammon projection for the each subcluster at level 2using 2D coordinates of the superclasters as fixed points • Repeat the process for each subclaster (or object) of the level 3 and so on Operational time – for balanced tree with depth L Special case: O[N2] – for balanced tree with depth 2 Modification of method (MCM):Use 2D coordinates of top level clusters for each subcluster (or object) at any level

  13. Proposed Methods: Restrictive Combined Method (CMR) • Map centers xu1 of top level clusters Сu1C0 to the 2D vectors yu1 using dimensionality reduction method (Sammon or two-phase method). Set boundaries of the whole displayed area 0= • For each cluster СukCvk-1 of the current level k carry out points 3-6 • Construct boundaries uk of the cluster Cuk in 2D space using centers coordinates ymk in 2D space of the clusters Cmk, m=1..|Cvk-1| of the current level k • Complete cluster boundaries uk using boundaries vk-1 of the parent cluster Cvk-1 at the previous level: uk =uk vk-1 • Map centers xik+1 of all subclusters Сik+1Сuk (or immediately images Oi) at level k+1 to 2D vectors yik+1, using boundaries uk of the cluster applying the following recurrence relation 6. Apply described in points 3-5 procedure to map child clusters Cik+1 in the recursive order

  14. Proposed Methods: Modifications for CMR can be selected based on minimization of Function functional consisted of Sammon error and boundary function Two models were considered 1. Full correction rule (CMR-1) – if yi exceeds the bounds of the cluster then the correction value ensure yi to be on the boundary at the next step 2. Piece-wise linear rule (CMR-2)– correction value ensure the “attraction” to the center of the cluster or to the boundary when yi comes near or exceeds the boundary Example of CMR-1

  15. Experimental Research

  16. Example of MCM sample size: 10 000 images

  17. Example of CMR sample size: 10 000 images

  18. Example of navigation (CMR) region “б” region “а”

  19. Example of navigation (CMR) region “г” region “в”

  20. Selection of features • Main requirement to the feature system: • Configuration of images in navigation space must be understandable to user Note: “Measures that are more effective for retrieval tend to be more complex, and thus lose their advantage over the simpler measures when forced into two dimensions” (K.Rodden, W.Basalaj, D.Sinclair, K.Wood A comparison of measures for visualising image similarity. In The Challenge of Image Retrieval. British Computer Society Electronic Workshops in Computing, 2000) Features: Color histograms in CIE L*a*b color space Metrics: Euclidian

  21. Conclusions • The requirements to the navigation method are considered • Novel navigation method is proposed • Novel combined method and its modifications for dimensionality reduction are proposed • Proposed methods are compared to known method • The results of experimental analysis of methods being used are present Future plans • Exploring new feature systems • Method improvement • Estimation of effectiveness of navigation method including expert estimation

  22. THANK YOU FOR YOUR ATTENTION Acknowledgements This work was financially supported by Yandex (www.yandex.ru) The dataset “Image database” was provided by Yandex

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