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Presenter : YAN-SHOU SIE Authors : Marco Piastra 2013. NN

Self-organizing adaptive map: Autonomous learning of curves and surfaces from point samples. Presenter : YAN-SHOU SIE Authors : Marco Piastra 2013. NN. Outlines. Motivation Objectives Methodology Experiments Conclusions Comments. Motivation.

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Presenter : YAN-SHOU SIE Authors : Marco Piastra 2013. NN

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  1. Self-organizing adaptive map: Autonomous learning of curves and surfaces frompoint samples Presenter : YAN-SHOU SIE Authors : Marco Piastra2013. NN

  2. Outlines • Motivation • Objectives • Methodology • Experiments • Conclusions • Comments

  3. Motivation • In here we want from a point cloud image to reconstruct it original structure, but preliminary version SOAM algorithm is can not effective to produced the expected topology.

  4. Objectives • In here we present a improve version SOAM algorithm, its has a much more predictability and includes some new concepts.

  5. Methodology • Topological and geometrical background Term • homeomorphic • manifold • Voronoicell • Delaunay triangulation

  6. Methodology • Restricted Delaunay complex ： • Homeomorphism and ε –sample • Witness complex

  7. Methodology • Finite sets of witnesses and noise • Growing self-organizing networks • Positioning the units: ‘gas-like’ dynamics • adaptation strategy of the first kind

  8. Methodology • second kind of strategy • Competitive Hebbian learning and dynamic units • Growing networks, insertion threshold

  9. Methodology • Self-Organizing Adaptive Map (SOAM) • Stateful units

  10. Methodology • Adaptive insertion thresholds • The SOAM algorithm

  11. Methodology-distance measures • -window-based similarity • -document co-occurrence similarity • Suppose that we have a document with four concepts: ‘Ad,’‘Bert,’ ‘Cees,’ and ‘Dirk.’ If the window size is 2, the following windows are created for this document: {Ad}, {Ad, Bert}, {Bert, Cees},{Cees, Dirk}, and {Dirk}. ex : ‘System’ appears in documents {1,3,6,8} and windows {1,5,10,14,18,20,28}; ‘Process’ appears in documents {1,3,6,12} and windows {1,5,12,14,18,25,30}. • the similarities are converted to distances: window similarity : document similarity : Avg = 0.15

  12. Experiments • Experimental setup

  13. Experiments • Algorithm behavior

  14. Experiments • Performances

  15. Experiments • Undersampling and noise: when things go wrong • Boundaries and non-manifold units

  16. Conclusions • The SOAM algorithm represents an interesting alternative to deformable models in that it can effectively deal with changes in topology and execution speedup.

  17. Comments • Advantages • SOAM can be dynamically self-growth, and the results will be generated close to the result we want, for the field of 3D technology has considerable value.. • Applications - medical imaging , 3D sample, etc.

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