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Deep structure (Matching)

Deep structure (Matching). Arjan Kuijper arjan@itu.dk. Deep structure. What was found in the deep structure: Spatial critical points In L(x,y;t c ): L = 0 Critical curves In L(x,y;t): L = 0 Catastrophe points In L(x,y;t): det(H) = 0 Scale space saddles In L(x,y;t): L = 0, D L = 0.

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Deep structure (Matching)

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  1. Deep structure (Matching) Arjan Kuijper arjan@itu.dk

  2. Deep structure • What was found in the deep structure: • Spatial critical points • In L(x,y;tc): L = 0 • Critical curves • In L(x,y;t): L = 0 • Catastrophe points • In L(x,y;t): det(H) = 0 • Scale space saddles • In L(x,y;t): L = 0, DL = 0 Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  3. What to match • We could match several things: • Regions in n-D • Regions in (n+1)-D • Points in (n+1)-D • Hierarchies in (n+1)-D • The advantage of Gaussian scale space is that it blurs everything away… • … in a pre-defined way. Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  4. Blurred region matching • Segment the original images – or their blurred versions at some scale and try to match similar areas • Basically using non-scale space approaches • Rigid or non-rigid registration methods • Possibly match blurred images • Hardly attempted Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  5. Scale space region matching • Construct a volume in scale space. • The volume is a measure of importance. • For example: Lindebergs blob algorithm. • No matching algorithms known. Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  6. Matching Points • Find the catastrophe points and / or the scale space saddles of two images and try to match them • Handle the difference in number of points • Handle the difference in location • spatial • scale • Earth Movers Distance may be useful. • Preliminary results by Frans Kanters Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  7. Hierarchy matching • This is really fully using the deep structure Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  8. Combining manifolds and critical curves • At a scale space saddle two manifolds intersect. • Manifolds are limited: they have a top. Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  9. Nesting of manifolds in scale space • Manifolds are related to other manifolds. Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  10. Void scale space saddles • Beware that not all scale space saddles connect two separate manifolds. Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  11. HierarchicalAlgorithm • Initializing • Build a scale space. • Find the critical points at each scale level. • Construct the critical branches. • Find the catastrophe points. • Construct and label the critical curves, including the one remaining extremum. • Find the scale space saddles. • Determining the manifolds • Find for each annihilations extremum its critical iso-intensity manifold. • Construct the dual manifolds. Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  12. Hierarchical Algorithm • Labeling • Assign to each extremum the dual manifolds to which it belongs, sorted on intensity. • Build a tree: • Start with the remaining extremum at the coarsest scale as root. • Trace to finer scale until at some value it is labeled to a dual manifold. • Split into two branches, on the existing extremum, one the extremum having the critical manifold. • Continue for all branches / extrema until all extrema are added to the tree. Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  13. Consider the blobs Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  14. R D e C e 5 5 D e C e 3 3 D e C e 1 1 D e C e 2 2 e e e e e 4 2 1 3 5 Example: manifolds and hierarchy Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  15. A real example Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  16. Noise addition Mathematica If time. Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  17. Several Trees • Trees can be build up using the • Catastrophe Points • Scale Space Saddles • Iso-Manifolds through them • Different paradigms can be used • Gaussian scale space itself • Watersheds based on GSS • … Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  18. Matching trees • The next step is to match these Multi-Scale Singularity Trees. • This is part of the reseach done at the DSSCV project. • Eindhoven (NL) • 3DLab, Kopenhagen University (DK) • Image Group, ITU (DK) • Algorithms Group, ITU (DK) Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  19. Sources • Scale Space Hierarchy A. Kuijper, L.M.J. Florack, M.A. ViergeverJournal of Mathematical Imaging and Vision 18 (2):169-189, 2003. • The hierarchical structure of images A. Kuijper, L.M.J. FlorackIEEE Transactions on Image Processing 12 (9): 1067-1079, 2003. • The deep structure of Gaussian scale space images Arjan Kuijper • Generic Image StructureOle Fogh Olsen • Scale-Space Theory in Computer VisionTony Lindeberg • Multiscale Hierarchical Segmentation Bram Platel, Luc Florack, Frans Kanters, Bart ter Haar Romeny, ASCI 2003 Conference, June 4-6, 2003. • Content Based Image Retrieval using Multiscale Top PointsFrans Kanters, Bram Platel, Luc Florack, Bart ter Haar Romeny, Scale Space 03, LNCS 2695: 193-204, 2003 Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

  20. Sinterklaas Deep Structure Matching; PhD course on Scale Space, Cph 1-5 Dec 2003

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