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Watershed transform Integrated approach SegmentIt Interactive image segmentation with integrated use of the markers and the hierarchical watershed approaches Bruno Klava and Nina Sumiko Tomita Hirata Institute of Mathematics and Statistics

  1. Watershed transform Integrated approach SegmentIt Interactive image segmentation with integrated use of the markers and the hierarchical watershed approaches Bruno Klava and Nina Sumiko Tomita Hirata Institute of Mathematics and Statistics University of S˜ ao Paulo Brazil 06 February, 2009 This work is supported by CNPq, Brazil. Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  2. Watershed transform Integrated approach SegmentIt Outline Watershed transform 1 Classical watershed Watershed from markers Hierarchical watershed Integrated approach 2 Interactive segmentation From markers to the hierarchical watershed From hierarchical watershed to markers Integrated approach SegmentIt 3 Demonstration Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  3. Watershed transform Integrated approach SegmentIt Watershed transform [Beucher and Meyer, 1993] Classical watershed - Flooding simulation from the regional minima (Loading animation...) Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  4. Watershed transform Integrated approach SegmentIt Classical watershed Oversegmentation problem - Primitive catchment basins Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  5. Watershed transform Integrated approach SegmentIt Classical watershed Oversegmentation problem - Primitive catchment basins Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  6. Watershed transform Integrated approach SegmentIt Watershed from markers Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  7. Watershed transform Integrated approach SegmentIt Watershed from markers Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  8. Watershed transform Integrated approach SegmentIt Watershed from markers Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  9. Watershed transform Integrated approach SegmentIt Watershed from markers Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  10. Watershed transform Integrated approach SegmentIt Watershed from markers Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  11. Watershed transform Integrated approach SegmentIt Watershed on graphs WT can be formulated as a graph optimization problem: WS ( G I , M ) 19 22 27 60 98 98 98 93 G I = ( V , E , ω ) : a graph 100 124 169 169 166 19 19 22 76 19 22 100 124 169 169 169 166 representing the input image I 155 155 169 169 169 140 19 19 33 15 33 155 155 155 159 169 140 Granularities: 168 162 145 159 170 152 14 15 83 14 83 168 168 162 90 170 170 Pixel Adjacency Graph PAG I 139 168 162 170 152 19 19 72 90 Region Adjacency Graph 19 139 168 168 139 55 170 170 168 152 139 119 170 152 30 30 55 RAG I 30 152 168 168 85 119 170 170 152 168 170 170 152 30 32 85 55 ω : dissimilarity measure 32 152 156 156 46 170 170 170 140 140 152 159 170 170 120 between the vertices 61 61 140 152 159 159 61 167 167 167 140 140 137 159 102 102 167 167 120 M : the set of markers 129 137 157 157 102 164 164 164 129 139 147 179 169 169 164 164 133 139 147 179 179 169 169 163 157 129 139 104 179 169 169 163 157 133 33 104 168 168 158 158 115 115 Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  12. Watershed transform Integrated approach SegmentIt Watershed on graphs WT can be formulated as a graph optimization problem: WS ( G I , M ) G I = ( V , E , ω ) : a graph representing the input image I Granularities: Pixel Adjacency Graph PAG I Region Adjacency Graph RAG I ω : dissimilarity measure between the vertices M : the set of markers Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  13. Watershed transform Integrated approach SegmentIt Watershed on graphs P = WS ( G I , M ) is obtained by propagating the label of the markers for all the vertices of G I using minimum cost paths; WS ( G I , M ) can have multiple optimal solutions (minimum cost paths can be not unique), the obtained solution depends on the implementation details (queue policies, processing order of vertices, neighbors and markers, etc.) Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  14. Watershed transform Integrated approach SegmentIt Hierarchical watershed Tree of Critical Lakes (TCL) [Meyer, 1996] Hierarchy: nested set of partitions, where the finest partition is given by the classical watershed. I H E E F G D D C C A A A B C D E B B (a) Original image (b) Finest partition (c) MST of the (d) TCL RAG (simplified) Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  15. Watershed transform Integrated approach SegmentIt Hierarchical watershed Construction of the Tree of Critical Lakes (TCL) C A B A B C Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  16. Watershed transform Integrated approach SegmentIt Hierarchical watershed Construction of the Tree of Critical Lakes (TCL) D A D A B C Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  17. Watershed transform Integrated approach SegmentIt Hierarchical watershed Construction of the Tree of Critical Lakes (TCL) E E D A B C Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  18. Watershed transform Integrated approach SegmentIt Hierarchical watershed Limitation of partitions that can be found on the TCL C A E B D A B C Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  19. Watershed transform Integrated approach SegmentIt Hierarchical watershed Navigating through the partitions of the TCL [Zanoguera et al., 1999] E E G D D C C F F H I I I H H H F G F G F G A B C D E A B C D E A B C D E (a) Threshold (b) Split (c) Merge Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  20. Watershed transform Integrated approach SegmentIt Interactive segmentation Systems based on automatic segmentation are usually restricted to specific domains and for two classes of objects (foreground / background) Formal specification of the parameters of a segmentation algorithm can be very difficult; A post-processing of the partition (obtained through automatic techniques) may be necessary to achieve a satisfactory result; The concept of a good partition may depend on the purpose of its use and may be highly subjective. Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  21. Watershed transform Integrated approach SegmentIt Watershed from markers Strong points easy to segment a specific region works on both granularities (pixels and regions) easy to “force” inexistent borders Weak points a marker has to be drawn for each region of interest high interaction effort to design markers for complex regions Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  22. Watershed transform Integrated approach SegmentIt Hierarchical watershed Strong points easy to segment several objects according to their metrics works on the regions granularity (efficiency) Weak points works on the regions granularity (borders are always borders of the primitive catchment basins) the partitions are limited due to the structure of the TCL hard to segment a specific region Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  23. Watershed transform Integrated approach SegmentIt Proposal Integrate the watershed from markers and the hierarchical watershed in order to allow the full use of the strengths of both approaches. Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

  24. Watershed transform Integrated approach SegmentIt Problem From markers to the hierarchical watershed Given: Set of markers M Partition P = WS ( G I , M ) of the image I We want: Hierarchy of partitions of I which contains P From hierarchical watershed to markers Given: Partition P selected from a hierarchy of partitions of the image I We want: Set of markers M such that WS ( G I , M ) = P Bruno Klava and Nina Sumiko Tomita Hirata Interactive image segmentation with integrated use of the markers . . .

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