Graph based image segmentation with sub- pixel precision

Graph based imagesegmentation with subpixelprecisionFilip MalmbergCentre for Image analysisSwedish University of Agricultural SciencesUppsala University

Image segmentation and feature2●●●measurementsImage analysis: Measure properties of objects,based on a sampled image.Usually requires segmentation.Measurement accuracy limited by imageresolution.namn@cb.uu.se

3Crisp/Fuzzy segmentation●●A crisp segmentation maps each imageelement to exactly one object category.A fuzzy segmentation allows an image elementto partially belong to many different objectcategories.namn@cb.uu.se

4Pixel coverage segmentation●●Special case of fuzzy segmentationLet the degree of membership to a certain classbe proportional to the extent to which the imageelement is covered by that object.namn@cb.uu.se

5Pixel coverage segmentation-How to digitize?vs.namn@cb.uu.se

6Pixel coverage segmentation●●By using feature estimators that work directlyon this type of representation, we can get muchmore precise feature measurements!To benefit from this in practice, we needsuitable segmentation methods.namn@cb.uu.se

7Graph based segmentation●●Interpret image as an edge weighted graph.Two common ways to represent asegmentation: Graph cuts and graph labelingnamn@cb.uu.se

Pixel coverage segmentation on8●●graphsHow do we define ”pixel coverage” on graphs?No notion of the ”shape” of a pixelnamn@cb.uu.se

9General idea●Interpret edges as paths between vertices.● We can parametrize a path by t ∈ [0,1].●Define segmentation labels for all points alongthe edges – Edge segmentation.namn@cb.uu.se

10Located cuts●Define a point along each edge in the cut wherethe transition occurs.namn@cb.uu.se

11Vertex coverage segmentation●●Integrate labels over the domain of each vertex.The domain (”shape of a vertex”) is the set of”half-edges” adjacent to the vertex:●For an edge segmentation generated by alocated cut, we get closed formulas that areeasy evaluate.namn@cb.uu.se

12Vertex coverage segmentationnamn@cb.uu.se

13Computing located cuts in practice●Two methods proposed:▬▬Sub-pixel IFTSub-pixel ”defuzzification”namn@cb.uu.se

14Does it make a difference?namn@cb.uu.se

15Yes!namn@cb.uu.se

16Synthetic objects● Measurements were made on 2000 objects.namn@cb.uu.se

17Interactive segmentation●Study variation of area measurement withrespect to changes in seed-point placement.namn@cb.uu.se

18Results●Both experiments show that using the proposedframework leads to significantly better stabilitywhen measuring object features.namn@cb.uu.se

19●Results, exampleStandard deviation of relative measurementerror reduced by a factor 5.namn@cb.uu.se

20Ideas for future work●●Use located cuts as a general objectrepresentation on graphs?Can we perform operations (e.g. Morphology)directly on this representation?namn@cb.uu.se

21References●●●Sub-pixel Segmentation with the Image Foresting Transform,F. Malmberg, J. Lindblad, I. Nyström, In Proceedings of the 13th International Workshop onCombinatorial Image Analysis 2009 (IWCIA'09)Image Foresting Transform: On-the-fly Computation of RegionBoundaries, F. Malmberg, In Proceedings of Swedish symposium on image analysis 2010(SSBA'10).A graph based framework for Sub-pixel Image Segmentation,F. Malmberg, J. Lindblad, N. Sladoje, I. Nyström. Submitted for publication.namn@cb.uu.se