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Quantification and Spatial Relationship Karsten Rodenacker, Martina Hausner, Anna A. Gorbushina, g Forschungszentrum Neuherberg München Oldenburg Content  Introduction from perception to image analysis  Measurement objects, groups of objects inter- and intra-relationships   Examples Conclusion Introduction    Perception – recognition – differentiation – description Quantification Relation of qualitative and quantitative terms Introduction  The difficulty NOT to see something Introduction  The difficulty to see anything Introduction  The ease to see the impossible Introduction  Quantitative terms Introduction  How to relate qualitative and quantitative terms? Introduction   Digitisation Segmentation Introduction  Sub sectioning and change of scale Introduction Measurement (of one object)     Extension Size Shape Structure Introduction Measurement (of several objects)    Arrangement Relation Neighbourhood Measurement   Examples of measurements, objects and groups of objects Spatial relationships Measurement    Area Perimeter Extension Measurement    Shape Growth shape Density, intensity Measurement  Extensions Length (skeleton) =1621 px mean thickness =2.27 px Measurement  Neighbourhood closing on filaments Measurement  Spatial Relationship Delaunay triangulation nearest neighbours minimum spanning tree convex hull Skeleton neighbourhood Measurement  Spatial Relationship Example from pathology Measurement  Spatial relationship (objects of different type) Double marked sludge flocks Distances to the red phase Measurement   Measurement continuum Measurement hierarchy object content location external properties object pixel object content location properties object object Example  Bacterial growth in flow chambers Differentiation of wild and mutant bacteria pseudomonas aeruginosa by CLSM imaging Example  Wild (PA) and mutant (MW) bacteria Growth over time (slice # = depth) Example  Substrate coverage (closing) Wild type bacteria Mutant bacteria Example  Bacterial growth in flow chambers Conjugative genetic transfer in bacterial biofilm Example  Quantification of colonies of micro colonial fungi from sub aerial biofilms coniosporium sp. and sarcinomyces sp. under soil (b), sand (s) coverage and in air (l) Example  Colonies of micro colonial fungi Example  Colonies of micro colonial fungi Conclusion   Perception, description and measurement of objects and object groups in images Exclusions (e.g. texture, filtering, fractals, etc.)  Faith and (apparent) truth