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Multidimensional Image Processing IWR, Univ. of Heidelberg Statistical Characterization of Technical Surface Microstructure Jochen Schmähling 1,2 Fred Hamprecht 2 1 Corporate Research Robert Bosch GmbH Stuttgart / Tokyo 2 Multidimensional Image Processing Interdisciplinary Center for Scientific Computing (IWR) University of Heidelberg

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Multidimensional Image Processing IWR, Univ. of Heidelberg Overview 1.Microtopology of technical surfaces 2.Microtopology analysis using Minkowski Functionals 3.Models for technical surfaces 4.Experimental results 5.Summary Common Rail Injector shim („Ausgleichscheibe“) 5mm

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Multidimensional Image Processing IWR, Univ. of Heidelberg Overview 1.Microtopology of technical surfaces 2.Microtopology analysis using Minkowski Functionals 3.Models for technical surfaces 4.Experimental results 5.Summary

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Multidimensional Image Processing IWR, Univ. of Heidelberg The topology of technical parts is investigated on three scales: Form is the (intended) macroscopic shape Waviness occurs due to irregularities during the machining process Microtopology results from surface finishing process, e.g. grinding, shot- blasting, polishing or eroding. Magnitude of microtopology of technical surfaces is usually of order of µm Microtopology of technical surfaces Form Waviness Microtopology 15mm 5mm 0,3mm

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Multidimensional Image Processing IWR, Univ. of Heidelberg What is the role of microstructure? Miniaturization: The smaller the part, the more important small-scall structures, e.g. injection valve, injection nozzle Higher requirements for industrial parts: Higher stress, lower tolerances Optimization of functionality: Friction Wear Sealing Lubrication properties

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Multidimensional Image Processing IWR, Univ. of Heidelberg Measuring microtopology First devices for surface roughness measurement around 1930 Profilometer: Scanning of the surface using a stylus + Established and highly refined technique + widely accepted norms for analysis Permanent contact necessary, slow Optical measurement instruments, especially white light interferometry + Fast and contactless + Twodimensional measuring area z White light interferometer principle Profilometer principle

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Multidimensional Image Processing IWR, Univ. of Heidelberg Overview 1.Microtopology of technical surfaces 2.Microtopology analysis using Minkowski Functionals 3.Models for technical surfaces 4.Experimental results 5.Summary

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Multidimensional Image Processing IWR, Univ. of Heidelberg Features used in technical surface description Goal: compact numeric description of relevant features Questions: –How smooth/rough is a surface? Comparison of different surfaces –Which properties does the surface have? (lubrication, wear,…) Description using only a few features In practice usually a very limited set of simple features is used. –Example: Mean squared deviation between the height data and the form of the part Shot-blasted surface ground surface shot-blasted surface

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Multidimensional Image Processing IWR, Univ. of Heidelberg 1D and 2D microstructure parameters 1D microstructure parameters (Roughness parameters) –Developed for the analysis of 1D profiles –Limited information content –Established standard 2D microstructure parameters –Analysis of 2D height maps –All techniques (math. morphology, texture analysis) from image processing can be used Microstructure parameters allow for –the comparison of surfaces –the prediction of functional properties Currently used 2D microstructure parameters are not satisfactory. How can the 2D height map information be used efficiently? 2D-analysis 1D-analysis

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Multidimensional Image Processing IWR, Univ. of Heidelberg Microtopology analyis by thresholding Binarization by thresholding Transformation of the height map to a stack of level sets (excursion sets) Microstructure description: –Description of the level sets for all thresholds –Analysis of random sets Simulated surface

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Multidimensional Image Processing IWR, Univ. of Heidelberg Minkowski functionals Apart from the relative area, which other descriptors are useful for random set description? Hadwiger theorem: Additive, rotation invariant and convex continous functionals on 2D sets can be expressed as linear combination of area, contour length and Euler characteristic of the set. Minkowski functionals offer a complete (in the above sense) description of the level sets. + -+

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Multidimensional Image Processing IWR, Univ. of Heidelberg Euler Characteristic: The calculation of the three Minkowski measures for 2D sets yields three characterizing functions. Minkowski Measures =104 Schnitte durch eine simulierte Oberfläche auf verschiedenen Schnitthöhen =-92 =2

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Multidimensional Image Processing IWR, Univ. of Heidelberg Characterizing functions + -+

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Multidimensional Image Processing IWR, Univ. of Heidelberg Area: Bearing behaviour Contour length: General smoothness assessment Euler characteristic: –Number of peaks –percolation threshold Interpretation of the characterizing functions =104 material void =2

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Multidimensional Image Processing IWR, Univ. of Heidelberg One-class learning for change detection Only works for homogeneous class

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Multidimensional Image Processing IWR, Univ. of Heidelberg Klassifikation Confidence band corresponds to hyperrectangle. Alternative: –Nächster Nachbar-Klassifikator mit K Klassen –Lernstrategie z.B. K-means Clustering, Principal Component Analysis

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Multidimensional Image Processing IWR, Univ. of Heidelberg Overview 1.Microtopology of technical surfaces 2.Microtopology analysis using Minkowski Functionals 3.Models for technical surfaces 4.Experimental results 5.Summary

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Multidimensional Image Processing IWR, Univ. of Heidelberg Why are surface models helpful? Model = simplified image of reality Allows to describe a complex system with few parameters Using a surface model, the surface structure can be predicted from process parameters Example: Modelling a laser structuring process Process parameter: #Craters raw materialprocessingmeasurement

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Multidimensional Image Processing IWR, Univ. of Heidelberg [Adler, 1981]

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Multidimensional Image Processing IWR, Univ. of Heidelberg

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Limitations Four GRF all have same marginal first three have same τ

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Multidimensional Image Processing IWR, Univ. of Heidelberg χ 2 random field [Schmalzing, 1999]

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Multidimensional Image Processing IWR, Univ. of Heidelberg Sinter materials: material consists of metal grains welded in a thermal process to form a solid material Modelling with a Boolean grain model –Objects (“grains˝) are positioned randomly –Surface given by union of grains Applications in material science for modelling porous materials, e.g. sinter, sandstone Complementary to random fields: random amplitudes random positions Boolean Grain models 0.5mm Simulation of a Boolean model Measurement data Microscope image

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Multidimensional Image Processing IWR, Univ. of Heidelberg Parametrizing Boolean Models Density of grains Shape of grains Convex grains are easiest to investigate Boolean model in 2D Extension to 3D += +=

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Multidimensional Image Processing IWR, Univ. of Heidelberg Area, contour length and Euler characteristic depend on shape (,, ) and number () of grains Boolean grain model [Molchanov, 1995; Weil, 1995]

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Multidimensional Image Processing IWR, Univ. of Heidelberg Greenwood-Williamson model grains as capped cylinders Gaussian grain height distribution

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Multidimensional Image Processing IWR, Univ. of Heidelberg

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Overview 1.Microtopology of technical surfaces 2.Microtopology analysis using Minkowski Functionals 3.Models for technical surfaces 4.Experimental results 5.Summary

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Multidimensional Image Processing IWR, Univ. of Heidelberg Structured hard-chrome surfaces Source: www.topocrom.com Material: hard chrome Structure: Hemispheres of random size positioned randomly Perfect example for a Boolean grain model Applications: Sheet metal production (texturing, feeding) Wear-resistant tubes Coating of forming tools

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Multidimensional Image Processing IWR, Univ. of Heidelberg Structured hard-chrome surfaces Applications: Sheet metal production Source: www.topocrom.com 10000x

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Multidimensional Image Processing IWR, Univ. of Heidelberg Stochastic Geometry: Prediction of surface features Model Expected characterizing functions Model parameters Optimization Comparison with optimal characterizing functions

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Multidimensional Image Processing IWR, Univ. of Heidelberg Find simulation parameters such that empirical and analytically calculated MF fit. Practical application: Find process parameters such that the resulting material fulfills given functionality requirements formulated in terms of the shape of the MF Model estimation Simulation Measurement

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Multidimensional Image Processing IWR, Univ. of Heidelberg

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Shot-blasted surface

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Multidimensional Image Processing IWR, Univ. of Heidelberg Sinter material

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Multidimensional Image Processing IWR, Univ. of Heidelberg Overview 1.Microtopology of technical surfaces 2.Microtopology analysis using Minkowski Functionals 3.Models for technical surfaces 4.Experimental results 5.Summary

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Multidimensional Image Processing IWR, Univ. of Heidelberg Summary Current methods for surface microstructure analysis are not satisfactory for 2D data Minkowski measures are natural descriptors for binary images Minkowski measures computed for level sets give characterizing functions These characterizing functions can extend / generalize existing analysis techniques Using surface models, surfaces with specific properties can be engineered. Dilation on the level sets allows for a homogeneity analysis Outlook

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Multidimensional Image Processing IWR, Univ. of Heidelberg 29 th Annual meeting of the DAGM Heidelberg, Sept. 12 th -14 th, 2007

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Multidimensional Image Processing IWR, Univ. of Heidelberg Topics - Image Analysis and Computer Vision Mathematical Foundations Low-level Vision, Segmentation Biological Vision and Natural Scene Statistics Graphical Models and Probabilistic Inference Combinatorial Methods, Perceptual Grouping Shape Representation and Analysis Surface Reflectance Recovery and Modeling Motion, Matching and Registration Tracking and Video Analysis Multi-View Geometry and 3D Reconstruction Object (Class) Recognition and Detection Knowledge Representation and High-Level Vision - Machine Learning and Statistical Data Analysis - Speech Recognition and Language Understanding - Biomedical Data Analysis and Imaging, Biometrics - Applications of Pattern Recognition in Natural Sciences - Industrial and Technical Applications of Pattern Recognition and Image Processing

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Multidimensional Image Processing IWR, Univ. of Heidelberg Acknowledgement Deutsche Forschungsgemeinschaft (DFG) Bundesministerium für Bildung und Forschung (BMBF) Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF) H.-L. Merkle Stiftung Heidelberger Druckmaschinen Athenaeum Stiftung Studienstiftung des deutschen Volkes Yxlon Security GmbH Hansgrohe GmbH

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Multidimensional Image Processing IWR, Univ. of Heidelberg Acknowledgement Andres, Bjoern Eisele, Heiko Feistner, Lars Goerlitz, Linus Hader, Sören Hayn, Michael Heck, Daniel Hissmann, Michael Humbert, Silke Jaeger, Mark Kaller, Jochen Kelm, Michael Kirchner, Marc Koenig, Thomas Lerch, Kristoffer Li, Xin Menze, Bjoern Plaue, Matthias Renard, Bernhard Schmähling, Jochen Saussen, Benjamin Trittler, Stefan Wieler, Matthias Zhang, Huaizhong Group for Multidimensional Image Processing

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Multidimensional Image Processing IWR, Univ. of Heidelberg Acknowledgement Thank you! (It is safe to wake up now.)

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