Transcript Slide 1

Multidimensional Image Processing
IWR, Univ. of Heidelberg
Statistical Characterization of Technical
Surface Microstructure
Jochen Schmähling
1,2
Fred Hamprecht
2
1Corporate
Research
Robert Bosch GmbH
Stuttgart / Tokyo
2Multidimensional
Image Processing
Interdisciplinary Center for Scientific Computing (IWR)
University of Heidelberg
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
5mm
Common Rail Injector shim
(„Ausgleichscheibe“)
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
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Microtopology of technical surfaces
The topology of technical parts is investigated on three scales:
Waviness
5mm
15mm
Form
0,3mm
Microtopology
Form is the (intended) macroscopic shape
Waviness occurs due to irregularities during the machining process
Microtopology results from surface finishing process, e.g. grinding, shotblasting, polishing or eroding.
Magnitude of microtopology of technical surfaces is usually of order of µm
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
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
Profilometer principle
• Optical measurement instruments, especially
white light interferometry
+ Fast and contactless
+ Twodimensional measuring area
z
White light interferometer principle
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
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,…)
Shot-blasted surface
• 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
2
shot-blasted surface
2
ground surface
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
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2D microstructure parameters
– Analysis of 2D height maps
– All techniques (math. morphology, texture analysis) from
image processing can be used
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1D-analysis
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
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Microtopology analyis by thresholding
• Binarization by thresholding
Simulated surface
• 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
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
Minkowski Measures
• Euler Characteristic:
Schnitte durch eine
simulierte Oberfläche auf
verschiedenen
Schnitthöhen
 =104
 =2
 =-92
• The calculation of the three Minkowski measures for 2D sets yields
three characterizing functions.
Multidimensional Image Processing
Characterizing functions
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Multidimensional Image Processing
IWR, Univ. of Heidelberg
Interpretation of the characterizing functions
• Area: Bearing behaviour
• Contour length: General smoothness assessment
• Euler characteristic:
– Number of peaks
– percolation threshold
material
void
 =104
 =2
Multidimensional Image Processing
IWR, Univ. of Heidelberg
One-class learning for change detection
Only works for homogeneous class
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
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 material
processing
measurement
Multidimensional Image Processing
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[Adler, 1981]
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Limitations
Four GRF
• all have same
marginal
• first three have
same τ
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Boolean Grain models
• 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
Measurement data
0.5mm
Simulation of a
Boolean model
Microscope image
• Applications in material science for modelling
porous materials, e.g. sinter, sandstone
• Complementary to random fields:
random amplitudes  random positions
Multidimensional Image Processing
Parametrizing Boolean Models
• Density of grains
• Shape of grains
Convex grains are easiest to investigate
• Boolean model in 2D
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=
• Extension to 3D
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=
IWR, Univ. of Heidelberg
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Boolean grain model
Area, contour length and Euler characteristic depend on shape
( ,
, ) and number () of grains
[Molchanov, 1995; Weil, 1995]
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Greenwood-Williamson model
grains as capped cylinders
Gaussian grain height distribution
Multidimensional Image Processing
IWR, Univ. of Heidelberg
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
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Structured hard-chrome surfaces
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
Source: www.topocrom.com
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Structured hard-chrome surfaces
Applications:
Sheet metal production
10000x
Source: www.topocrom.com
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Stochastic Geometry: Prediction of surface features
Model parameters
Model
Optimization
Comparison with
optimal characterizing
functions
Expected
characterizing
functions
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Model estimation
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Simulation
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Measurement
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height
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Area fraction A
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measured
simulated
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Euler characteristic 
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Contour length C
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
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Multidimensional Image Processing
IWR, Univ. of Heidelberg
Multidimensional Image Processing
Shot-blasted surface
IWR, Univ. of Heidelberg
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
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.
Outlook
• Dilation on the level sets allows for a homogeneity analysis
Multidimensional Image Processing
IWR, Univ. of Heidelberg
29th Annual meeting of the DAGM
Heidelberg, Sept. 12th-14th, 2007
Multidimensional Image Processing
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
IWR, Univ. of Heidelberg
Multidimensional Image Processing
Acknowledgement
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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
IWR, Univ. of Heidelberg
Multidimensional Image Processing
IWR, Univ. of Heidelberg
Acknowledgement
Group for Multidimensional Image Processing
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
Multidimensional Image Processing
Acknowledgement
Thank you!
(It is safe to wake up now.)
IWR, Univ. of Heidelberg