Multidimensional Image Processing IWR, Univ. of Heidelberg Statistical Characterization of Technical Surface Microstructure Jochen Schmähling 1,2 Fred

Multidimensional Image Processing IWR, Univ. of Heidelberg

Statistical Characterization of Technical Surface Microstructure

Jochen Schmähling 1,2 Fred Hamprecht 2

1Corporate ResearchRobert Bosch GmbH

Stuttgart / Tokyo

2Multidimensional Image ProcessingInterdisciplinary Center for Scientific Computing (IWR)

University of Heidelberg


Overview

1. Microtopology of technical surfaces2. Microtopology analysis using Minkowski Functionals3. Models for technical surfaces4. Experimental results5. Summary

Common Rail Injector shim („Ausgleichscheibe“)

5mm


Overview



The topology of technical parts is investigated on three scales:

Form is the (intended) macroscopic shapeWaviness occurs due to irregularities during the machining processMicrotopology 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


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:FrictionWearSealingLubrication properties


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


Overview



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


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


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


Minkowski functionalsApart from the relative area, which other descriptors are useful for

random set description?

Hadwiger theorem: Additive, rotation invariant and convex continous functionalson 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.

+- +


• 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


Characterizing functions

+- +


• Area: Bearing behaviour• Contour length: General smoothness assessment• Euler characteristic:

– Number of peaks– percolation threshold

Interpretation of the characterizing functions

=104

material

void

=2


One-class learning for change detection

Only works for homogeneous class


Overview



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 processProcess parameter: #Craters

raw material processing measurement


[Adler, 1981]


Limitations

Four GRF• all have same

marginal • first three have

same τ


• 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


Parametrizing Boolean Models

• Density of grains• Shape of grains

Convex grains are easiest to investigate

• Boolean model in 2D

• Extension to 3D

+ =

+ =


Area, contour length and Euler characteristic depend on shape ( , , ) and number () of grains

Boolean grain model

[Molchanov, 1995; Weil, 1995]


Greenwood-Williamson model

grains as capped cylinders Gaussian grain height distribution



Overview



Structured hard-chrome surfaces

Source: www.topocrom.com

Material: hard chromeStructure: Hemispheres of random size

positioned randomlyPerfect example for a Boolean grain model

Applications:Sheet metal production (texturing, feeding)Wear-resistant tubesCoating of forming tools


Structured hard-chrome surfacesApplications:

Sheet metal production

Source: www.topocrom.com

10000x


Stochastic Geometry: Prediction of surface features

ModelExpected

characterizing functions

Model parameters OptimizationComparison with

optimal characterizing functions


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

100 200 300 400

100

200

300

400

500

600-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

SimulationMeasurement

-0.02 -0.01 0 0.01 0.020

0.5

1

Are

a fr

act

ion

A

measuredsimulated

-0.02 -0.01 0 0.01 0.020

10

20

30

Con

tou

r le

ng

th C

-0.02 -0.01 0 0.01 0.02

-100

0

100

200

Eul

er

char

act

eri

stic

height100 200 300 400 500 600

100

200

300

400

500

600-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

100 200 300 400 500 600

100

200

300

400

500

600-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01



Shot-blasted surface


Overview



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


29th Annual meeting of the DAGM

Heidelberg, Sept. 12th-14th, 2007


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


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


Acknowledgement

Andres, Bjoern Eisele, HeikoFeistner, LarsGoerlitz, Linus Hader, SörenHayn, Michael Heck, DanielHissmann, MichaelHumbert, SilkeJaeger, Mark Kaller, Jochen

Kelm, Michael Kirchner, Marc Koenig, ThomasLerch, Kristoffer Li, Xin Menze, BjoernPlaue, MatthiasRenard, BernhardSchmähling, Jochen Saussen, BenjaminTrittler, StefanWieler, Matthias Zhang, Huaizhong

Group for Multidimensional Image Processing


Acknowledgement

Thank you!(It is safe to wake up now.)

Documents

Multidimensional Image Processing IWR, Univ. of Heidelberg Statistical Characterization of Technical Surface Microstructure Jochen Schmähling 1,2 Fred