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Czech Technical University in Prague Faculty of Transportation Sciences Department of Mechanics and Materials Assessment of Pore Size Distribution using Image Analysis master thesis Bc. Tom´ s Doktor Supervisor: Ing. Daniel Kyt´ r Prague, 2011

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Page 1: Czech Technical University in Prague Faculty of ...mech.fd.cvut.cz/projects/k618x2nm/DT_Doktor.pdf · Czech Technical University in Prague Faculty of Transportation Sciences Department

Czech Technical University in Prague

Faculty of Transportation Sciences

Department of Mechanics and Materials

Assessment of Pore Size

Distribution using Image Analysis

master thesis

Bc. Tomas Doktor

Supervisor: Ing. Daniel Kytyr

Prague, 2011

Page 2: Czech Technical University in Prague Faculty of ...mech.fd.cvut.cz/projects/k618x2nm/DT_Doktor.pdf · Czech Technical University in Prague Faculty of Transportation Sciences Department
Page 3: Czech Technical University in Prague Faculty of ...mech.fd.cvut.cz/projects/k618x2nm/DT_Doktor.pdf · Czech Technical University in Prague Faculty of Transportation Sciences Department

ČESKÉ VYSOKÉ UČENÍ TECHNICKÉ

FAKULTA DOPRAVNÍ Ústav: K618 Akademický rok: 2010/11

Z A D Á N Í D I P L O M O V É P R Á C E ( PROJEKTU, UMĚLECKÉHO DÍLA, UMĚLECKÉHO VÝKONU )

pro Bc. Tomáše Doktora ..................................................................................................................................................................................................................

obor Inženýrská informatika v dopravě a spojích ..................................................................................................................................................................................................................

Název tématu: Hodnocení distribuce porozity materiálů pomocí obrazové analýzy .......................................................................................................................................................................................

Zásady pro vypracování:

Cílem práce je vytvořit algoritmy pro hodnocení porézních materiálů z hlediska rozdělení velikosti pórů na základě obrazové analýzy snímků obdržených optickou a elektronovou mikroskopií a počítačovou mikrotomografií. Materiál bude popsán ohodnocenou sítí pórů odpovídající jeho vnitřní struktuře. Algoritmy budou vytvořeny v jazyce výpočetního prostředí Matlab. Verifikace metody bude provedena analýzou materiálových vzorků známých vlastností a porovnáváním výsledků s měřením pomocí porozimetru. Parametry získané z křivky distribuce pórovitosti budou použity pro získání materiálových vlastností popisujících chování reprezentativního objemu materiálu v elastické oblasti.

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Declaration

I hereby declare that this master thesis ”Assessment of Pore Size Distribution using

Image Analysis” is completely my own work and that I used only the cited sources in

accordance with CTU law No. 1/2009 ”Metodicky pokyn o eticke prıprave vysokoskolskych

zaverecnych pracı”.

I have no reason against use of this school work in accordance to §60 of czech law

No. 121/2000 Sb. ”o pravu autorskem, o pravech souvisejıcıch s pravem autorskym a o

zmene nekterych zakonu”.

Prague, April 26, 2011...........................................

Tomas Doktor

4

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Acknowledgement

I would like to thank my supervisor Ing. Daniel Kytyr, for patient guidance and useful

advice and for his kind and helpful approach.

I was delighted to cooperate with Ing. Jaroslav Valach, Ph.D. (CTU, Faculty of Trans-

portation Sciences and Institute of Theoretical and Applied Mechanics, AS CR, v.v.i.)

during scanning electron microscopy, Ing. Michaela Kostelecka-Dudıkova (CTU, Klokner

institute) during laser confocal microscopy and RNDr. Libor Nosal (ITAM AS CR) during

MIP measurements. I would like to thank Ing. Zuzana Slızkova, Ph.D. and Mgr. Dita

Frankeova for the specimena of frit glass and lime mortars.

My colleagues from Department of biomechanics at ITAM AS CR, v.v.i. deserve thanks

for making the lab a pleasure and inspirative place to work.

This work was supported by the Grant agency of the Czech Technical University

in Prague (grant No. SGS10/218/OHK2/2T/16), Grant agency of the Czech republic

(grant No. P105/10/2305), Ministry of education, youth and sports (research plan

No. MSM6840770043) and Grant agency of the Academy of sciences of the Czech republic

(research plan No. AV0Z20710524). All the support is gratefully acknowledged.

5

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Abstract

Doktor, T.: Assessment of pore size distribution using image analysis, master thesis,

Czech technical university in Prague Faculty of transportation sciences, Department of

mechanics and materials, Prague, 2011

The paper deals with development of a software tool for assessment of pore size distri-

bution of porous materials. Six types of materials were chosen for testing of the developed

algorithms: lime mortars, frit glass, polyurethane foam (artificial pumice), polyvinylchlo-

ride foam (artificial cork) and trabecular structure of mammalian (human and porcine)

proximal femur. Process of preparation of samples is described in order to achieve suit-

able specimen for image acquisition. For the acquisition of two-dimensional image data

different devices and approaches were tested: CCD camera, scanning electron microscope,

laser confocal microscope and high resolution flatbed scanner. The algorithms used for

the pore size distribution assessment were developed in language of computational envi-

ronment MatLab. The procedure consists of image segmentation, connected component

analysis and stereological calculation. A series of mercury intrusion porosimetry measure-

ments was carried out and the results were compared with the results of image analysis.

In the comparison of both groups of results a satisfactory agreement was observed. Suit-

ability of developed tool is discussed regarding to type of tested material and to range of

pore sizes present in the material structure.

Keywords: porous materials, pore size distribution, image analysis, MatLab, mercury

intrusion porosimetry

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Abstrakt

Doktor, T.: Hodnocenı distribuce velikosti porovitosti pomocı obrazove analyzy, diplo-

mova prace, Ceske vysoke ucenı technicke v Praze Fakulta dopravnı, Ustav mechaniky a

materialu, Praha, 2011

Prace se zabyva vyvojem softwaroveho nastroje pro hodnocenı distribuce velikosti poru.

Pro testovanı vyvıjenych algoritmu bylo zvoleno sest typu materialu: vapenne malty,

poreznı sklo, polyuretanova pena (umela pemza), polyvinylchloridova pena (umela vinna

zatka) a tramcita struktura z hlavice lidske a veprove stehennı kosti. V praci je popsan

postup prıpravy vzorku vhodnych ke snımanı obrazovych dat. Dvojrozmerna obrazova

data byla zıskavana pomocı ctyr ruznych zarızenı: digitalnı fotoaparat, radkovacı elek-

tronovy mikroskop, laserovy konfokalnı mikroskop a plosny skener s vysokym rozlisenım.

Algoritmy byly vyvıjeny v jazyce vypocenıho prostredı MatLab. Analyza sestavala ze seg-

mentace obrazu, hodnocenı identifikovanych komponent v segmentovanem obrazu a stere-

ologickeho prepoctu do trojrozmerneho prostoru. Pro overenı vysledku obdrzenych po-

mocı vytvorenych nastroju byla provedena merenı rtutovym porozimetrem. Pri srovnanı

vysledku obrazove analyzy a rtutove porozimetrie byla pozorovana uspokojiva shoda.

Vhodnost pouzitı vyvinuteho nastroje je hodnocena s ohledem na druh materialu, charak-

ter snımanych vzorku a rozsah velikostı poru.

Klıcova slova: poreznı materialy, distribuce velikosti poru, analyza obrazu, MatLab,

rtutova porozimetrie

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Contents

1 Introduction 14

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.2 Aims and objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3 Methodical approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Porous materials 17

2.1 Classification of porous materials . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Characteristics of the porous structure . . . . . . . . . . . . . . . . . . . . 19

2.3.1 Porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.2 Specific surface area . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.3 Pore size distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 Estimation of the pore size distribution . . . . . . . . . . . . . . . . . . . . 20

2.4.1 Intrusion porosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.2 Observation of the porous structure . . . . . . . . . . . . . . . . . . 20

3 Investigated materials 21

3.1 Mortars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Frit glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Polyurethane foam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4 Polyvinylchloride foam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

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3.5 Human trabecular bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.6 Porcine trabecular bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4 Specimen preparation 25

4.1 Specimena for image acquisition . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1.1 Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1.2 Delipidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1.3 Fixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.1.4 Polishing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2 Specimena for mercury intrusion porosimetry . . . . . . . . . . . . . . . . . 26

4.2.1 Drilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2.2 Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5 Image acquisition 28

5.1 Optical microscope with a CCD camera . . . . . . . . . . . . . . . . . . . . 28

5.2 High resolution flatbed scanner . . . . . . . . . . . . . . . . . . . . . . . . 28

5.3 Scanning electron microscopy . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.4 Confocal microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6 Image analysis 32

6.1 Image segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6.1.1 Global thresholding . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6.1.2 Local thresholding . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6.1.3 Morphological operations . . . . . . . . . . . . . . . . . . . . . . . . 34

6.2 Connected component analysis . . . . . . . . . . . . . . . . . . . . . . . . . 36

7 Assessment of pore size distribution 38

7.1 Stereological calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

7.1.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

7.1.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

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8 Mercury intrusion porosimetry 42

8.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

8.1.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

8.1.2 Advantages and limitations . . . . . . . . . . . . . . . . . . . . . . 42

8.2 Experimental conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

8.3 Results of MIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

9 Results and discussion 45

9.1 Lime mortars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

9.2 Frit glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

9.3 Polyurethane foam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

9.4 Polyvinylchloride foam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

9.5 Human trabecular bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

9.6 Porcine trabecular bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

10 Conclusions 54

10.1 Summary of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

10.2 Suitability of used methods . . . . . . . . . . . . . . . . . . . . . . . . . . 55

10.2.1 Image analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

10.2.2 Mercury intrusion porosimetry . . . . . . . . . . . . . . . . . . . . . 55

10.3 Suggestions for further work . . . . . . . . . . . . . . . . . . . . . . . . . . 56

10.3.1 Stereologic method . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

10.3.2 Extraction of anisotropic morphological parameters . . . . . . . . . 56

10.3.3 Estimation of mechanical properties based on pore size distribution 56

Bibliography 57

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List of Figures

2.1 Classification of porous material based on pore size (recommended by In-

ternational Union of Pure and Applied Chemistry) [14] . . . . . . . . . . . 17

3.1 Lime mortar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2 Frit glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Polyurethane foam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4 Polyvinylchloride foam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.5 Human femur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.6 Porcine trabecular bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1 Human trabecular bone during the preparation process . . . . . . . . . . . 26

5.1 Scheme of a SEM device [10] . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.2 Principle of the laser scanning confocal microscope [16] . . . . . . . . . . . 30

5.3 Result of image acquisition. Comparison of used techniques. . . . . . . . . 31

6.1 Connected component labeling [19] . . . . . . . . . . . . . . . . . . . . . . 34

6.2 Disc shaped structuring element with radius 2 px . . . . . . . . . . . . . . 35

6.3 Connected component labeling [19] . . . . . . . . . . . . . . . . . . . . . . 37

7.1 Principles of the stereological calculation [24] . . . . . . . . . . . . . . . . . 39

7.2 GUI layout of the analysis tool . . . . . . . . . . . . . . . . . . . . . . . . 41

8.1 Principles of MIP [14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

8.2 Pore size distribution of porcine trabecular bone obtained by MIP . . . . . 44

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8.3 Pore size distribution of human trabecular bone obtained by MIP . . . . . 44

9.1 Pore size distribution of lime mortars (image data obtained by CCD camera) 46

9.2 Pore size distribution of lime mortars (image data obtained by flatbed

scanner) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

9.3 Pore size distribution of frit glass (image data acquired by confocal micro-

scope) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

9.4 Pore size distribution of frit glass (image data acquired by flatbed scanner) 47

9.5 Pore size distribution of polyurethane foam (image data acquired by high

resolution flatbed scanner) . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

9.6 Pore size distribution of polyurethane foam (image data acquired by CCD

camera) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

9.7 Pore size distribution of polyvinylchloride foam (image data acquired by

flatbed scanner) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

9.8 Pore size distribution of polyvinylchloride foam (image data acquired by

laser confocal microscope) . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

9.9 Pore size distribution of human trabecular bone (image data acquired by

CCD camera) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

9.10 Pore size distribution of human trabecular bone (image data acquired by

flatbed scanner) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

9.11 Pore size distribution of porcine trabecular bone (image data acquired by

SEM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

9.12 Pore size distribution of porcine trabecular bone (image data acquired by

flatbed scanner) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

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List of Tables

3.1 Pore sizes of frit glass discs declared by producer . . . . . . . . . . . . . . 22

4.1 Polishing procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

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Chapter 1

Introduction

1.1 Motivation

Knowledge of inner structure of the heterogeneous materials is an important prerequisite

for a deeper understanding of relationships between structure, properties and function of

the materials.

In porous materials the pore size distribution, i.e. frequencies of various sized voids

present in the structure, provides a possibility to develop a representative volume element

of the material. This study is focused on assessment of pore size distribution using image

analysis.

1.2 Aims and objectives

This work was carried out as a part of an extensive student research project ”Hybrid

measurement system of thermo-mechanical parameters of advanced materials and struc-

tures in limiting loading states” (partial results presented in annual report of the project

[22]). This project is focused on combining of experimental and numerical techniques to

enable estimation of mechanical properties of material with complex structure, because

these characteristics are often unavailable by common used experimental techniques.

14

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This study covers the part of the project aimed to the description of the inner structure

of heterogeneous materials to provide the opportunity to estimate relations between the

inner structure and thermo-mechanical properties. The main aim of this work was to

develop a software tool for assessment of pore size distribution. As input data of the

proposal tool two-dimensional (2D) image data were considered.

1.3 Methodical approach

The process of assessment of the pore size distribution was divided into four main steps

with a crucial influence on the results. The concatenation of the steps of the analysis

process is listed below.

� Specimen preparation

� Image acquisition

� Image analysis

� Stereological calculation

The first and second step are aimed to provide suitable image data for the image analysis.

Regarding to different nature of investigated material the preprocessing part is challeng-

ing because the accuracy and reliability of the results is determined by the quality of the

input data. For the software part of the developed methodology (image analysis and stere-

ological calculation) algorithms were implemented in MatLab language (MatLab R2009b,

MathWorks, Inc., Natick, USA). The implemented parts were tested using image data

obtained from specimens of six types of investigated materials. For two types of material

obtained results were compared with mercury intrusion porosimetry (MIP).

1.4 Limitations

This study is focused development of a analysis tool for pore size distribution assessment.

It does not cover development or implementation of new image analysis algorithms but it

consists in a design of a suitable concatenation of image processing algorithms. The main

15

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purpose of this tool is to be a part of proposal hybrid experimental-numerical system and

provide the output in suitable form for further usage in analysis of advanced materials.

Nevertheless, not only the image analysis process was studied and described. The

specimen preparation and image acquisition procedure has frequently a crucial importance

on accuracy of obtained results. Therefore in this study attention is also paid to the

specimen preparation and image acquisition.

16

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Chapter 2

Porous materials

Porous materials are defined by Ishizaki [14] as solids containing pores. This type of

material is frequently present in the nature and it is also widely used as artificial material

in both common and advanced applications.

2.1 Classification of porous materials

The most coarse classification is from the morphological point of view according to pore

size. Porous material are divided into three main groups: micro-porous materials, meso-

porous materials and macro-porous materials. Affiliation to the groups in dependency on

the pore size is depicted in Fig. 2.1. (From this point of view only macro-porous materials

are considered in this study.)

Figure 2.1: Classification of porous material based on pore size (recommended by Inter-

national Union of Pure and Applied Chemistry) [14]

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More complex classification of the porous materials presented in [11] or [14] based

on the origin of the dense phase of the porous material. Examples of porous materials

classified from this viewpoint is listed below.

� Artificial materials

– Ceramics, porous glasses

– Polymer foams

– Metal foams

– Mortars

– Concrete

� Natural materials

– Soils

– Porous rocks

– Bones

– Wood

2.2 Applications

Porous materials are used in a wide range of application and they are also found widely

in the nature. A list of the frequent applications was presented e.g. by Ishizaki [14] or

Gibson [11].

� Isolation materials (acoustic, thermal)

� Filtration

� Energy absorption

� Carriers for lubricants, dyes or inks

18

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2.3 Characteristics of the porous structure

The main characteristics estimated on porous materials are porosity (volume fraction

of pore volume to total volume), pore surface and pore size distribution. However the

thermo-mechanical properties (e.g. young modulus, thermal conductivity or thermal ca-

pacity) are not only determined by the above mentioned characteristics but by shape of

pores and other parameters also (described by Gibson and Ashby [11]).

2.3.1 Porosity

Porosity (pore volume ratio) is defined as the volume of pores to the total volume. Porosity

can be determined by fluid displacement method based on the Archimedian principle . It

consits in comparison of weight of dry sample, sample put in liquid with known density

and dry sample. Common range of porosity values is from 0.20 to 0.95 [14].

2.3.2 Specific surface area

Specific surface area is an important characteristic especially for materials used as filters or

catalysts. The most common method to determine specific surface area is gas adsorption

[14].

2.3.3 Pore size distribution

Pore size distribution describes frequencies of pores with different size present in the

porous structure. To determine the pore size distribution different approaches can be

used: intrusion porosimetry, gas adsorption or water vapour adsorption (described and

compared by Sneck [20]) or observation of the porous structure [1], [14].

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2.4 Estimation of the pore size distribution

2.4.1 Intrusion porosimetry

Mercury intrusion porosimetry was introduced by E. A. Washburn in 1921 [23]. It is based

on the non-wetting nature of mercury. Wood’s metal (a low melting point alloy) can be

also used as the intrusion fluid. This kind of measurement is reported e.g. by Abell in [1]

(comparison of mercury intrusion porosimetry, Wood’s metal intrusion porosimetry and

image analysis).

2.4.2 Observation of the porous structure

Pore size distribution can be evaluated by observation of the inner structure. The range

of registered pore sizes is determined by resolution of the image acquisition. Since the

acquired image is influenced by many factors (illumination, properties of the surface)

the evaluation of the structure cannot be fully automatic. A partial automation can be

achieved if suitable image analysis method is employed. By analysis of the cross-sections

not the spatial information but the two-dimensional one can be obtained. For estimation

of the pore size distribution on three-dimensional space a stereological method have to be

employed. A complex description of stereological method was presented by Saxl in [17].

Specialised methods for estimation of particle size (also applicable for porous structures)

were introduced by Saltykov [18] or Xu [24].

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Chapter 3

Investigated materials

To assess reliability of the developed software tool and its suitability for different mate-

rials, specimens of different origins were tested. For the tests six types of material were

chosen, lime mortars, frit glass, polyurethane foam and polyvinylchloride foam as repre-

sentatives of artificial materials and human and porcine trabecular bone as representatives

of biologic materials. Because the tool is proposed to be robust and work independently

on investigated material, the choice of tested materials could be determined by the avail-

ability of the specimens.

3.1 Mortars

Lime based mortars belong to old building materials used for connective, protective or

aesthetic purposes. Mortars are multi-phased composites containing agregates, binder and

voids [21]. As representatives of lime mortars six specimens were tested. The specimens

were extracted from historical buildings placed in central Bohemia (chateau Lysa, chateau

Kolın, chateau Roudnice). Specimen of lime mortar is depicted in Fig. 3.1.

3.2 Frit glass

Frit glass is a laboratory tool used by chemists as a very fine filter. This type of glass

contains longitudinal pores with very narrow and known distribution of pore size. This

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Figure 3.1: Lime mortar

fact was the reason to use frit glass as a testing specimen. In this study three frit glass

discs were used with defined pore size listed in Tab 3.1. The specimens are shown in Fig.

3.2

Sample No. [µm]

1 10–16

2 16–40

3 40–100

Table 3.1: Pore sizes of frit glass discs declared by producer

Figure 3.2: Frit glass

3.3 Polyurethane foam

Six specimens of polyurethane foam used as artificial replacement of the pumice rock were

tested in this study. This material was chosen because of this regular structure of convex

voids. The original block of this material is depicted in Fig. 3.3.

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Figure 3.3: Polyurethane foam

3.4 Polyvinylchloride foam

Three specimens of polyvinylchloride foam (used as artificial cork) were tested. This

material was chosen regarding to low pore sizes present in the structure suitable for

testing of the high resolution scanning. Specimena are depicted in Fig. 3.4

Figure 3.4: Polyvinylchloride foam

3.5 Human trabecular bone

Trabecular bone (termed as cancellous or spongy also) is present in epihyses and meta-

physes of long bones (Fig. 3.5a). The structure and properties of the trabecular bone

are described in detail by Currey in [2] and the relationships between pore characteristics

and mechanical properties are discussed e.g. by Cowin [3]. This type of bone consists of

trabeculae and intertrabecular spaces. (Fig. 3.5b).

For this study six specimens were harvested from proximal femur (male donor, 72 years

old) and tested using MIP and image analysis.

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(a) Parts of a long bone [5] (b) Trabecular structure

Figure 3.5: Human femur

3.6 Porcine trabecular bone

Six specimens were extracted from porcine proximal femur for image analysis and MIP

measurements. The specimens are depicted in Fig. 3.6.

Figure 3.6: Porcine trabecular bone

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Chapter 4

Specimen preparation

4.1 Specimena for image acquisition

For all image data acquisition method specific properties of specimens were required ac-

cording to limit dimensions of scanned specimen and contrast between voids and compact

material. In case of high resolution scanning techniques there is a requirement on a very

low surface roughness.

4.1.1 Cutting

To achieve a well prepared surface for high resolution image capturing techniques a precise

cutting device was required. For this purpose a low speed saw Isomet 1000 (Buehler, Ltd.,

Dusseldorf, Germany) was used. This device was used for samples of mortars and bones.

For cutting of soft materials (polymer foams) a sharp blade was used.

4.1.2 Delipidation

The trabecular structure after harvesting from both human and porcine proximal femur

contained marrow (fatty tissue in intertrabecular space [2]). Therefore the bone specimens

were delipided using an ultrasonic cleaner Polsonic SONIC 3 (Polsonic Palczynski Sp. J.,

Warsaw, Poland) and a detergent solution Alconox (Alconox, Inc., White Plains, USA).

Comparison of the trabecular bone during the preparation process is depicted in Fig. 4.1.

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(a) harvested (b) cut (c) delipided

Figure 4.1: Human trabecular bone during the preparation process

4.1.3 Fixing

In special cases the specimens were fixed to pass requirements for the corresponding image

acquisition methods. There were two reasons for fixing: to enable polishing to achieve a

low surface roughness (required for high resolution scanning devices) and to increase the

color contrast between voids and compact material by embedding into a coloured material

(resin or paraffin).

4.1.4 Polishing

For scanning using the confocal microscope (described in section 5.4) the results are

highly influenced by the surface roughness. The specimens used for this image acquisition

method were polished using TegraPol-11 (Struers A/S) grinding and polishing machine.

The concatenation of grinding and polishing steps is listed in Tab. 4.1.

An optimised grinding procedure (in detail presented in [9]) was employed. By the

optimisation was suggested a balanced combination of properties of the polishing steps

(grain size, speed, grinding head force and duration time) to decrease the consumption of

time and polishing fluids.

4.2 Specimena for mercury intrusion porosimetry

There are three main requirements on specimens used for mercury intrusion porosime-

try: purity and low humidity of the specimens (to avoid distortion of test results) and

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abrasive type grain size load speed duration time

[µm] [N] [rpm] [s]

diamond disk 35 5 120 120

diamond disk 15 5 120 120

diamond suspension 9 15 120 360

diamond suspension 3 10 120 240

diamond suspension 1 5 120 240

SiO2 suspension 0.05 2.5 120 300

Table 4.1: Polishing procedure

dimensions of the specimens corresponding with dimensions of the testing chamber.

4.2.1 Drilling

For MIP measurements (described in section 8.2) cylindrical specimens were required.

The specimens were drilled using a diamond hollow drill (Narex, s.r.o., Ceska Lıpa, Czech

republic). Diameter of the cylinders was 5mm and height was 10mm.

4.2.2 Drying

The specimens were dried using a hot air dryer at temperature 40°C for 15 hours. The

temperature was chosen closely to the body temperature to avoid possible changes of the

trabecular bone structure in higher temperature.

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Chapter 5

Image acquisition

To obtain suitable image data different techniques for each type of material were tested.

The choose of methods of the image acquisition was determined by three main factors:

range of pore sizes, dimensions of the available specimens and properties of the sample’s

surface. Because the distinction between compact material and pores is based on the

brightness values of the pixels, a high contrast is one of the most important requirements

on the acquired image data.

5.1 Optical microscope with a CCD camera

Using of CCD camera CCD-1300F (VDS Vosskuhler GmbH, Germany) with resolution

1280 × 1024 px attached to optical microscope (Navitar Imaging Inc., USA) allows to

capture 8 bit colour depth images with up to 24× magnification. The advantage of this

method consists in smooth magnification setup (3− 24×), but the image quality is very

sensitive to illumination conditions.

5.2 High resolution flatbed scanner

In the second case, the images of the samples were obtained by a high resolution flatbed

scanner EPSON Perfection V350 (Seiko Epson Corporation, Japan). Maximal resolution

4800 dpi was used (1 px corresponds to 5µm) with 16 bit colour depth. The physical size

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of the scannable area was up to 210×297 mm. This method is suitable for materials with

larger pores, because samples with dimensions corresponding to representative area were

required to register enough wide population of voids. The limitation of this acquisition

method is mainly constant magnification.

5.3 Scanning electron microscopy

For specimens with low poresizes image data acquisition using scanning electron micro-

scope (SEM) was tested. SEM performs the scanning of the surface by a finely focused

beam of electrons (described by Czichos in [4]). The electrons are emitted from a wolfram

wire and the beam is focused by electric field. The image is then reconstructed using

reflected beam of electrons, electrons emitted from the scanned surface and from emitted

radiation. To make the scanning possible a conductive surface is necessary, therefore the

surface of non-conductive specimens is required to be covered by gold or graphite powder.

To avoid the noise in the obtained image caused by electrons present in the test chamber

a high vacuum is required for the scanning. A scheme of the SEM arrangement is depicted

in Fig. 5.1

For the scanning an SEM device Tescan MIRA-II-LMU (Tescan, a.s., Brno, Czech

republic). Value of pressure in the testing chamber was 10−3 Pa, electron emission current

was 16.7 · 10−6 A and the accelerating voltage was 3 · 103 V.

Figure 5.1: Scheme of a SEM device [10]

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5.4 Confocal microscopy

For materials with very small pores images with a very high resolution can be obtained

using a confocal laser scanning microscope. This device performs the reconstruction of the

scanned surface using a laser beam (principle of the scanning is depicted in Fig. 5.2). In

this work confocal laser scanning microscope LEXT OLS3000 (Olympus, Inc) was used.

This device provides result of the scanning in form of high resolution images or in the

raw form of 2D matrix of ascertained heights. The physical size of the scanned area was

640× 480µm with magnification 480×.

Figure 5.2: Principle of the laser scanning confocal microscope [16]

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(a) porcine trabecular bone,

SEM

(b) porcine trabecular bone,

flatbed scanner

(c) human trabecular bone,

CCD camera

(d) human trabecular bone,

flatbed scanner

(e) polyvinylchloride foam, confocal

microscope (matrix of heights)

(f) polyvinylchloride foam,

flatbed scanner

Figure 5.3: Result of image acquisition. Comparison of used techniques.

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Chapter 6

Image analysis

In this part of the analysis process digital images are used to extract required information

about captured surfaces of tested specimens. A digital image is defined by Shapiro [19]

as ”a 2D image I[r,c] represented by a discrete 2D array of intensity samples of which

is represented using a limited precision”. The digital images obtained during the image

acquisition process were converted into binary ones (”digital images with all pixes values

0 or 1” [19]). The process of the conversion of grayscale of colour images into binary ones

is termed as image segmentation. In the binary images the values of 0 are assigned to

the background and values of 1 to the object in foreground (in this study cross-sections

of pores were considered as the foreground).

6.1 Image segmentation

6.1.1 Global thresholding

Principles

The basic segmentation technique is thresholding [12] based on the premise that distinct

objects in the image have different levels of brightness and in pixels of an continuous object

the value of brightness is same or similar. Thresholding is defined by equation (6.1), where

f(x, y) is the original image, g(x, y) is the image transformed by thresholding and T is

the threshold value.

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g(x, y) =

1 if f(x, y) ≥ T

0 if f(x, y) < T(6.1)

Determining of the threshold value

The most challenging part of the thresholding process is to find the optimal threshold

value. This step cannot be fully automatic and requires often a manual check (and

correction respectively). For the initial estimation of the threshold value the Otsu method

was used. This method was introduced by Otsu in 1979 [15] and in the Image Processing

Toolbox (IPT) is implemented as in the function graythresh.

The Otsu method is based on minimization of variance within two parts of the image

separated by the thresholding operation [19]. The optimal threshold value is determined

iteratively by a sequential search all possible threshold values while as the fitness-criterion

homogeneity of two separated groups of pixels expressed by the variance of intensity

values.

6.1.2 Local thresholding

The segmentation using the global thresholding can be unfavorable to use in case of

illumination inhomogeneity [12]. Therefore a pixel-by-pixel thresholding was tested. The

initial threshold value was determined by median value in chosen neighborhood. By the

manual correction size of considered neighborhood can be changed and an offset for the

threshold value can be selected. Determination of the initial threshold value is described

by equation 6.2, where f(x − d2

: x + d2, y − d

2: y + d

2) is the neighborhood of pixel

f(x, y) (dimensions of the neighborhood are d× d) and c is offset added to the estimated

threshold value. The local thresholding is defined by equation 6.3. To obtain the median

values two-dimensional median filter implemented in IPT by function medfilt2 was used.

Comparison of images segmented by local and global thresholding is depicted in Fig. ??.

T (x, y) = median[f(x− d

2: x+

d

2, y − d

2: y +

d

2)] + c (6.2)

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g(x, y) =

1 if f(x, y) ≥ T (x, y)

0 if f(x, y) < T (x, y)(6.3)

(a) original image (b) global thresholding

(c) local thresholding

Figure 6.1: Connected component labeling [19]

6.1.3 Morphological operations

By analysis of materials with connected pores the cross-sections of the pores were also

connected. Therefore it was necessary to separate the cross-sections. As tool for the

separation morphological operations were used, opening followed by closing.

In morphological operations the value of given pixel is based on values of pixels in

defined neighborhood. The neighborhood is defined by structuring element i.e. a scheme

of pixels considered in the morphological operation. In this study as a most suitable shape

of the structuring element a disc was chosen. An example of a disc-shaped structuring

element with radius 2 px is depicted in Fig. 6.2.

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0 0 1 0 0

0 1 1 1 0

1 1 1 1 1

0 1 1 1 0

0 0 1 0 0

Figure 6.2: Disc shaped structuring element with radius 2 px

Dilatation

By dilatation the value of each is set to the maximum value of all pixels in the neigh-

borhood defined by the structuring element. In case of binary images the value of given

pixel is set to one if there is a pixel with value of one in the neighborhood. This operation

is denoted by equation (6.4), where B is the original binary image, S is the structuring

element defining neighborhood for the dilatation and Sb is the structuring element with

centre placed in b ∈ B.

B ⊕ S =⋃b∈B

Sb (6.4)

Erosion

By erosion the value of each pixel is set to the minimum value of the pixels in the neigh-

borhood. A pixel of a binary image is set to one if all in pixels in the neighborhood are

values of one. Binary erosion is denoted by equation (6.5).

B S = {b | b + s ∈ B ∀ s ∈ S} (6.5)

Opening

Opening is in [19] defined by erosion followed by dilatation using the same structuring

element (shown in equation (6.6)). It breaks narrow connections and removes objects

smaller than the structuring element [12]. The opening operation (implemented in IPT

as function imopen) was used to separate cross-section of voids connected by a narrow

neck.

B ◦ S = (B S)⊕ S (6.6)

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Closing

Closing is in [19] defined by dilatation followed by erosion using the same structuring

element (shown in equation (6.7)). It fills holes smaller than the structuring element and

fills narrow gulfs [12]. The closing operation (implemented in IPT as function imclose)

was used to remove islands of background present inside of voids (caused by noise in the

image) and to smooth the objects.

B • S = (B ⊕ S) S (6.7)

6.2 Connected component analysis

To obtain sizes of recognized cross-sections of voids a procedure of connected component

labeling was used. In this procedure a binary image is divided into isolated object and a

unique label is assigned to all pixels of each object. After this step size and shape char-

acteristics of each distinguished object can be extracted. The principle of the connected

component labeling is depicted in Fig. 6.3.

For this purpose algorithm for connected component analysis implemented in IPT for

MatLab was used. This algorithm is implemented in the MatLab function bwconncomp

and the extraction of characteristics of the labeled components was performed using the

function regionprops. As result of this operations the size (number of pixels) of the

cross-section for each entity were obtained.

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1 1 0 1 1 1 0 1

1 1 0 1 0 1 0 1

1 1 1 1 1 0 0 1

0 0 0 0 0 0 0 1

1 1 1 1 0 1 0 1

0 0 0 1 0 1 0 1

1 1 0 1 0 0 0 1

1 1 0 1 0 1 1 1

(a) binary image

1 1 0 1 1 1 0 2

1 1 0 1 0 1 0 2

1 1 1 1 1 0 0 2

0 0 0 0 0 0 0 2

3 3 3 3 0 4 0 2

0 0 0 3 0 4 0 2

5 5 0 3 0 0 0 2

5 5 0 3 0 2 2 2

(b) labeled image

(c) binary image (d) labeled image

Figure 6.3: Connected component labeling [19]

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Chapter 7

Assessment of pore size distribution

7.1 Stereological calculation

As result of the image analysis frequencies of differently sized cross-sections were obtained.

This 2D information was transformed into the pore size distribution in the 3D space using

a stereological calculation method.

7.1.1 Principles

For estimation of the pore size distribution stereological method termed 25F association

method was used. This method was described by Xu and Pitot in 2003 [24] for descrip-

tion of pathologic changes in rat liver. The method is based on geometric properties of

a sphere. The expected frequencies of voids (in [24] particles were considered) are esti-

mated regarding to probability of affiliation of a cross-section to differently sized spheres

(depicted in Fig. 7.1).

The 25F association method was introduced as an improvement of Saltykov method

presented by S. A. Saltykov in 1967 [18]. This method allows to estimate frequencies

of spheres in 12 size classes using equation (7.1). NVk is number of spheres in kth size

class expected in the considered region, NAk is number of cross-sections in kth size class

registered in the 2D image data.

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Figure 7.1: Principles of the stereological calculation [24]

NVk =1

Dk

(1.6461NAk − 0.4561NAk−1 − 0.1162NAk−2 − 0.0415NAk−3

−0.0173NAk−4 − 0.0079NAk−5 − 0.0038NAk−6 − 0.0018NAk−7 (7.1)

−0.0010NAk−8 − 0.0003NAk−9 − 0.0002NAk−10 − 0.0002NAk−11)

The 25F association method is based on the same principle as the Saltykov method

and its main improvements consist in increased number of size classes and a more precise

estimation of association factors indicating probability of affiliation of a cross-section of

given diameter to differently sized spheres. The calculation of the association factors is

described by equation (7.2), where fj are values of association factors, j = 1, 2 . . . 25 are

indexes of the size classes and s is scale factor (ratio between diameters of two neighboring

size-classes), in this method equal to 10−0.1 (as in the Saltykov method). Equation (7.3)

shows normalisation of obtained association factors.

fj =√

1− s2j −√

1− s2(j−1); i = 1, 2, . . . 25 (7.2)

Fj =fjf1

; i = 1, 2, . . . 25 (7.3)

After this step the cross-sections are ordered according to expected affiliation to the

spheres in 25 size-classes. Equations (7.4), (7.5) and (7.3) describe relationship between

39

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obtained numbers of cross-sections in ith size-class (NA(i)) and expected number of cross-

sections in ith size-class produced by a void in jth size-class (NA(i,j)).

NA(i) =25∑j=i

NA(i,j); i = 1, 2, . . . 25 (7.4)

NA(i,i) = NA(i) −25∑

j=i+1

NA(i,j); i = 1, 2, . . . 25 (7.5)

NA(i,j) = NA(j,j) · F(25−i); i = 1, 2, . . . 25 (7.6)

Number of voids in all size-classes are then estimated by equation (7.7). The constant

1.646121 is derived from the original Saltykov equation.

NV(j) =1

Dk

· 1.646121 ·NA(j,j); i = 1, 2, . . . 25 (7.7)

7.1.2 Implementation

The stereological method described in section 7.1.1 was implemented as a set of MatLab

functions. Following list describes main steps of the stereological calculation.

� Order list of pore sizes obtained by connnected component analysis described in

section 6.2

� Arrange the poresizes into 25 size classes

� Calculate association factors

� Using association factors fill 25-by-25 array with numbers of cross-sections produced

by all possible voids (i.e. same-sized or larger)

� Estimate numbers of voids in all size-classes

� Apply scale of the used image to obtain values in required units

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To make the usage of the functions effective a graphical user interface (GUI) was devel-

oped. To create the GUI a MatLab toolbox GUIDE (acronym for Graphical User Interface

Design Environment) was used. As the functions developed in this study are dedicated

to be a part of a complex analysis system [22] the created GUI is very simple, because a

joint of all parts with an unified interface is proposed to be carried out. The front-end of

developed GUI is depicted in Fig. 7.2.

Figure 7.2: GUI layout of the analysis tool

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Chapter 8

Mercury intrusion porosimetry

8.1 Method

8.1.1 Principles

A series of MIP measurements was performed for two types of material (human and

porcine trabecular bone). MIP technique for determining of pore size distribution was

introduced in 1921 by E. W. Washburn [23]. The method is based on the non-wetting

nature of mercury, and the pore radii can be derived form the pressure required for the

intrusion of mercury into the pores [1]. The applied pressure is coupled with the radius

of intruded pores by the equation (8.1) [23], where d is diameter of pores intruded by the

pressure P and γ and ψ are characteristics of mercury, surface tension and contact angle.

A scheme of the MIP measurement is depicted in Fig. 8.1.

P =−4γcosθ

d(8.1)

8.1.2 Advantages and limitations

In dependency on the increments of applied pressure during the intrusion the MIP can

provide very high accurate results. The range of registered pores can be from 10−4 mm

to 1 mm.

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(a) MIP device (b) pores under pressure P (c) pores under pressure P +∆P

Figure 8.1: Principles of MIP [14]

Because of the principles of the MIP measurements only opened pores can be registered.

If higher number of small openings (necks) are present in the structure, the results are

affected by overestimation of the smallest pore size [13].

8.2 Experimental conditions

MIP measurements were performed using PoreMaster 60 GT device (Quantachrome In-

struments, Inc, Boynton Beach, USA). Pressure of mercury up to 413.6 · 106 Pa was used,

mercury surface tension was 0.48 Nm−1 and mercury contact angle was 140°.

8.3 Results of MIP

Using MIP pore size distribution curves were obtained. Frequencies of pores in given sizes

are depicted in Fig. 8.2 (porcine trabecular bone, presented in [6]), in Fig. 8.3 (human

trabecular bone, presented in [7]).

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0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.001 0.01 0.1 1 10 100 1000

vo

lum

e r

atio

of

po

res o

f g

ive

n d

iam

ete

r [-

]

Pore diameter [µm]

Pore size distribution in porcine trabecular bone obtained by MIP

specimen 1specimen 2specimen 3

Figure 8.2: Pore size distribution of porcine trabecular bone obtained by MIP

0

0.05

0.1

0.15

0.2

0.25

0.001 0.01 0.1 1 10 100 1000

fre

qu

en

cy o

f p

ore

s o

f g

ive

n s

ize

[cm

3/g

]

Pore diameter [µm]

Comparison of pore size distribution in human trabecular bone obtained by MIP

specimen 1specimen 2specimen 3

Figure 8.3: Pore size distribution of human trabecular bone obtained by MIP

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Chapter 9

Results and discussion

Specimena of materials specified in chapter 3 were tested using developed analysis tools

to obtain histograms and curves of pore size distribution and volume porosity ratio. In

this chapter the results are listed and discussed both in comparison with results of MIP

and regarding to used image acquisition method.

9.1 Lime mortars

Image data of lime mortars specimens were acquired by CCD camera and flatbed scanner.

Pore size distribution curves obtained by both methods are depicted in Fig. 9.1 and Fig.

9.2.

In comparison of results obtained using image data from flatbed scanner and CCD

camera a good agreement was observed both in the mean pore size and shape of the pore

size distribution curve.

9.2 Frit glass

Image data of frit glass specimens were acquired by laser confocal microscopy and flatbed

scanner. Pore size distribution curves obtained by both methods are depicted in Fig. 9.3

and Fig. 9.4.

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0

50

100

150

200

250

1 10 100 1000 10000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution (lime mortars ; CCD camera)

specimen 1specimen 2specimen 3

Figure 9.1: Pore size distribution of lime mortars (image data obtained by CCD camera)

0

50

100

150

200

250

10 100 1000 10000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution (lime mortars; flatbed scanner)

specimen 1specimen 2specimen 3

Figure 9.2: Pore size distribution of lime mortars (image data obtained by flatbed scanner)

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0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0.1 1 10 100 1000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution (frit glass; flatbed scanner)

10-16µm16-40µm

40-100µm

Figure 9.3: Pore size distribution of frit glass (image data acquired by confocal microscope)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

1 10 100 1000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution in (frit glass, confocal microscope)

10-16µm16-40µm

40-100µm

Figure 9.4: Pore size distribution of frit glass (image data acquired by flatbed scanner)

47

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The pore size distribution curve obtained from image data acquired by confocal micro-

scope shows a good agreement was observed with the pore sizes declared by the producer.

The results obtained using the image data from the flatbed scanner show a wider range

of pore sizes in comparison with the declared values. The discrepancy was probably

caused by two reasons: the shiny nature of the specimen surface and pore sizes near to

the resolution limit of the flatbed scanner.

9.3 Polyurethane foam

Image data of specimens of polyurethane foam were acquired by CCD camera and flatbed

scanner. Pore size distribution curves obtained by both methods are depicted in Fig. 9.5

and Fig. 9.6.

0

100

200

300

400

500

600

700

800

1 10 100 1000 10000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution (artificial pumice; flatbed scanner)

specimen 1specimen 2specimen 3

Figure 9.5: Pore size distribution of polyurethane foam (image data acquired by high

resolution flatbed scanner)

In comparison of results obtained using image data from flatbed scanner and CCD

camera a good agreement was observed both in the mean pore size and shape of the pore

size distribution curve.

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0

100

200

300

400

500

600

1 10 100 1000 10000

Cum

ula

tive v

olu

me [m

l/g]

Pore diameter [µm]

Pore size distribution (artificial pumice, CCD camera)

specimen 1specimen 2specimen 3

Figure 9.6: Pore size distribution of polyurethane foam (image data acquired by CCD

camera)

9.4 Polyvinylchloride foam

Image data of specimens of polyvinylchloride foam were acquired by laser confocal mi-

croscopy and flatbed scanner. Pore size distribution curves obtained by both methods are

depicted in Fig. 9.8 and Fig. 9.7.

In comparison of results obtained using image data from flatbed scanner and confocal

microscope a good agreement was observed in the mean pore size. The different shape

of the pore size distribution curve was probably caused by low colour difference between

voids and the compact phase of the foam.

9.5 Human trabecular bone

Image data of specimens extracted from human proximal femur were acquired by CCD

camera and flatbed scanner. Pore size distribution curves obtained by both methods are

depicted in Fig. 9.9 and Fig. 9.10.

In comparison of results obtained using image data from flatbed scanner and CCD

camera a good agreement was observed in the mean pore size value. The difference in

49

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0

5000

10000

15000

20000

25000

30000

0.1 1 10 100 1000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution in (polyvinylchloride foam; flatbed scanner)

specimen 1specimen 2specimen 3

Figure 9.7: Pore size distribution of polyvinylchloride foam (image data acquired by

flatbed scanner)

0

500

1000

1500

2000

2500

3000

0.1 1 10 100 1000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution (polyvinylchloride foam; confocal microscope)

specimen 1specimen 2specimen 3

Figure 9.8: Pore size distribution of polyvinylchloride foam (image data acquired by laser

confocal microscope)

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shape of the pore size distribution curves was observed. The reason can consist in lower

resolution of the scanner in comparison with SEM or in comlplex shape of the voids

present in the trabecular structure.

By comparison of results obtained by image analysis and MIP a good agreement was

observed in the range from 10µm to 1000µm. Lower pore sizes were detected only by

MIP because of the resolution limit of the image acquisition methods.

0

200

400

600

800

1000

1200

1400

1600

1800

1 10 100 1000 10000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution (human trabecular bone ; CCD camera)

specimen 1specimen 2specimen 3

Figure 9.9: Pore size distribution of human trabecular bone (image data acquired by CCD

camera)

9.6 Porcine trabecular bone

Image data of specimens of trabecular structure of porcine proximal femur were acquired

by laser confocal microscopy and flatbed scanner. Pore size distribution curves obtained

by both methods are depicted in Fig. 9.11 and Fig. 9.12.

In comparison of results obtained using image data from flatbed scanner and CCD

camera a good agreement was observed both in the mean pore size and shape of the pore

size distribution curve.

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0

200

400

600

800

1000

1200

1400

1600

1800

2000

1 10 100 1000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution (human trabecular bone; flatbed scanner)

specimen 1specimen 2specimen 3

Figure 9.10: Pore size distribution of human trabecular bone (image data acquired by

flatbed scanner)

0

500

1000

1500

2000

2500

1 10 100 1000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution (porcine trabecular bone; SEM)

specimen 1specimen 2specimen 3

Figure 9.11: Pore size distribution of porcine trabecular bone (image data acquired by

SEM)

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0

500

1000

1500

2000

2500

1 10 100 1000

Fre

quency o

f pore

s in 2

5 s

ize c

lasses [1/c

m3]

Pore diameter [µm]

Pore size distribution (porcine trabecular bone; flatbed scanner)

specimen 1specimen 2specimen 3

Figure 9.12: Pore size distribution of porcine trabecular bone (image data acquired by

flatbed scanner)

By comparison of results obtained by image analysis and MIP a good agreement was

observed in the range from 10µm to 1000µm. Lower pore sizes were not registered using

the image analysis because of the limit resolution of the image acquisition methods.

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Chapter 10

Conclusions

This study was focused on description of inner structure of porous materials. A software

tool for assessment of pore size distribution based on image analysis was developed and

tested. The tool was used for pore size distribution measurement on specimens of different

materials to test its reliability and robustness. To compare the obtained results of image

analysis with results of a well established experimental technique a series of mercury

intrusion porosimetry (MIP) measurements was carried out for two types of materials.

10.1 Summary of results

Obtained results show a satisfactory agreement between image analysis and MIP mea-

surements. Observed discrepancies of the results are caused by different nature of both

types of the measurement. Image analysis compared with MIP omits pores below a size

limit determined by resolution of the image acquisition device, segmentation methods and

range of pore sizes considered by used stereological method. On the other hand, using

MIP only opened pores are registered, but by image analysis both opened and closed ones

are detected.

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10.2 Suitability of used methods

In all phases of the process of pore size distribution assessment different approaches were

tested and its suitability for different types of materials was discussed.

10.2.1 Image analysis

The image analysis provides the possibility of pore size distribution assessment also for

materials with a high frequency of large voids (over 1000µm) or with closed voids or

materials with unfavorable mechanical properties. The range of the pore sizes registered

using the image analysis is limited by the resolution and the dimensions of the captured

images and by the used stereological calculation method. The method used in this work

allows to register pores in 25 size classes with the ratio between the smallest and largest

size-class equal to 250 (determined by the scale factor between size classes).

Used segmentation using local thresholding avoids complications caused by inhomoge-

neous illumination. Therefore in many cases the analysis is possible despite imperfections

in specimen preparation or image acquisition.

10.2.2 Mercury intrusion porosimetry

The main advantages of MIP are in a wide range of registered pore sizes and a high

resolution. Suitability of MIP is limited due to high mercury pressure applied by the

measurement and due to the requirements for the specimens – limited sample volume and

low humidity. The limited dimensions of the specimens make the measurements impossible

for materials with high frequency of large voids. For some biologic materials (e.g. fungi)

the intrusion measurements are impossible because of the requirement on the low specimen

humidity or due to the high pressure applied during the intrusion measurement (both can

cause undesirable changes of the inner structure).

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10.3 Suggestions for further work

Some issues related to the studied objectives remain to the further work. The issues consist

both in the improvements of presented analysis tool and in utilising of obtained results

by description of the inner structure of complex materials. Both groups of improvements

are considered as proposal objectives of author’s doctoral studies.

10.3.1 Stereologic method

It can be helpful to improve the stereologic method by increasing of number of the size

classes. This improvement can results in two changes of the developed tool: it can enable

to estimate pore sizes in a wider range or it can make the obtained pore size distribution

curves smoother and more accurate.

10.3.2 Extraction of anisotropic morphological parameters

A significant limitation of the presented image analysis method consists in the ideali-

sation of the voids by spheres. The used algorithm for connected component analysis

provides also information about shape of pore cross-sections and therefore the analysis

can be extended by estimation of predominant orientation of pores to allow estimation of

anisotropic properties of the porous structure.

10.3.3 Estimation of mechanical properties based on pore size

distribution

To exploit obtained results for estimation of mechanical properties of complex materials

a finite element model based on the pore size distribution can be developed to predict

response of the porous materials on physical loading.

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