czech technical university in prague faculty of...
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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. Tomas Doktor
Supervisor: Ing. Daniel Kytyr
Prague, 2011
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.
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
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
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
6
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
7
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
8
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
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
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
11
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
List of Tables
3.1 Pore sizes of frit glass discs declared by producer . . . . . . . . . . . . . . 22
4.1 Polishing procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
13
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
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
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
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]
17
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
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].
19
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].
20
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
21
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.
22
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.
23
(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
24
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.
25
(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
26
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.
27
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
28
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]
29
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]
30
(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.
31
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.
32
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)
33
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.
34
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)
35
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.
36
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]
37
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.
38
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
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
40
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
41
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.
42
(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]).
43
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
44
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.
45
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)
46
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
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.
48
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
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)
50
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.
51
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)
52
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.
53
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.
54
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).
55
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.
56
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