New computational solution to quantify synthetic material porosity from

optical microscopic images

Victor Hugo C. de Albuquerque1, Pedro P. Rebouças Filho2, Tarique S. Cavalcante2,

João Manuel R. S. Tavares3

1Universidade de Fortaleza (UNIFOR), Centro de Ciências Tecnológicas (CCT), Núcleo de

Pesquisas Tecnológicas (NPT), Av. Washington Soares, 1321, Sala NPT/CCT, CEP

60.811-905, Edson Queiroz, Fortaleza, Ceará, Brasil

Universidade Federal da Paraíba (UFPB), Departamento de Engenharia Mecânica (DEM),

Laboratório de Solidificação Rápida (LSR), Centro de Tecnologia - Campus I, Cidade

Universitária, 58059-900 - Joao Pessoa, PB - Brasil

Email: victor.albuquerque@fe.up.pt

2Universidade Federal do Ceará (UFC), Centro de Tecnologia (CT), Departamento de

Engenharia de Teleinformática (DETI)

Campus do PICI S/N, Bloco 723, CP. 60455-970, Fortaleza, Ceará, Brazil

Email: pedrosa_rf@hotmail.com, tariquesc@hotmail.com

3Instituto de Engenharia Mecânica e Gestão Industrial (INEGI) / Faculdade de Engenharia

da Universidade do Porto (FEUP), Departamento de Engenharia Mecânica (DEMec)

Rua Dr. Roberto Frias, S/N, 4200-465, Porto, Portugal

Email: tavares@fe.up.pt

Corresponding author:

Prof. João Manuel R. S. Tavares

Faculdade de Engenharia da Universidade do Porto (FEUP)

Departamento de Engenharia Mecânica (DEMec)

Rua Dr. Roberto Frias, s/n

4200-465 PORTO - PORTUGAL

Phone: +315 22 5081487, Fax: +315 22 5081445

New computational solution to quantify synthetic material porosity from

optical microscopic images

Abstract

This paper presents a new computational solution to quantify the porosity of synthetic

materials from optical microscopic images. The solution is based on an artificial neuronal

network of the multilayer perceptron type and a backpropagation algorithm is used for

training. To evaluate this new solution, 40 sample images of a synthetic material were

analyzed and the quality of the results was confirmed by human visual analysis.

Additionally, these results were compared with ones obtained with a commonly used

commercial system confirming their superior quality and the shorter time needed. The

effect of images with noise was also studied and the new solution showed itself to be more

reliable. The training phase of the new solution was analyzed confirming that it can be

performed in a very easy and straightforward manner. Thus, the new solution demonstrated

that it is a valid and adequate option for researchers, engineers, specialists and other

professionals to quantify the porosity of materials from microscopic images in an

automatic, fast, efficient and reliable manner.

Key words: Artificial neuronal network; Multilayer perceptron; Computational vision;

Image processing and analysis; Image segmentation and quantification; Materials Science.

1. Introduction

One of the major challenges to develop new systems is to integrate higher intelligent

features into those systems, so they can perform tasks similar to humans or even with

superior quality and efficiency. Recently there have been important advances in the

artificial intelligence field, in the developing of new computational algorithms and in

technological solutions to help to perform such tasks. However, these human tasks are

extremely complex. Such actions as seeing, hearing, walking and talking are commonly and

naturally carried out by man but are very complex for artificial systems. Of the human

senses associated to these complex actions and capabilities, sight has been given special

attention by the scientific community, essentially, because of the considerable number of

existing applications.

Initially from the artificial intelligence field, computational vision has become a

distinct research area and its main aim is to develop computational and hardware solutions

for digital image processing and analysis that can be used for visual analysis and

interpretation, assisting man in his tasks in a rapid, reliable and precise manner (Acha &

Serrano, 2000). In pursuit of these goals, this new and very active branch of computer

science uses techniques of artificial intelligence, digital signal processing and analysis and

pattern recognition among others (van der Heidjen, 1995).

Numerous works have been developed based on computational vision techniques.

For example: numerical simulation of segmentation cracking in thermal barrier coatings by

means of cohesive zone elements (Białas et al., 2005), automatic identification of

automotive aluminum sheet alloys from images based on global thresholding (Lievers &

Pilkey, 2004), evaluation of pitting corrosion thought morphology (Codaro et al., 2002,

2003), evaluation of delamination damages in composite plates by image segmentation and

analysis (Albuquerque et al., 2009a; Durão et al., 2009), Brinell and Vickers hardness

measurements from indentation images (Rebouças Filho et al., 2010), among others.

For the analysis of material porosity from images some computational vision

techniques have been used, for example: Malcolm et al. (Malcolm et al., 2007) used an

edge linking approach to refine the image segmentation step and the porosity analysis

results are obtained by 2D characterization; Du and Sun (Du & Sun, 2006), developed an

automatic method for pore characterization of pork ham from images, considering three

steps: ham extraction, enhancement of the input image and pore segmentation, and a

watershed algorithm in the segmentation of the input images. Taud et al. (Taud et al. 2005),

used a method, called the grey level method, that considered the input computed

tomography (CT) image as a surface and then the volumes required for the porosity

estimation were obtained by integrating this surface with simple operations applied to the

input image histogram.

Nowadays, artificial neuronal networks are commonly used in areas like artificial

intelligence, pattern recognition and materials science. Predominantly, they have been used

in applications that involve the recognition of shapes from images, with high levels of

parallelism, high speeds of classification and of great importance they have the ability to

learn from example data (Plaut et al., 1986).

Various applications for artificial neuronal networks can be found in material

sciences, for example: predict the porosity percent in Al-Si casting alloys (Shafyei et al.,

2006), evaluate the shear mechanical properties in epoxy composites reinforced with

carbon and E-glass fibers (Bezerra et al., 2007), evaluate the epitaxial growth of Ti6Al4V

weldment (Karimzadeh et al., 2006), model the mechanical alloying process for

synthesizing of metal matrix nanocomposite powders (Dashtbayazi et al., 2007), estimate

the microstructures and the mechanical properties of steels (Kusiak & Kusiak, 2002), model

the deformation mechanism of titanium alloys in hot forming (Xiao- li & Miao-quan,

2005), predict the weld parameters in pipeline welding (Kim et al., 2003) and predict the

flow stress and the evolution of the microstructures of a hydrogenised titanium alloy (Wang

et al., 2007).

Many computational vision systems have also been developed based on artificial

neuronal networks, see, for example, (Albuquerque et al. 2008, 2009b), which presented

and evaluated computational solutions for the segmentation and quantification of the cast

iron microstructures from metallographic images based on multilayer perceptron and self-

organizing map neuronal networks.

Synthetic materials are used in various engineering applications such as in gas

sensors (Galeazzo et al., 2008), bone tissue engineering (Mathieu et al., 2006; Pereira et al.,

2005), porous mullite obtained using silica from rice husk and aluminum acetate (Menezes

et al., 2008) and in medicine (Langer & Tirrell, 2004). The pores in the structures of

synthetic materials are extremely important as they can represent unique and enhanced

properties, which make them possible candidates to replace more expensive materials in

various applications (Corrigan et al., 1997; Lee et al., 2008; Tang et al., 2008). However,

the enhanced use of synthetic materials demands the trustworthy and efficient

quantification of their porosity, in particularly from microscopic images.

In this paper, a new computational solution to quantify the porosity of synthetic

materials from microscopic images based on an artificial neuronal network is presented. As

far as the authors know, this is the first custom developed computational approach to

accomplish the enumerated task that is based on a neuronal network that presents low

computational complexity, high efficiency, considerably accuracy and stableness.

Moreover, the novel solution is less dependent on the operator’s skill and subjectivity than

existing methodologies (Du & Sun, 2006; Malcolm et al., 2007; Taud et al., 2005) that, for

example, consider image segmentation based on global threshold binarization, which are

frequently defined by manual adjustment in function of the image to be analyzed, or on

local measurements, that are very propone to error due to noise in the image to be analyzed,

or on very complex algorithms, that require advanced computational resources and long

processing time.

To evaluate the proposed solution, 40 sample images of a synthetic material were

used. The quality of the results from the new computational solution was confirmed by

human visual inspection and quantification. Additionally, visual and analytical comparisons

were made with these results against ones obtained by a commercial software commonly

used for the same purpose. The time needed to perform the quantification was also

compared and its stability with noisy images was also studied. The effect of the training

phase of the neuronal network integrated in the new solution was analyzed as well.

This paper is organized in the following way. The next section gives more detail

about synthetic materials, porosity and artificial neuronal networks. The third section

describes the new solution to quantify the porosity of synthetic materials from microscopic

images. The fourth section shows the, experimental results, their comparison and holds a

discussion on them. Finally, in the fifth and last section of this paper, the main conclusions

are presented.

2. Synthetic Materials, Porosity and Artificial neuronal networks

As already explained, the main aim of this work is to develop a new customized

computational solution to quantify the porosity of synthetic materials from microscopic

images automatically. For this solution, a backpropagation artificial neuronal network was

used to segment the original images.

In the following subsections more detail is given of the materials used and their

porosity and also neuronal networks are introduced.

2.1 Synthetic Materials and Porosity

In recent years there has been a notable increase in the number of applications

involving synthetic materials and mainly due to the pores in their structure, presenting

unique properties that are of extreme importance in many applications (Lee et al., 2008).

Pores in materials allow these spaces to be filled with other materials, which in turn

can help improve the weaker characteristics of the original material (Tang et al., 2008).

However, to benefit from this feature, appropriate porosity of the base material is

necessary; high porosity could mean significant alterations in properties of the base

material and low porosity is often undesirable in many applications (Corrigan et al, 1997).

Therefore, accurate and reliable quantification of the porosity of the material is demanded.

Nowadays, as mentioned, synthetic materials are used in various fields, such as

instrumentation (Galeazzo et al., 2008), medicine (Mathieu et al., 2006) and engineering

(Pereira et al., 2005; Menezes et al., 2008; Langer & Tirrell, 2004). In engineering, for

example, some compressors use pistons made from a porous materials. The pores contain

oil, which appears on the surface of the pistons when the pressure increases and can thus

reduce the friction during operation (Langer & Tirrell, 2004). In instrumentation, gas

sensors have been developed by integrating a closed electric circuit made of a porous

synthetic material. When there is gas in the pores of the material, the circuit operates

normally; otherwise, the circuit closes and the alarm sensor is activated. So, in this case, the

level of porosity is used to control the sensitivity of the sensor (Galeazzo et al., 2008). In

medical applications, such as in synthetic bones, the pores of the materials allow the live

cells to integrate with the artificial parts therefore reducing the probability of rejection

(Mathieu et al., 2006).

2.2 Artificial Neuronal Networks

Artificial neuronal networks have been successfully used to solve a variety of

problems in engineering, such as function approximations and classification of shapes, even

when nonlinear relations between the dependent and independent variables are involved.

The principal goal of solutions based on neuronal networks is to develop a

computational model composed of several neurons with a large number of connections

between them, each neuron being a very simple processing unit. The information among

the neurons of the network is transmitted via the synaptic weights.

The flexibility and the capacity to learn and to generalize the information involved

are very attractive and important aspects of the artificial neuronal networks that justify their

widespread use. In fact, their generalization ability associated to their capacity to learn from

training sets and their facility to supply correct results from input data not presented in the

training sets, suggests that their competence goes further than just a direct establishment of

input/output relationships, indicating that they are able to extract information not presented

in an explicit form in the training data (Chow, 2007).

Nowadays, there are different topologies and algorithms that can be adopted in the

design and development of artificial neuronal networks. In this work, a neuronal network

multilayer perceptron, which is a feed forward neuronal network type (Albuquerque et al.,

2008, 2009a, 2009b) was used. A multilayer perceptron network is composed of several

layers that are built with neurons. The input data is presented into the first layer of the

network and then distributed through the internal layers. The last layer of the network is the

output layer that is responsible to turnout the solution found for that input data. The input

and output layers can be separated by one or more intermediate layers, often known as a

hidden layer. In many applications of neuronal networks, just one hidden layer is

considered.

The neurons of a layer are connected to the immediate neurons of the neighboring

layers and so all layers of the network are interconnected. Neurons of the same layer are not

interconnected.

As mentioned, the back propagation algorithm, which is the algorithm most adopted in the

training of this kind of neuronal networks, was used to train the multilayer perceptron

network in this work (Albuquerque et al., 2008, 2009b; Haykin, 2009). Then, input training

data with the correspond output are fed into the network. Subsequently, the input signal is

propagated through the hidden layers until it reaches the output layer with the

corresponding output value. In this process, the activation of neuron i in a hidden layer is

calculated as:

0

, with 1,...,p

i ij jj

u t w t x t i q

, (1)

where ijw are the synaptic weights, jx are the input values, p is the number of inputs and

q is the number of neurons in the hidden layer. On the other hand, the output of each

neuron of a hidden layer is calculated as:

0

p

i i i i ij jj

z t u t w t x t

, (2)

where i is some predefined function, commonly referred to as the activation function,

such the logistic function, also called sigmoid function, g t , (Elliott, 1993):

1

1 tg t

e

. (3)

The operations involved in equations (1) and (2) are repeated for the neurons of the

output layer. Then, the activation of neuron k in the output layer is calculated as:

0

, with 1,...,q

k ki ii

u t m t z t k M

, (4)

where kim are the synaptic weights, q is the number of inputs, iz are the inputs, that is, the

outputs of the previous hidden layer, and M is the number of neurons in the output layer.

Additionally, the output of each neuron of the output layer, that is, the classification, is

given as:

0

q

k k k k ki ii

y t u t m t z t

, (5)

where k is the activation function.

After the determination of the neurons activations and outputs by the previous steps,

the next phase consists in the calculation of the local gradients at the neurons of the output

layer, using the equation:

' , with 1,...,k k kt e t u t k M , (6)

where ke t corresponds to the error obtained from the desired output, kd t , and the

associated generated output, ko t , given as:

k k ke t d t o t . (7)

Considering the logistic function as the activation function for the neurons in the

hidden and output layers, then the term 'ku t present in equation (6), is given as:

' 1k k

k k kk

u tu t y t y t

u t

. (8)

Afterwards, local gradients at the neurons of the hidden layer are calculated as:

'

0

, with 1,...,q

i i i ki kk

t u t m t i q

, (9)

where the derivative 'i iu t is given as:

' 1 .i i

i i i ii

u tu t y t y t

u t

(10)

For the hidden layers the weights, ijw , are updated considering:

1ij ij ij ij i jw t w t w t w t t x t , (11)

where 0 1 corresponds to the learning rate. On the other hand, for the output

layer, the updating of the synaptic weights, kim , is given by:

1ki ki ki ki k im t m t m t m t t z t . (12)

3. Developed Solution

The solution developed to quantify the porosity of synthetic materials from

microscopic images was set up for Microsoft Windows computational platforms using the

C++ programming language.

To carry out the image segmentation task a neuronal network multilayer perceptron

is used. In this step, each pixel of an input image is classified as being part of a pore region

or not. Thus, after the training of the network, which only needs to be done once for each

kind of input image, as is explained later, the network is ready to segment the pores

presented in an input image: all image pixels are automatically fed into the neuronal

network that classifies each one as being part of a pore or not.

For the topology of the artificial neuronal network proposed, 3 inputs, 7 neurons in

the hidden layer and 3 neurons in the output layer were used, Figure 1. The number of

neurons used in the hidden layer was established following the heuristic rule proposed by

Kolmogorov (Bodyanskiy et al., 2005). As already described, the logistic function was used

as the activation function, which has three possible output values: 1 (one), 0 (zero) and -1

(one).

As the neuronal network used here has 3 inputs, it can be employed for color images

and also for gray scale images. In the former case, the red, green and blue components of

each image pixel are presented to the corresponding inputs of the network, and in the later

case the value of each image pixel is presented to an input of the network, the other two

being unused. Although in this application there are only 2 possible classes of classification

(porous and matrix), the network can classify up to 27 classes and, consequently, it can be

used to identify other material characteristics. Furthermore, each pixel of an input image is

individually processed in function of the network training performed and not dependent on

its neighbor.

The main reason to select the topology described here was its excellent performance

in the segmentation of microstructures from metallographic images (Albuquerque et al.,

2008, 2009a, 2009b), that involved similar segmentation problems to this work. However,

different neural network topologies could be used for the segmentation task in this work,

but probably with higher computational costs and complexity.

As mentioned and explained previously, for the training of the neuronal network

here the standard backpropagation algorithm (Haykin, 2009) and some pixels from an

adequate set of training images of each possible classification class of the synthetic material

to be analyzed, were used. This kind of training is usually known as supervised training and

only needs to be performed once for each kind of material. After the training phase, the

neuronal network is ready to carry out the segmentation of the input images and by

counting the pixels associated to each classification class the porosity of the material is

found.

The developed computational solution was experimentally evaluated using 40

microscopic images of a synthetic material and the results obtained are presented and

discussed in the next section.

4. Experimental Results and Discussion

For the experimental analysis 60 optical microscopy images of the synthetic

material were acquired, Figure 2a. Then, twenty of these images were randomly used to

train the neuronal network. In this training, an average of 5 sample pixels from the pore

regions and 7 sample pixels from non pore region were used per training image, Figure 2b,

and the following training parameters were adopted: learn rate of 0.1, moment rate of 0.001

and 2500 epochs. The stop criterion was the accomplishment of a predefined number of

epochs or an absolute error inferior to 0.001.

Afterwards, the remaining 40 images were analyzed by the new solution, Figure 2c,

and also by a commercial system, commonly used in this field, that had been adopted here

for comparison and validation purposes, Figure 2d. The results obtained by the two

computational systems were visually analyzed by a specialist in this metallographic area

who confirmed the superior quality of the results obtained by the proposed solution. Table

1 shows the percentage of porosity, that is, the percentage of porous pixels of the total

number of pixels, obtained using the developed solution and the adopted commercial

system from the 40 microscopic images of the synthetic material under study and the

differences between them as well. Analyzing the values presented in this table, a high level

of congruence can be seen, as the maximum difference is 1.85, the minimum difference is

0.15 and the average difference is 1.03, which leads to a low standard deviation. These

results confirm that the developed solution is efficient and accurate and even more precise

than the commercial system as it presents a lower standard deviation.

Additionally, the total time necessary to quantify the 40 images for the porosity of

the synthetic material were recorded: the developed solution required 3 minutes and 16

seconds (including the training phase), while the commercial software required 11 minutes

and 22 seconds, Figure 3. Thus, the developed solution gained 8 minutes and 6 seconds.

Based on the first experimental evaluation described above, the developed solution

obtains results superior to the commercial software, is easier and faster to use as the

calibration or the training of the neuronal network only needs to be carried out once for all

images, while the calibration of the commercial system requires manual adjustment for

each image, making its use slower and more dependent on the operator’s skill.

To analyze the influence of the training of the neuronal network used in the

developed solution, the number of pixels of each region to be segmented and the necessary

average time for the segmentation of each image under test were analyzed. In the first

analysis only 5 training pixels of each possible region (pore and non pore) were considered

and due to the excellent metallographic preparation of the samples with the correct

luminosity and contrast during the acquisition of the images and to the efficiency of the

neuronal network, good segmentation results were acquired with an average time of 6

seconds per analyzed image. In the second evaluation, 15 pixels of each region were used

and the same segmentation results obtained with a reduction in the average time to 5

seconds. Finally, when 25 pixels of each region to be segmented were used, the proposed

solution obtained the same segmentation results also in an average time of 5 seconds,

Figure 4. Thus, 5 sample pixels from each region of interest and per each training image are

enough to efficiently segment the pores of the synthetic material used in this work. In fact,

when more than 25 sample pixels from each region of interest and per each training image

were used, there was an increase in the time spent in the selection of the sample pixels

which was not reflected in any improvement in the segmentations.

In order to evaluate the reliability of the developed computational solution for input

noise Gaussian noise (Gonzalez & Woods, 2008) was added to 20 images randomly

selected from the 60 original images, Figure 2a, at levels of 5%, 10% and 15%, Figures 5a,

5b and 5c, respectively. Afterwards, 12 images were randomly selected to train the

neuronal network and the remaining 8 were used for its evaluation with the presence of

noise. The results from the images with 5% and 10% Gaussian noise show that the

developed solution did not have any difficulty to segment the pores, Figures 5d and 5e. For

these results, in the case of 5% Gaussian noise 28 sample pixels from the pore regions and

43 sample pixels from the non pore region per each training image were necessary; while in

the case of 10% Gaussian noise 36 and 59 pixels, respectively were used. In the case of the

images with 15% Gaussian noise, Figure 5f, the developed solution did not presented as

good segmentation results as in the previous cases, even when 57 sample pixels from the

pore regions and 72 sample pixels from the non pore region were used in the training of the

neuronal network. However, it must be pointed out that the segmentations that were

obtained by the commercial system from the images with Gaussian noise of 5% and 10%,

Figures 5g and 5h, did not presented the same quality of the segmentations as obtained by

the proposed solution. Moreover, when the commercial system was applied to the images

with 15% Gaussian noise the results were awful.

Figure 6 graphically represents the relation between Gaussian noise and the number

of pixels used in the training of the neuronal network and Figure 7 shows the total time

required for the solution proposed, including the training time needed and for the

commercial system to analyze the 3 sets of noise images.

As an example, Figure 8 presents the resultant images of the subtractions performed

between the segmentations obtained by the solution proposed and an input image with 10%

Gaussian noise (Figure 5b), Figure 8a, and between the commercial system and the same

noise image, Figure 8b. The resultant image of Figure 8a presents a better overlapping of

the segmented pore regions than the image of Figure 8b, showing that the segmentation

obtained by the solution proposed is more accurate. The same analysis was carried out

using the images with Gaussian noise 5% and 15%, resulting in the same conclusions.

It is important to notice that the segmentations carried out by the commercial system

from the noise images took a lot of time, as the metallographic analyst who was doing the

experimental study had difficulties to manually adjust the system due to the presence of the

added noises. Even so, the segmentations obtained were of weak quality.

Additionally, it is important to be aware that specialists in this area of materials

science frequently use the adopted commercial system to perform the segmentation of such

porosity images. However, other systems can be used, but always adopting the same image

segmentation philosophy, which is based on the color histogram built from the image under

analysis, thus being less efficient and not as reliable as the solution proposed here.

Finally, to verify the accuracy of the proposed solution, 8 images were randomly

selected from the experimental image set, and the represented porosity was quantified by

the proposed solution and by visual inspection, that is by visual classification of the pixels

of each image whether part of the porous regions or not, performed by a specialist in

microscopy analysis, Table 2. From the data presented in this table, one can conclude that

the results obtained are very similar, proving the accuracy of the proposed solution. As an

illustrative example, Figure 9 shows one of these experimental images, the image resultant

of the visual quantification performed by the specialist and the image resultant from the

proposed solution. From this figure, one can verify that the quantification by the new

computational solution is superior as it includes many micro-pores that were not detected

by the specialist.

5. Conclusions

This paper described a new computational solution based on an artificial neuronal

network that was applied to quantify the porosity of a synthetic material from microscopic

images.

For evaluation purposes, the results obtained by the new solution with those from a

commercial system, which is commonly used in materials science to quantify the porosity

of materials from images were visually and analytically compared. Based on this

comparison, one can clearly conclude that the new solution was easier and faster to use and

that its results were always of superior quality.

Summarizing: the experiments carried out confirmed advantages of the proposed

solution such as its reliability even with noise, which is often present in the input images,

mainly due to optic distortions and incorrect illumination during the image acquisition

process; its simplicity and ease to use and its high efficiency and accuracy. Thus, the

proposed solution is suitable for researchers, engineers, specialists and other materials

science professionals as an option to quantify the porosity of synthetic materials from

microscopic images in a very fast and accurate manner.

Acknowledgments

Authors would like to acknowledge the Federal Center of Technological Education

of Ceará – Brazil, in particularly the Mechanical Testing Laboratory and the Computer

System Engineering Laboratory of the Department of Teleinformatics Engineering, for all

the support provided in the successful accomplishment of this work.

In addition, the authors would like to acknowledge CNPq - The National Council

for Scientific and Technological Development – Brazil for the financial support given.

Finally, the authors would like to express their deep gratitude to David Graham

Straker for his valuable help in reviewing the English version of this paper.

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FIGURE CAPTIONS

Figure 1: Topology of the adopted artificial neuronal network.

Figure 2: Example of image segmentation in order to quantify the material porosity: a)

original image from optical microscopy, b) selection of the pixels to be used in the training

of the neuronal network used in the developed solution, c) resultant segmented image by

the developed solution and d) resultant segmented image by the commercial system.

Figure 3: Total time required to segment the images in analysis by the commercial system

and the proposed solution.

Figure 4: Analysis of the influence of the number of pixels used in the training of the

neuronal network in the time required for the segmentation.

Figure 5: Example images with 5%, a), 10%, b) and 15%, c) Gaussian noise added,

segmented images obtained for the same input images by the proposed solution, d), e) and

f) and by the commercial system, g), h) and i), respectively.

Figure 6: Relation between the number of pixels used in the training of the neuronal

network by segmentation class and per training image and the level of existing Gaussian

noise in the image to be segmented.

Figure 7: Total time necessary to segment the noise image samples.

Figure 8: Image resultant from the subtraction done between the segmented image obtained

by the proposed solution and an input example image with 10% Gaussian noise a) and

image resultant from the subtraction done between the segmented image obtained by the

commercial system and the same input noise image b).

Figure 9: An original optical microscopy image of the synthetic material a), the

segmentation manually accomplished by a specialist b), and the segmentation performed by

the proposed computational solution c).

TABLE CAPTIONS

Table 1: Results of the developed solution and the commercial system for porosity

quantification of a synthetic material from optical microscopic images.

Table 2: Comparison of the porosity quantification of a synthetic material from eight

optical microscopic images using the developed solution and visual inspection by a

specialist.

FIGURES

Figure 1

Figure 2a

Figure 2b

Figure 2c

Figure 2d

Figure 3

Figure 4

Figure 5a

Figure 5b

Figure 5c

Figure 5d

Figure 5e

Figure 5f

Figure 5g

Figure 5h

Figure 5i

Figure 6

Figure 7

Figure 8a

Figure 8b

Figure 9a

Figure 9b

Figure 9c

TABLES

Table 1

Image # Proposed Solution (%) Commercial System (%) Difference

1 16.00 16.56 0.56

2 13.17 13.88 0.71

3 12.93 13.52 0.59

4 16.11 15.43 0.68

5 18.61 19.13 0.52

6 17.24 18.14 0.90

7 16.89 17.73 0.84

8 14.03 13.54 0.49

9 16.53 17.14 0.61

10 20.50 20.65 0.15

11 27.23 28.13 0.90

12 16.56 17.15 0.59

13 26.83 27.75 0.92

14 29.26 30.15 0.89

15 27.47 28.46 0.99

16 26.88 27.61 0.73

17 26.69 27.30 0.61

18 25.40 26.12 0.72

19 25.73 26.63 0.90

20 26.80 25.95 0.85

21 25.69 25.76 0.07

22 26.42 26.10 0.32

23 25.49 25.15 0.34

24 28.33 28.64 0.31

25 25.92 26.75 0.83

26 27.50 26.63 0.87

27 27.67 26.14 1.53

28 28.36 27.64 0.72

29 28.41 29.73 1.32

30 27.30 29.15 1.85

31 27.16 28.23 1.07

32 28.11 29.41 1.30

33 27.40 28.95 1.55

34 27.77 28.19 0.42

35 28.14 27.54 0.60

36 28.44 27.93 0.51

37 28.25 29.16 0.91

38 28.93 30.22 1.29

39 31.09 32.20 1.11

40 28.89 29.15 0.26

Average 24.15 24.84 1.03 Standard Deviation 1.16 1.37 0.39

Table 2

Image # Proposed Solution (%) Specialist (%) Difference

1 16.89 15.65 1.24

2 16.53 15.23 1.30

3 20.50 20.42 0.08

4 25.69 24.68 1.01

5 26.42 25.50 0.92

7 26.69 24.89 1.80

8 27.23 26.74 0.49

Average 14.03 14.02 0.01

Standard Deviation 21.75 20.89 0.86