Microsoft word - sint2009_en.doc



1. General Objectives
2. Objectives execution phase
3. Phase Summary
4. Scientific description
4.1. Gastric cancer. Morphological and genetic features.
Experimental studies.
4.2. Considerations on modeling and control of cancer cell populations
4.3. Using independent component analysis to remove noise from images
1. General Objectives

Develop conceptual models and theories.
2. Objectives execution phase

Developing conceptual models. Studies on their potential use in predicting the development of cancerous
tumors. Using independent component analysis to eliminate the noise in images
3. Phase Summary

One of the issues facing the medical world, for years is that cancer is considered the second major cause of
mortality throughout the world. In Romania, the last decade, there has been a rapid increase in the number of
malignant tumors, which are the second leading cause of death after cardiovascular diseases immediately.
Powerful impact of cancer on the Romanian society is reflected not only in number of deaths (about 38,000 per
year, which represents 13-14% of deaths) but also the number of new cases reported (about 45,000 per year)
and sick of life (about 200,000). Based on these data, cancer became a national healthcare priority.
Mathematical modeling and simulation methods are very effective, commonly used in all areas. In recent years
there have been concrete steps toward involvement in systems theory and the study of living organisms.
Complexity of living systems, even if lower organisms, is far superior man-made technical structures. Isolation of
a biological subsystem, for his study, is, inevitably deteriorating price of their functions and behavior of the
system as a whole. For this reason, experimental data are different from those corresponding to normal
developments. Finally, the study recommended, if possible, the system as a whole.
Mathematical modeling synthesis achieved experimentally obtained data in a single system, internal structure
and highlight the causal links between components and measures the weight that comes with each subsystem
to achieve system functions. Simulation provides validation of competing theories, understanding the
pathophysiological changes and suggests relevant experiments.
It is a very powerful tool for analyzing problems and allows development and testing biological hypotheses that can lead to a better understanding of biological processes. Basic principles of a realistic model and available are: - Understanding and full appreciation of the biological problem - Realistic mathematical representation of biological phenomena - Useful solutions, preferably quantitative Biological interpretation of mathematical results in terms of understanding and predictions. In terms of systemic processes carried out at the cellular level (including cancerous tumors) are highly nonlinear. Although, in terms of shaping their study and have made remarkable progress, however, development and application of modern methods is lower in comparison with other areas. Moreover, a new philosophy in molecular biology and biotechnology, biology called the system builds a bridge between biologists and even clinicians, on the one hand and mathematicians and engineers, on the other hand. Thus, tumors avascular modeling is seen as a first step towards building models for fully vascularized tumors. Moreover there are a few questions about avascular tumors, including the recent controversy on the assumption that individuals all have tumors in their bodies avascular dormant. Gastric cancer is a major disease incidence and mortality ranking second in neoplastic disease mortality. Research in this area have not so far conclusive results on the dynamics of tumor cells, deciphering the mechanisms of tumor aggressiveness and invasive nor led to creating an effective treatment. Unlike other cancers, has a great variability of neoplasm gastric morphologic, histologic and genetic mutations and lack of stability of gene expression. Gastric cancer occurs in developing numerous internal and external factors, partially known. Growths of tumor cells in vitro do not provide the information necessary to obtain accurate predictive models, as different tumors developed in vivo. Extracellular matrix, cells in the environment in which the tumor develops, the tissues around it influences the kinetics of tumor growth, cancer cell survival, polarity and their orientation, level of invasive and sensitivity to chemotherapy drugs. Build models based on experimental studies of the type: - Culture of human tumor cells in vitro using cell lines printed, which were obtained pure by removal of stromal elements. In the laboratory using several types of culture media, experimental protocols and different ways to increase from one laboratory to another. Results of these methods vary according to each laboratory experience and are not consistent with the natural development of gastric cancer. Methods were used for culture 3D 2D monolayer co-culture with neoplastic cells and chemotherapy drugs. - Models of primary gastric cancer in laboratory animals made transgenic. Gastric cancer is not specific; using drugs with different mechanisms of action would provide a 5 year survival less than 22%. Constructed mathematical models are useful for studying tumor growth, and optimize and streamline invazive drug therapy. Until now the practical application of mathematical models was not feasible because: Not enough is known cell cycle at the molecular level Lack of computing power makes it impossible to run sufficiently complex models - No one could have anticipated the effect of changes at the molecular level variables based on mathematical models of existing experimental data Common objectives in gastric cancer research through experimental methods and mathematical modeling: Study of the cell cycle, the body's immune response, and tumor cell growth dynamics. Migrating cells chemotaxie, angiogenesis Modeling and optimization of treatment with chemotherapy drugs Growth and regeneration of tissues
4. Scientific description

4.1. Gastric cancer. Morphological and genetic features.

Gastric cancer is a disease with significant impact, the second leading cause of cancer death in developed
countries. Geographically specific incidence and mortality have been declining in developed Western countries
ƒ Disease incidence is higher in men (B / F = 2.3 / 1), and mortality is twice the men against women. ƒ Affected age: 65-70 years, disease incidence increases in parallel with age. ƒ Race: gastric cancer is 2.2 times more frequently in African Americans compared to whites. ƒ Geographical distribution: 40% of diseases are in Asia, especially China and Korea. ƒ Survival over 5 years is 22%
Risk factors:
ƒ Diet with low fruit and vegetables and increased consumption of salt, nitrites, smoked foods, preserved. ƒ Occupation: exposure from coal mines, processing plants to nickel, rubber, timber increases the risk of ƒ Smoking is an important risk factor. ƒ Pre-cancerous lesions: intestinal metaplasia is present in 80% of cases. ƒ Blood group AII is recognized as a risk factor for infiltrating carcinoma. ƒ Gastric resection for lesions bening. ƒ Anemia megaloplastic by lack of vitamin B12 is associated with gastric cancer. ƒ Family history increases the risk of gastric cancer. ƒ Pair Helicobacterpylori infection is present in 40% - 50% of cases and gastric adenocarcinoma linfom. Cyclooxygenase 2 (COX 2) potential mechanisms involved in oncogenesis by: stimulating tumor angiogenesis, inhibiting apoptosis, immune suppression and increased invasive potential.
Diagnostic use:
ƒ Clinical Methods ƒ Imaging methods (radiography, CT, MRI examination, endoscopy, etc.) which can detect only tumor ƒ Immunological methods by which tumor cells synthesize phosphorescent proteins those allow tumor detection in early stages of the emergence of a small number of tumor cells.
For gastric cancer screening methods are not effective in the population.
Pathologist based criteria have been described following gastric cancer tumors:
ƒ 95% of these Adeno-carcinoma cases are the starting point glandular cells of gastric mucosa. ƒ Primary lymphoma, has as its starting point the immune tissue of gastric wall stromal tumors: are mesenchymal tumors that express KIT (CD 117) and mutations in C-KIT or PDGFR ƒ Other histological types: squamous cell tumors, small cell tumors, carcinoid tumors and tumors of other ƒ Metastases from gastric cancer occur A direct extension into the peritoneum, liver, diaphragm, spleen, pancreas, colon A distant lymph nodes Blood on the path of the liver, lung, bone, brain
Macroscopic aspects:

Gastric cancer is located 60% and 25% antru cardia stomach area.
ƒ Forms vegetante (36%) are tumors or growths protrusion rounded or irregular red or gray, which bleeds easily loose touch ƒ Forms ulcerated (25%) are irregular bleeding ulcers base, friable or vegetable surface with necrosis, false membranes and infiltration of the wall. ƒ Forms infilitrative (26%) appears as a raised thickened irregular conglomerate that includes the entire gastric wall thickness, a third of cases presented to the entire stomach tumor extension. The infiltration of neoplastic cells and extensive stromal fibrosis. Lauren histological classification of gastric carcinoma [2]. ƒ Type gut: starting point is atrophic gastritis, intestinal metaplasia, gastric epithelium, is more common among elders, is less aggressive than the diffuse type, the cells are adherent, have a good cohesion and spread like adenocarciom differentiated cells formed structures similar tubular gastric glands, have a high level of proliferation and apoptosis process, have changes in chromosome 10 and mutations in the p53 gene. ƒ Diffuse type: has as its starting point the stem cells of gastric glands of the neck, is more common in young than in the capacity of muscle invasion, lymph vessels and lymph nodes, cells have low cohesion, like the gastric wall extends to poor adenocarcinoma differential.
In a few cases were highlighted the multi-focal lesions with different histological sub-types and varying degrees
of differentiation. Morphological heterogeneity is specific phenotypes of intestinal type gastric cancer and has
been explained by progressive accumulation variable oncogenic mutation in genes E2F-4 and type II receptor
genes of growth factor β.
Prognostic factors:
ƒ Aneuploidia ƒ Increased plasma levels of vascular endothelial growth factor ƒ The presence of antigen carcinoembrionic ƒ Elevated dihydropyrimidine dehydrogenase ƒ Mutations in tumor suppressor genes and oncogenes ƒ Diffuse type is unfavorable to the intestinal type prognostic ƒ Tumor diameter [3]. ƒ Early detection ƒ The potential proliferative activity Proliferative activity potential was explored in the following ways: ƒ In-vitro fixation index of tritium thymidine ƒ The determination of proliferation index in the presence of immuno-peroxidase ƒ Fixation index bromodeoxiuridine in-vivo.
Have not found significant associations of clinical and pathological aspects of gastric cancer development and
aggressiveness, respectively prognosis of age, symptoms, gastric wall invasion, tumor invasion and lymph
So far no specific treatment was found effective. Surgical treatment by resection of tumor may be associated
with pre-and postoperative radiotherapy and chemotherapy. If unresectable tumors palliative treatment with
chemotherapy and radiotherapy are. Survival without treatment is about six months.
Following treatment with chemotherapy regimens used:
ƒ Single chemotherapeutic agents: 5-FU, cisplatin, oxaliplatin, mitomycin, Etoposide, anthracycline, taxane, irinotecan, etc. ƒ Combinations of chemotherapeutic agents: 5-FU and doxorubicin, FAMTX (5FU, doxorubicin and methotrexate), ELF (Etoposide, leucovorin, 5FU), etc.
Genetic abnormalities associated with gastric cancer
ƒ Mutations of p53 tumor suppressor gene ƒ Changes cKi-ras oncogenes, HER-2lneu (c-erb-B2, C-MZC most) ƒ Germline mutations of E-cadherin gene
Typing of gastric cancer to the following investigations:
ƒ Morphological study of neoplastic cells ƒ Evaluation of growth by measuring the density of neoplastic cells in culture 2D - 3D and monolayer ƒ Assessment of gastric cancer secretions associated antigens CEA, CA19-9 and TPA. ƒ Extraction of genomic DNA and to sequencing ƒ PCR-SSCP screening for mutations in the p53 gene, c-ki-ras
Experimental studies.

Cell cultures
The laboratory methods used in studying the morphology of gastric cancer, tumor growth dynamics and to
deliver models to assess the therapeutic methods and optimizing the management's treatment of gastric cancer.
Cell cultures using cell lines derived from gastric tumors in laboratory processed for separation of the
extracellular matrix, their isolation and purification. The number of cell lines identified experimentally is a
growing phenomenon which explains the high variability and low stability of gastric cancer compared with other
Culture cells from gastric cancer or gastric mucosa is still normal at first because of technical difficulties, the
protocol and experience of each laboratory. Cell growth is done in 2D and 3D monolayer on different matrices or
liquid medium in which float [4], [5]. Spheroidal formations were obtained compact (solid tumors) corresponding
poorly differentiated gastric cancer in-vivo and spheroidal formations corresponding channel central glandular
well differentiated adenocarcinoma. 3D cultures were obtained of gastric cancer cells with chemotactic agents to
study the effectiveness of treatments [4]. Spatial structures obtained and study tumor growth kinetics in cell
culture was used to obtain models of gastric cancer. Correspondence with the in vitro development of gastric
cancer is not satisfactory because a central role environment plays in cancer development or extra-cellular
matrix in which cells multiply. Extra-cellular matrix (stroma) is a molecular network composed of collagen,
adhesive proteins (fibro-nectine, proteo-glicani), elastin organized in three-dimensional network. Stroma is
central to morphogenesis, tissue repair, growth of new vessels sanghine and neoplastic invasion by the
transmission of biochemical signals from outside to inside the cell and mediate mechanical forces and cell
growth in cell shape and meaning change their orientation to increase tumor [ 5]. Integrins are proteins that
cross the cellular membrane and transmit information from inside the cell to the extra-cellular matrix, regulate
the actin cytoskeleton necessary for the cell mobility. This facilitates cell migration towards aligning the fiber
matrix. Another mechanism that ensures the mobility of cells is haptotaxia fibronectină (extracellular matrix
adhesive glycoproteins). Missed connections with the matrix cause a decrease in cell adhesion to tumor
formation, stopping the cell cycle and apoptosis. Cells produce enzymes that degrade matrix proteins and can
synthesize matrix components (collagen, fibronectine, growth factors) to reorganize the network matrix and
oriented by mechanical traction exerted by cells and the information received from other cells and the
environment [6]. Matrix support tumor growth in anisotropic medium is a permanent modification to allow cell
growth and / or newly formed vessels sanguine. Parameters required to obtain mathematical modeling of tumor
growth are studied:
- Cell adhesion - cell - Cell adhesion - matrix - Structure anisotropic cellular matrix - Density Connector - Local proteolytic degradation of matrix - Align the fiber matrix - Non-homogenous fibers - Shape, orientation and polarity of tumor cells In vivo studies
To study the in vivo growth of gastric cancer develops models of primary gastric cancer in laboratory animals
transgenic [7].
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Characterization of gastric adenocarcinoma cell lines established from CEA424/SV40 T antigen-transgenic mice with or without a human CEA transgene,, BMC Cancer 2006
4.2. Considerations on modeling and control cell populations' cancer

With a history of over four decades, mathematical modeling of the dynamics of cancer and cancer therapy has
helped to develop ideas for planning chemotherapy protocols multimedicament, recruitment (addition) and
synchronization, and enhance resistance gene clones. Also, modeling the dynamics of cancer has helped to
refine the mathematical tools of control theory applied to the dynamics of cell populations. However, with few
exceptions, the practical results were very poor. Reasons for these failures were not always well understood.
These may come from both biomedicine and the mathematical, in that important biological processes important
parameter is ignored and are not known, and complexity of mathematical models is not adequately appreciated.
But thanks to recent advances in methods of monitoring populations of cancer cells, became possible in
November understanding (knowledge) and more precise measurements. These, together with progress in
mathematical tools, have renewed (renewed) hopes to improve chemotherapy protocols. Moreover, a new
philosophy in molecular biology and biotechnology, biology called the system builds a bridge between biologists
and even clinicians, on the one hand and mathematicians and engineers, on the other hand. The same effect is
observed in control engineering and computer science specialists from the community which has emerged a
new generation of scientists appointed bioinformatiques.
Two major obstacles to successful chemotherapy are dependent phase cytotoxic drugs and drug resistance.
The specificity of cell cycle stage is important because it indicates that cancer drugs must be applied when the
cells are sensitive phases of the cycle. This can be done by considering a division of the cell cycle in an
increased number of disjoint compartments, with drug action limited to a few. In literature there are several
works [34] - [37] has been made a classification of different models of this sort and analyze optimization
problem based on this protocol. Mathematical problems encountered include non-uniqueness and singularity of
solutions and providing a rational for periodic protocols.
For the first time, the emergence of resistance to chemotherapy was considered a model of transformation point
of Coldman and Goldie (see [6]) and then in the context of amplification (expansion) by Harnevo and Aguri
genes [20]. The main idea is that there is spontaneous or induced mutations of cancer cells to drug resistance
and treatment planning should anticipate it. Specific transformation model can be transformed into simple
recommendations that should be tested in clinical trials. Analysis and simulation model of amplification
(extension) gene also led to recommendations for optimizing therapy.
A model of chemotherapy based on stochastic approach to the development of cancer cells is presented in [35],
[37] - [39]. Several papers deal with tridiagonale matrix models. This leads to developing a methodology for
investigating such systems and form a basis for a broader generalization. More recently, research has made a
further step by studying the properties of a model in which there were fewer and simplifications have been
required fewer assumptions [24], [31]. Furthermore, models have been combined so far been studied
separately, taking account of both the phenomenon of gene amplification and chemotherapy multimedicament,
in their various aspects. It was also proposed population control fazospecific drug-sensitive cancer. Actually,
each drug affects cells located in a particular phase and then the effect is to combine these drugs so that their
cumulative effect over the population cancer is the most powerful. Initially fazo-specific chemotherapy was
considered without taking into account any issue of increasing drug resistance emerged.
Combining the infinite dimensional model of drug resistance with specific phase model of chemotherapy could
lead to a mathematical model closer to its potential clinical application. Despite a long research and a relatively
rich literature devoted to modeling and control problems of infinite dimensional systems, almost all effective
methods they have developed appropriate approaches for models of differential equations with partial
derivatives (EDPD) and optimized solutions are mostly limited to linear-quadratic problem (LQ). However,
infinite dimensional model study results may lead to compact, convenient to further analysis results would be
very difficult or impossible to obtain a finite dimensional approximation [27, 45]. Moreover, the optimality
conditions for such systems are usually much weaker than those for finite dimensional systems and their
analysis viewpoint is far from being mathematically rigorous. Therefore, below we compare the results of such
systems with the results for finite dimensional models that have already been studied (see [27]). Optimizing
chemotherapy in the presence of drug resistance evolution can be seen as a step in overcoming this
phenomenon. An important factor to be considered is that while drug resistance is obtained by cancer cells
prevents normal tissue sensitivity to drugs. This negative feature of chemotherapy may be used as an
advantage in anti-angiogenic therapy is directed to the normal tissues and kill tumor cells only indirectly: this is
why it was called by Kerbel [22] therapy resistant to resistance drug. To find conditions for tumor eradication in
asymptotic sense and anti-angiogenic therapy protocols for optimizing a class of models we use Hahnfeldt
proposed in [19].

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Bull. Math. Biol. vol. 60, pp.857-864, 1998. [2] Axelrod D.E., Baggerly K.A. and Kimmel M. "Gene amplification by unequal chromatid exchange: Probabilistic modelling and analysis of drug resistance data", J. Theor. Biol. vol. 168, pp. 151-159, 1994. [6] Coldman A.J. and Goldie J.H., "A stochastic model for the origin and treatment of tumors containing drug-resistant cells", Bull. Math. Biol. vol. 48, pp. 279-292, 1986. [11] D'Onofrio A., Gandolfi A., "Tumour eradication by antiangiogenic therapy analysis and extensions of the model by Hahnfeldt et al (1999)". Math. Biosci., vol. 191, pp. 159-184, 2004. [12] Ergun A., Camphausen K., Wein L.M., "Optimal scheduling of radiotherapy and angiogenic inhibitors", Bull. Math. Biol., vol. 65, pp. 407-424, 2003. [19] Hahnfeldt P., Panigraphy D., Folkman J., Hlatky L. "Tumor development under angiogenic signaling: A dynamic theory of tumor growth, treatment response and postvascular dormacy", Cancer Res., vol. 59, pp.4770-4778, 1999. [20] Harnevo L.E. and Agur Z.: "Use of mathematical models for understanding the dynamics of gene amplification", Mutat. Res., vol. 292, pp. 17-24, 1993. [22] Kerbel R.S. "A cancer therapy resistant to resistance", Nature, vol. 390, pp. 335-340, 1997. [23] Kimmel M. and Axelrod D.E.: "Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity", Genetics, vol. 125, pp. 633-644, 1990. [24] Kimmel M., Swierniak A. "Control Theory Approach to Cancer Chemotherapy: Benefiting from Phase Dependence and Overcoming Drug Resistance," in: Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer (A. Friedman-Ed.), Lecture Notes in Mathematics, Mathematical Biosciences Subseries, v.1872, Springer, Heidelberg, pp.185-222, 2006. [26] Ledzewicz U., Schattler H., "A synthesis of optimal control for a model of tumour growth", Proc. 44th IEEE CDC and ECC 2005, pp.934-939, 2005. [27] Ledzewicz U., Schattler H., Swierniak A.: "Finite dimensional models of drug resistance and phase specificity", J. Medical Inf.Techn.8, pp.IP5-IP13, 2004. [31] Smieja J., Swierniak A.: "Comparison of Phase Specific Chemotherapy Models with and without taking into account drug resistance", Proc. IASTED BioMED 2004, Innsbruck 2004, CD ROM, #417-131, 2004. [33] Swierniak A. "Cell cycle as an object of control", J. Biol. Syst., vol. 3, 1995. [34] Swierniak A., Duda Z., "Singularity of optimal control problems arising in cancer chemotherapy", Math. Comp. Modeling, vol. 19, pp.255-262, 1994. [35] Swierniak A., Polanski A. "Irregularity of optimal control problem in scheduling cancer chemotherapy", Appl. Math. Comp. Sci., vol. 4, pp.263-271, 1994. [36] Swierniak A., Ledzewicz U., Schattler H. "Optimal control for a class of compartmental models in cancer chemotherapy", Int. J. Appl. Math. Comput. Sci., vol. 13, pp.357-368, 2003. [37] Swierniak A., Polanski A., Duda Z., Kimmel M.: "Phase-Specific Chemotherapy of Cancer: Optimisation of Scheduling and Rationale for Periodic Protocols", Biocybernetics and Biomedical Eng., vol. 16, pp.13-43, 1997. [38] Swierniak A., Kimmel M., Polanski A.: "Infinite dimensional model of evolution of drug resistance of cancer cells", J. Math. Syst, Estim Cont., vol. 8, pp.1–17, 1998. [39] Swierniak A., Polanski A., Kimmel M., Bobrowski A., Smieja J. "Qualitative analysis of controlled drug resistance model – inverse Laplace and semigroup approach", Cont. Cybern., vol. 28, pp.61-74, 1999. [40] Swierniak A., Polanski A., Smieja J., Kimmel M., J. Rzeszowska-Wolny, "Control theoretic approach to random branching walk models arising in molecular biology", Proc of ACC Conference, pp. 3449-3453, Anchorage 2002. [42] Swierniak A. "Control problems arising in combined antiangiogenic therapy and radiotherapy", Proc. Nat., Conf. Math. Appl. Biol. Medic., pp. 105-110, Koninki, 2006. [44] Zadeh L.A., Desoer C.A.: Linear System Theory. The State Space Approach, New York: Mc. Graw-Hill, 1963. [45] Swierniak A., "Understanding and combating cancer - control theoretic approach", 13-th IEEE IFAC International Conference on Methods and Models in Automation and Robotics, 27-30 August 2007, Poland, pp. 19-30.
4.3. Using independent component analysis to eliminate noise image

Technique made possible the modern digital signal handling multi-dimensional covering three distinct
• Image processing (in an image starts to get to the source and transform it into a form of output)
• Image Analysis (starts from an image source and obtain significant values of specific output size)
• Develop and understanding images (starts from a source image to get a semantic description, the high level
An image is defined as a function of two real variables, eg (x, y) is the amplitude (light intensity) of the image
point coordinates (x, y). An image can be divided into subimages interesting for a certain type of processing or
analysis. This is called the terminology subimages regions of interest (RDI). We can thus infer that any image is
made up of collections of objects that can be aggregated in terms of specific elaboration / analysis in areas of
particular interest.
Therefore, a digital image A (m, n) described in a 2D discrete space is derived from an analog image A (x, y)
described in a 2D continuous space through a sampling process (also called and digitization). Image A (x, y) of
2D continuous space is divided into M rows and N columns. Intersection of lines with one column identifying a
pixel (in English, picture element). Integer value assigned coordinates [m, n] is A [m, n], where m = (0, 1, 2, M -
1) and n = (0, 1, 2, N - 1). Pixels assigned mean values are rounded to whole. Process 2D representation of the
amplitude of a signal by integer value N levels of color is known as amplitude-based quantization. In practice, in
most cases, A (x, y) is a function with more than two variables (as in fact a broader description of the physical
signal that comes in contact with the capture probe). Among these variables mention depth (z), color (λ) and
time (t).
Techniques and algorithms to reduce / suppress image noise

Noise reduction is the process of removal / reduction of noise from a signal. Noise reduction techniques are
basically the same regardless of signal type processed. However, early knowledge of signal characteristics can
lead to different implementations of these techniques.
Filters mediation. In general, the arithmetic mean and geometric filters are suitable for noise-type Gaussian
random noise or uniform.
ƒ Arithmetic mean filter. Is the simplest of the filters of mediation? Sxy be a set of coordinates in a
rectangular region of interest centered on the point (x, y) and size m x n. arithmetic mean filter calculates the average value of image degraded target region. Therefore, the restored image is obtained from the arithmetic average pixel values of Sxy region. A filter will only pave the mediation of local variations in an image. Noise is reduced by the effect of blur. ƒ Geometric mean filter. Geometric mean filter produces a comparable smoothing filter presented earlier
arithmetic average, but has the advantage of losing far fewer details / information from the processed image. ƒ Uniform filter. Image is obtained based on an average local input filter to filter all the values used were
the same weight. ƒ Median filter. The filter replaces a pixel value by the mean gray levels that are near the pixel in
question. Median filters are common because they provide images with an effective random noise disposal without entering / stress phenomenon blur (blurring) as usually happens with smoothing filters. The effectiveness of these filters increases even more when impulse noise counter unipolar / bipolar. Therefore, these filters are frequently used to improve the quality of these types of images corrupted with noise. ƒ Filter Max-and-min (maximum and minimum). Max filter is useful to determine the brightest pixel in an
image. If pepper type noise has very small values, such a filter it through the selection process will reduce the maximum values in the region of interest Sxy. Similarly, the filter is minimal when determining follows the darkest pixel in an image. Min filter therefore reduces noise by eliminating type jump in the selection process of the brightest points. ƒ Filter midpoint. The filter calculates just the midpoint between maximum and minimum pixel values of
subimage subjected to filtration. The particularity of this filter is to combine operations and the statistical ordering mediation. Therefore, the filter is very effective for type Gaussian noise, uniform type and the uncertain. ƒ Kuwahara filter. Edge / edges play a major role in how we perceive images and in how they analyze. It
is therefore useful clarification / smoothing images without affecting any clarity and edge position. A filter that achieves this goal is the Kuwahara filter. Can be used for a variety of forms (for subimages). Consider window square shape where one side is the size 4L + pixels, L being an integer. The window can be divided into four sub-quadratic size 2L x 2L. In each of the four sub-filters calculates the average light intensity and variance. Output value for the central pixel, the coordinates (2L + 1 2L + 1) is the average of the region which has the smallest variance. ƒ Wiener filters. In the category of linear filters, an effective filter for image restoration in the presence of
noise is a Wiener filter. Filter is optimal from the standpoint of minimizing the average quadratic error. Since the quadratic root extraction operation is monotone increasing, the optimal filter minimizes the square error (root mean square error - RMSE).
Smoothing techniques. In the field of image processing, smoothing (the term in English, smoothing) of data
sets is the process of approximation to a function able to reveal important patterns within the crowd and to
eliminate or reduce as much as possible disturbing phenomena such as noise. A series of algorithms is used in
smoothing the process specific data set images. Often, these algorithms are not only designed to reduce /
eliminate the noise but also to prepare a set of relevant data for further development of an image such as image
segmentation. The first classifications of smoothing algorithms distinguish two categories: linear algorithms
(Fourier analyzed in the field) and the Nonlinear. A second classification in terms of implementing these
algorithms see also divided into two categories: those with implementations based on filters with rectangular
support the implementation of filters based on ring support.
Techniques for noise suppression in images. Noise removal techniques can be divided into techniques that
rely on temporal information and those based on spatial information. The temporal information means a
sequence of images (ap [m, n] p = 1,2 ,., P), files available that contain the exact same items but differ only in
terms of noise included. In such a scenario, and if additive noise is a time when a simple mediation (temporal)
will result that the average value of each pixel will remain unchanged. If mediation is not possible when temporal
spatial mediation can be used to reduce image noise. Noise reduction by the space environment but will cost in
terms of image contrast. Mediation can be achieved by any space of smoothing algorithms and the median filter,
or by Kuwahara filter.

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