Breast Tumor Classification Using FFT based Fractal Analysis

Breast Tumor Classification Using FFT based Fractal Analysis B.MONICA JENEFER V.CYRILRAJ Abstract Breast cancer is formed by abnormal cells, it causes fast death among human and it is shapeless. The growth of the cancer is also fast and it should be removed from the earlier stage itself. In this study, we have introduced and implemented an FFT based fractal model to analyze the breast tumor and classify it as benign or malignant according to their shapes. The benign and malignant are different in contour and shape where benign have a smooth contour and macrolobulated shapes and malignant have rough contour and irregular shapes. In this study, the contours are classified using fractal based Fourier transform method. The magnitude and frequency based features are utilized for classification. This approach achieved 92% of accuracy in tumor classification using fractal based fourier transform. Keywords: Fractal Analysis, Breast Cancer, Background study A fractal is a mathematical object representing a fractional dimension [1] where fractal geometry is vocabulary of irregular shapes.Due to uncontrolled growth of the bad cells, breast cancer occurs in breast tissue [2]. Fractal analysis helps the clinical experts for pre-screening the breast cancer in earlier stage itself. Various shape based object detection and classification can be obtained mostly using the bounding box method in digital image processing. Since, the shape of the breast cancer has been irregular and it cannot be obtained by bounding method [3]. Malignancy associated changes in the breast cells are discussed for computing the distance between the tumor cells and non-tumor cells is an effective method for screening breast cancer [4, 5]. The main symptoms of breast cancer are increasing DNFA –[De Novo Fatty Acid] and cholesterol synthesis where it related to tumor growth and poorer prognosis [6, 7].Present studies are discussing about fractal geometry to genera te a sampling model for tumor appearance and its impacts. According to the wonderful growth of present researches in understanding the molecular mechanisms of cancer, most of the medical diagnosis is done by examining visual objects for radiological images, direct observation of tissues and microscopy of biopsy specimens and so on [1].These fractal model analyses are used to classify abnormality of medical images due to the structure or high indices of mitosis. This modeling method is one of the reproducible methods which helps to analyze the medical images with computational tools. Also fractal analysis is a morphometric measure of the shapeless structure of tumor growth.Various comprehensive reviews used and discussed mathematical models for medical image diagnosis, especially in pathology is currently appearing in the literature [8-16]. From the digital mammogram image, the shape of the benign tumor is round and smooth, but the shape of the malignant tumor is irregular and roughly bounded. This main difference is utilized to categorize the benign tumor and malignant tumor. The following Figure-1 depicts the morphological spectrum of the breast masses frequently seen in digital mammograms. Figure-1:(a). Round Benign (b). Lobulated benign (c). Malignant (d). Malignant Proposed Model Most of the medical image processing applications used fractal analysis and which is focused in various researches on the digital mammograms. In this study, it is experimenting using the FFT based fractal analysis and classifying the breast lesions. The complete flow of this study is depicted in Figure-2. Figure-2: Overall Flow of the Proposed Approach The structure of this study is described as given below, section-III discussed about the hybrid filter and its applications. Section-IV discussed about the basic information about the fractal analysis method. Section-V described about Fractals based or Fourier Transform method. Section-VI described about our experiment and results. Section-VI provides the conclusion about this study and suggestion for further enhancement work. Hybrid Filter The hybrid filter combines morphological filter with the Gabor filter for removing the noise from the mammogram image to improve the quality of the image. Morphological filter is a non-linear filter work based on the set theory rules and Gaussian filter is a linear filter work based on vectors and both are used to remove noise.The main motto of this hybrid filter is to completely remove various noises occur under different conditions in the image, to improve the performance of the proposed approach. Morphological filter can remove the noise on the contour of the image and Gabor filter remove the noise in the inside of the image. Morphological filter utilized various morphological transform using different structuring elements. In this study also, different morphological transform is tested while experimenting to improve the appearance of the contour. The morphological functions are defined as: (1) Where denotes the opening operation and denotes the dilation and denotes the morphological erosion operation. Device’s mechanism introduced two kinds of noise such as coherence and no-coherence noise. The Gaussian noise is represented by statistical noise, having a probability density function, which is called as a Gaussian distribution. The original pixel value in the image is changed from its inventive value by a minute amount in the Gaussian noise. Due to the central bound theorem, Gaussian distribution is generally can provide a good quality representation. The probability density function of a Gaussian random variable is given by: (2) Alternatively, a process is Gaussian if and only if for every finite set of indices in the index set (3) It is a multivariate Gaussian random variable. The Gaussian property can be formulated by using the features functions of random variables as:, such that (4) The hybrid filter can effectively remove all the noise in the mammogram image which can provide more accuracy in classification. Fractal Analysis There are various fractal analysis techniques are existing but most of the techniques follow power law basics. In the exisiting work [17], tumor growth was studied with the help of a model which says that the tumor is a rising tissues. Mathematical model and numerical simulations of this model were examined to obtain the macroscopic dynamics of the tumor growth. It experimented and well known that the growth of the tumor is proportional to the time [17] suggested from power law. It is also can be simulated using a one-dimensional (1D) CA model, shows the linear growth of the entire cells. From this, it is observed that in both the 1D and 2D cases, tumor diameter grows linearly according in terms of time.The dimension of the fractal model is estimated using various techniques such as sandboxes, bounding-box, Fourier spectrum and so on. When applying these techniques, the scaling relationships of the cells are obtained according to a power law relationship. The basic geometric objects can be understood by the Euclidean objects as lines, planes and circles. All the objects do not resemble the Euclidean objects. By utilizing the fractal geometry, it is easy to create models for nature objects and which can provide a better definition in various conditions. Mandelbrot [9] introduced the first fractal theory. The unique difference among the Euclidean and fractal geometry is the self similarity denoting by un-uniform scaling. The variance of the shape of the objects continuously varying in increasing or decreasing the size of the objects. It is clear that one of the problems in scaling is texture, and describing the texture also depends on scaling. Hence, this problem can be overcome by the fractal geometry of texture. The definition of Hausdroff-Besicovitch of the fractal dimension is described using the following equation (5). (5) Where is the self similar pieces 1/r is the magnificent factor. Since, the fractal dimension indicates the surface roughness, people always use the texture as fine, coarse, gained and smooth etc. Mostly the fractal dimension of an image can be estimated by the bounding-box, fractal Brownian motion and fractal interpolation method. In this study, the fractal of filtered contour of the breast tumors are analyzed and tested using FFT based methods. Fractal based Fourier Transform In this study, it is adopted that Fourier fractal methodology is used for classifying the tumors. The filtered contour is taken and fed as input for testing. The growth of the tumor is randomness and it is in certain degrees, complex irregular in shape. So that, the fractal analysis can give a good measure in order to measure the complex patterns than the traditional Euclidean geometry. In this study, the fractal dimension is measures using Fourier transform method. In our experiment the radical magnitude accusations are calculated and plot in the form of log-log magnitude plot for classifying the tumors. From the centroid to all directions, the magnitude variation is measured to compute the magnitude accumulation testing. The Fourier transforms and phase angle calculations are obtained using Equations (3) and 4) respectively. The filtered contour is defined in X-axis with M – mean value and it can be implemented as: (6) (7) In this study, the fractal dimension of the breast tumor is calculated according to the average slop variations of log-log magnitude plot. Also the log-log plot can be drawn among the magnitude accumulation in entire radial components and number radial components of the respective input images. The accurate and absolute values of average variations are more for malignant tumor than the benign tumors. Experiment and Results To experiment Fractal based fourier transform analysis method the matlab software is choosen to implement, due to its capability in image processing. In this study, it is considered that some of the available contours are the input for the experiment. For pre-processing the image, to remove, the higher order frequency components are taken as artifacts, the input contours are applied into hybrid filters. The result of the hybrid filter is separated into small segments with dissimilar radius length by dividing the contour uniformly in all directions. In our experiment, the contour is divided into 24 equal parts. Then the fractal dimension method using FFT is applied to extract shape variables in each segment. In our experiment, five contours are considered as the input, at five, three contours are the type of malignancy and the remaining contours belongs to the type of benign. The following Table-1 depicts the log-log magnitude plot and absolute values of the slop variations in terms of respective contour. After filtering the input contour it is divided into 24 segments in all the directions with equal radial distance and then the magnitude variation of all the directions is counted and accumulated for all the radial components. It is well known that the malignant tumor has more variations than the benign tumors. According to the accumulations of the magnitude variations the malignant tumors are having more variations than the benign masses. The fractal dimension is calculated using the log-log plot drawing method between the accumulations of magnitude variations and the number of radial components. The absolute value [a threshold value used for decision making] is drawn in the log-log plot to compute the average variation of the magnitude. To provide difference the slop, the colors used to plot are different. The absolute value of the average slop variation according to the threshold is used to classify the tumors. In this experiment, a threshold value is used for decision making, for tumor classification. The absolute value of the average slop difference is high for malignant and for the same value it is less for benign. From this scenario, it is observed that, the variations of magnitude accumulations in terms of number of radius are more for malignant tumor and small for a benign tumor. Table-1: Fractal Analysis based on FFT Tumor classification In most of the cases the average slope values are greater than the threshold values for our test images used in the experiment. Originally the test image 1 is the benign and the other images are the malignant images. Generally Image 4 is malignant image, but according to the average slop variations and threshold values it is defined as benign. In this paper, we experiment with 25 images[ but in table-1 only five images and their results are displayed]. Out of 25 it correctly classifies 23 images. From this experiment 92% of success rate. Conclusion and Future Enhancement The FFT based fractal analysis method is easy to implement and classify the tumors based on the shape of the tumors. In this study, from the experiment, FFT based fractal analysis method achieved 92% of the classification accuracy. Since this study can provide better results than the existing approaches. The accuracy can be improved in the future enhancement of this study. FFT based fractal analysis is one of the easiest methods and best software for doctors to prescribing the tumor and understand the tumor shapes accurately and fast. References [1].James W. Baish and Rakesh K. Jain, â€Å"Fractals and Cancer†, American Association for Cancer Research -2000. [2]. Breast cancer facts and figures http://www.breastcancer.org/. [3]. Syed Abdaheer.M and Ekram Khan, â€Å"Shape Based Classification Of Breast Tumors Using Fractal Analysis†, IEEE-2009. [4] Us-Krasovec M, Erzen J, Zganec M et. Al, â€Å"Malignancy associated changes in epithelial cells of buccal mucosa: a potential cancer detection test†, Anal Quant Cytol Histol. 27(5): 254-62, Oct. 2005. [5] Andrushkiw R.I., Boroday N.V., Klyushin D.A., â€Å"Petunin Yu.A. Computer-aided cytogenetic method of cancer diagnosis†, New York: Nova Science Publishers, 2007. [6]. Pelton K, Freeman MR, Solomon KR, â€Å"Cholesterol and prostate cancer†, Curr Opin Pharmacol 12: 751 – 759-2012. [7]. Zadra G, Photopoulos C, Loda M, â€Å"The fat side of prostate cancer†, Biochim Biophys Acta 1831: 1518 – 1532-2013. [8]. Ramis-Conde I, Drasdo D, Anderson AR, Chaplain MA, â€Å"Modeling the inuence of the e-cadherin-beta-catenin pathway in cancer cell invasion: a multiscale approach†, Biophys J 1: 155–165-2008. [9]. Rietman EA, Friesen DE, Hahnfeldt P, Gatenby R, Hlatky L, et al, â€Å"An integrated multidisciplinary model describing initiation of cancer and the warburg hypothesis†, Theor Biol Med Model 10-2010. [10]. Gillies RJ, Verduzco D, Gatenby RA, â€Å"Evolutionary dynamics of carcinogenesis and why targeted therapy does not work†, Nat Rev Cancer 12: 2012. [11]. Preziosi L, Vitale G, â€Å"A multiphase model of tumor and tissue growth including cell adhesion and plastic reorganization†, Math Models Methods Appl 21: 1901–32-2011. [12]. Bellomo N, Delitala M, â€Å"From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells†, Physics of Life Reviews 5: 183–206-2008. [13]. Anderson AR, Quaranta V, â€Å"Integrative mathematical oncology†, Nat Rev Cancer 8: 227–34-2008. [14]. Anderson AR, Weaver AM, Cummings PT, Quaranta V, â€Å"Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment†, Cell 127: 905–15-2008 [15]. Agur Z, Vuk-Pavlovic ´ S, â€Å"Mathematical modeling in immunotherapy of cancer: personalizing clinical trials†, Mol Ther 20: 2012. [16]. Silva AS, Gatenby RA,†A theoretical quantitative model for evolution of cancer chemotherapy resistance†, Biol Direct 5-2010. [17]. Vainstein, V., Kirnasovsky, O.U., Kogan, Y., Agur, Z.: â€Å"Strategies for cancer stem cell elimination: Insights from mathematical modeling†. J. Theor. Biol. 298, 32-41 (2012).

Truancy: A Symptom of a Larger Problem Essay -- mental health, justic

The movie, Ferris Bueller’s Day Off, is the epitome of adolescent rebellion and independence – the benchmark of free-spirited insubordination that lies in the heart of all teenagers. Sure, the movie depicts skipping school as nothing more than a harmless and fun pastime, something that is enjoyable due in large part to its riskiness. But essentially, it documents the day of a truant. A truant whose wild antics entertain, but a truant nonetheless. Like most things, Hollywood’s characterization of adolescent truancy is incorrect, not just in the sense that most kids will not be singing in parades whilst cutting class. It downplays the rather serious nature of chronic absences that permeates all levels of society. Adolescent rebellion and the need to distance away from authority figures and find ones’ own individuality is a normal part of growing up and the developmental process (Steinberg, 1987). However, problems arise when this distinctive need manifests itself in overtly negative activities. Whether it be experimenting with drugs and alcohol or skipping out on class, the undercurrent of teenage self-exploration is present. Going back to the point of truancy, this need, coupled with boredom and peer pressure, can increase the occurrence of absenteeism. Nevertheless, a number of other factors do play a significant role. Chronic absenteeism is often a symptom of larger problems than teen rebellion. Bullying, family issues, financial difficulties, drug use, and lack of academic skills are only some of the potential causes of truancy within the United States (Reid, 2012). And while schools across the country continue desperately to try and mitigate truancy, it seems to be on the rise; in 2012, data indicated that up to 15 percent... ...tiative. Crime & Delinquency, 214-234. National Institute of Mental Health . (2011). The Teen Brain: Still Under Construction . Besthesda : U.S. Department of Health and HUman Services . Prevention, O. o. (1996). Truancy: First Step to a Lifetime of Problems . Washington : U.S. Department of Justice . Reid, K. (2012). The causes, views and traits of school absenteeism and truancy: An analytical review. Research in Education, 59-82. Statistics, B. (2010). Bullying Statistics 2010. Retrieved from Bullying Statistics: http://www.bullyingstatistics.org/content/bullying-statistics-2010.html Steinberg, L. D. (1987). Family processes at adolescence: A developmental perspective. Family Therapy, 77-86. Zik, M. (2009). The Effects of Participation in Contingent Music Experiences on Truancy Rates of Junior High School Students . Dayton : University of Dayton.

Gloria Macapagal-Arroyo Essay

Gloria Macapagal-Arroyo (born April 5, 1947) is a Filipino politician who served as the14th President of the Philippines from 2001 to 2010, as the 12th Vice President of the Philippines from 1998 to 2001, and is currently a member of the House of Representativesrepresenting the 2nd District of Pampanga. She was the country’s second female president (after Corazà ³n Aquino), and the daughter of former President Diosdado Macapagal. Arroyo was a former professor of economics at Ateneo de Manila University where Benigno Aquino III was one of her students. She entered government in 1987, serving as assistant secretary and undersecretary of the Department of Trade and Industry upon the invitation of President Corazon Aquino. After serving as a senator from 1992 to 1998, she was elected to the vice presidency under President Joseph Estrada, despite having run on an opposing ticket. After Estrada was accused of corruption, she resigned her cabinet position asSecretary of Social Welfare and Development and joined the growing opposition to the president, who faced impeachment. Estrada was soon forced from office by the EDSA Revolution of 2001, and Arroyo was sworn into the presidency by Chief Justice Hilario Davide, Jr. on January 20, 2001. She was elected to a full six-year presidential term in the controversial May 2004 Philippine elections, and was sworn in on June 30, 2004. Following her presidency she was elected to the House of Representatives, making her the second Philippine president—after Josà © P. Laurel—to pursue a lower office after their presidency. On November 18, 2011, Arroyo was arrested following the filing of criminal charges against her for electoral fraud. As of December 9, 2011, she is incarcerated at the Veterans Memorial Medical Center in Quezon City under charges of electoral sabotage.

Biography of Sociologist George Herbert Mead

When fields such as psychology and sociology were still new, George Herbert Mead became a leading pragmatist and pioneer of symbolic interactionism, a theory that explores the relationships between people in societies. More than a century after his death, Mead is widely considered to be one of the founders of social psychology, the study of how social environments influence individuals. Having taught at the University of Chicago for much of his career, he is also associated with what is now known as the Chicago school of sociology. Early Years and Education George Herbert Mead was born on  Feb. 27, 1863, in South Hadley, Massachusetts. His father Hiram Mead was a pastor of a local church but moved the family to Oberlin, Ohio to become a professor at Oberlin Theological Seminary in 1870. His mother Elizabeth Storrs Billings Mead also worked as an academic; she taught at Oberlin College and would go on to serve as president of Mount Holyoke College in South Hadley, Massachusetts. In 1879, George Herbert Mead enrolled in Oberlin College, where he pursued a bachelors degree focusing on history and literature, which he completed four years later. After a brief stint as a school teacher,  Mead worked as a surveyor for the Wisconsin Central Railroad Company for a few years. Following that, he enrolled in Harvard University, where he studied psychology and philosophy, but he left in 1888 without a graduate degree. After Harvard, Mead joined his close friend Henry Castle and his sister Helen Kingsbury Castle in Leipzig, Germany, where he enrolled in a Ph.D. program for philosophy and physiological psychology at the University of Leipzig. In 1889, Mead transferred to the University of Berlin, where he began to study economic theory. The University of Michigan offered Mead a teaching position in philosophy and psychology two years later and he stopped his doctoral studies to accept this post, never actually completing his Ph.D. Prior to taking on his new role, Mead married Helen Castle in Berlin. Career At the University of Michigan, Mead met sociologist  Charles Horton Cooley, philosopher  John Dewey, and psychologist Alfred Lloyd, all of whom influenced the development of his thought and written work. Dewey accepted an appointment as the chair of philosophy at the University of Chicago in 1894  and arranged for Mead to be appointed assistant professor in the department of philosophy. Together with James Hayden Tufts, the three formed the nexus of American pragmatism, referred to as the Chicago Pragmatists. Meads Theory of the Self Among sociologists, Mead is most well known for his theory of the self, which he presented in his well-regarded and much-taught book Mind, Self and Society (published in 1934 after his death and edited by Charles W. Morris). Meads theory of the self maintains that the idea people have of themselves stems from social interaction with others. This theory opposes biological determinism  because it holds that  the self does not exist at  birth and may not be present at the beginning of a social interaction, but it is constructed and reconstructed in the process of social experience and activity.​ The self, according to Mead, is made up of two components: the â€Å"I† and the â€Å"me.† The â€Å"me† represents the expectations and attitudes of others (the generalized other) organized into a social self. Individuals define their behavior in reference to the generalized attitude of the social group(s) they occupy. When people can view themselves from the standpoint of the generalized other, self-consciousness in the full sense of the term is attained.  From this standpoint, the generalized other (internalized in the â€Å"me†) is the major instrument of social control, for it is the mechanism by which the community exercises control over the conduct of its individual members. The â€Å"I† is the response to the â€Å"me,† or the person’s individuality. It is the essence of agency in human action. So, in effect, the me is the self as object, while the I is the self as subject. According to Meads theory, the self is developed through three activities: language, play, and game. Language allows people to take on the â€Å"role of the other† and respond to their own behaviors through the symbolized attitudes of others. During play, individuals take on the roles of different people and pretend to be them to express their expectations. This process of role-playing is key to the generation of self-consciousness and to the general development of the self. People must comprehend the rules of the game and internalize the roles of everyone else involved. Meads work in this area spurred the development of symbolic interaction theory, now a major framework within sociology. In addition to Mind, Self, and Society, his major works include 1932s The Philosophy of the Present and 1938s The Philosophy of the Act. He taught at the  University of Chicago until his death on  April 26, 1931. Updated  by Nicki Lisa Cole, Ph.D.