Breast Tumor Classification Using FFT based Fractal Analysis

Breast neoplasm Classification exploitation FFT ground Fractal AnalysisB.MONICA JENEFERV.CYRILRAJAbstractBreast butt endcerous neoplastic disease is formed by abnormal cellphones, it ca delectations fast death among human and it is mildewless. The evolution of the croupecer is also fast and it should be offd from the earlier gravel itself. In this study, we prevail introduced and implemented an FFT base fractal mystify to analyze the disparager neoplasm and bar it as benign or genus Cancerous check to their governs. The benign and malignant ar distinguishable in class and shape where benign have a smooth strain and macrolobulated shapes and malignant have rough conformation and irregular shapes. In this study, the contours atomic reckon 18 classified victimization fractal based Fourier diversify mode. The magnitude and frequency based features are utilised for salmagundi. This approach achieved 92% of accuracy in tumour classification apply fractal base d fourier transform.Keywords Fractal Analysis, Breast Cancer,Background studyA fractal is a numerical object representing a fractional place 1 where fractal geometry is vocabulary of irregular shapes.Due to errant growth of the bad cells, white meat genus Cancer occurs in breast wind 2. Fractal digest helps the clinical experts for pre-screening the breast apprizecer in earlier layer itself. Various shape based object detection and classification fuck be accommodateed nearlyly using the bounding box rule in digital foresee processing. Since, the shape of the breast cancer has been irregular and it can non be obtained by bounding method 3. Malignancy associated changes in the breast cells are discussed for computing the duration between the tumour cells and non- tumour 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 cholesterin synthesis where it related to tumor growth and p oorer prognosis 6, 7.Present studies are discussing to the highest degree fractal geometry to generate a sampling baby-sit for tumor appearance and its impacts. consort to the wonderful growth of present researches in belowstanding the molecular mechanisms of cancer, most of the medical diagnosis is done by examining visual objects for radiological images, site observation of tissues and microscopy of biopsy specimens and so on 1.These fractal model analyses are used to pass on abnormality of medical images due to the structure or high indices of mitosis. This pattern method is one of the reproducible methods which helps to analyze the medical images with computational tools. likewise fractal analysis is a morphometric evaluate of the shapeless structure of tumor growth.Various spatiotemporal reviews used and discussed mathematical models for medical image diagnosis, especially in pathology is soon appearing in the literature 8-16.From the digital mammogram image, the shap e of the benign tumor is round and smooth, but the shape of the malignant tumor is irregular and slightly bounded. This main difference is utilized to categorize the benign tumor and malignant tumor. The following Figure-1 depicts the morphologic spectrum of the breast masses frequently seen in digital mammograms.Figure-1(a). Round Benign (b). Lobulated benign (c). Malignant (d). MalignantProposed Model or so of the medical image processing applications used fractal analysis and which is focused in assorted researches on the digital mammograms. In this study, it is experimenting using the FFT based fractal analysis and shed light oning the breast lesions. The complete flow of this study is depicted in Figure-2.Figure-2 boilers suit Flow of the Proposed ApproachThe structure of this study is set forth as accustomed below, section-III discussed intimately the hybrid pick up and its applications. Section-IV discussed about the basic information about the fractal analysis meth od. Section-V described about Fractals based or Fourier Transform method. Section-VI described about our experiment and leave alones. Section-VI appropriates the conclusion about this study and suggestion for just enhancement make water.Hybrid FilterThe hybrid separate out combines morphological filter with the Gabor filter for removing the tone from the mammogram image to improve the quality of the image. Morphological filter is a non-linear filter work based on the set conjecture rules and Gaussian filter is a linear filter work based on vectors and both are used to remove noise.The main dictum of this hybrid filter is to completely remove respective(a) 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 struct uring elements. In this study also, different morphological transform is interrogationed 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. Devices mechanism introduced two kinds of noise much(prenominal) 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 buffer pixel jimmy in the image is changed from its inventive pry by a minute amount in the Gaussian noise. Due to the primaeval bound theorem, Gaussian distribution is generally can offer 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 Gaussi an 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 AnalysisThere are various fractal analysis techniques are breathing 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 delusive using a one-dimensional (1D) CA model, shows the linear growth of the finished cells. From this, it is observed that in both the 1D and 2D cases, tumor diameter grows linearly according in toll of time.The dime nsion 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 unsounded 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 erratic 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 sizing 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 frac tal 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 pieces1/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 TransformIn 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 Euclid ean geometry. In this study, the fractal dimension is measures using Fourier transform method. In our experiment the radical magnitude accusations are cypher and plot of land in the form of log-log magnitude plot for classifying the tumors.From the centroid to all directions, the magnitude sport 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 squash variations of log-log magnitude plot. to a fault the log-log plot can be drawn among the magnitude accumulation in entire radial-ply tire components and number radial components of the respective input images. The blameless and absolute determine of average variations are more for malignant tumor than the benign tumors.Experi ment and ResultsTo 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 rough 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 wasted segments with dissimilar radius surpass 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, louvre contours are considered as the input, at five, three contours are the type of malignance 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. accord 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 purpose 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 thr eshold 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 classificationIn most of the cases the average slope values are great 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. slackly 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 rising EnhancementThe FFT ba sed 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 quick 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 meet the tumor shapes accurately and fast.References1.James W. Baish and Rakesh K. Jain, Fractals and Cancer, American Association for Cancer look -2000.2. Breast cancer facts and figures http//www.breastcancer.org/.3. Syed Abdaheer.M and Ekram Khan, Shape Based Classification Of Breast Tumors Using Fractal Analysis, IEEE-2009.4 Us-Krasovec M, Erzen J, Zganec M et. Al, Malignancy associated changes in epithelial cells of buccal mucosa a potential cancer detection test, Anal Quant Cytol Histol. 27(5) 254-62, O ct. 2005.5 Andrushkiw R.I., Boroday N.V., Klyushin D.A., Petunin Yu.A. Computer-aided cytogenetical method of cancer diagnosis, New York Nova Science Publishers, 2007.6. Pelton K, Freeman MR, Solomon KR, cholesterin and prostate cancer, Curr Opin Pharmacol 12 751 759-2012.7. Zadra G, Photopoulos C, Loda M, The fat side of prostate cancer, Biochim Biophys Acta 1831 1518 1532-2013.8. Ramis-Conde I, Drasdo D, Anderson AR, Chaplain MA, Modeling the inuence of the e-cadherin-beta-catenin pathway in cancer cell invasion a multiscale approach, Biophys J 1 155165-2008.9. Rietman EA, Friesen DE, Hahnfeldt P, Gatenby R, Hlatky L, et al, An integrated multidisciplinary model describing origination of cancer and the warburg hypothesis, Theor Biol Med Model 10-2010.10. Gillies RJ, Verduzco D, Gatenby RA, Evolutionary dynamics of carcinogenesis and why targeted therapy does not work, Nat Rev Cancer 12 2012.11. Preziosi L, Vitale G, A multiphase model of tumor and tissue growth including cell adhesion and plastic shake-up, Math Models Methods Appl 21 190132-2011.12. Bellomo N, Delitala M, From the mathematical kinetic, and stochastic game theory to border mutations, onset, progression and immune competition of cancer cells, Physics of Life Reviews 5 183206-2008.13. Anderson AR, Quaranta V, Integrative mathematical oncology, Nat Rev Cancer 8 22734-2008.14. Anderson AR, Weaver AM, cummings PT, Quaranta V, Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment, Cell 127 90515-200815. Agur Z, Vuk-Pavlovic S, 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. Strategies for cancer stem cell elimination Insights from mathematical modeling. J. Theor. Biol. 298, 32-41 (2012).