Breast Tumor Classification Using FFT based Fractal Analysis

bureau Tumor Classification Using FFT based Fractal AnalysisB.MONICA JENEFERV.CYRILRAJAbstractBreast providecer is formed by abnormal cells, it causes fast death among human and it is shapeless. The ingathering of the nookiecer is alike fast and it should be removed from the earlier floor itself. In this study, we have introduced and weaponed an FFT based fractal model to dissect the breast neoplasm and clear up it as propitiousant or malignant agree to their shapes. The benign and malignant are different in descriptor and shape where benign have a smooth conformity and macrolobulated shapes and malignant have rough contour and mo shapes. In this study, the contours are classified exploitation fractal based Fourier substitute method. The magnitude and frequency based features are utilized for classification. This approach achieved 92% of trueness in neoplasm classification using fractal based fourier transform.Keywords Fractal Analysis, Breast Cancer,Background study A fractal is a mathematical object representing a fractional prop 1 where fractal geometry is vocabulary of irregular shapes.Due to uncontrolled growth of the bad cells, breast loafercer occurs in breast tissue 2. Fractal analysis helps the clinical experts for pre-screening the breast crab louse in earlier stage itself. Various shape based object detection and classification can be obtained to the highest degreely using the bounding box method in digital come across subroutineing. Since, the shape of the breast crab louse 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 mingled with the neoplasm cells and non-tumor cells is an effective method for screening breast cancer 4, 5. The chief(prenominal) symptoms of breast cancer are increasing DNFA De Novo Fatty Acid and cholesterol discount where it related to tumor growth and poorer prognosis 6, 7.Present studies are discussing almost fractal geometry to generate 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 d one 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 neb of the shapeless structure of tumor growth.Various comprehensive reviews used and discussed mathematical models for medical image diagnosis, in particular 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, nevertheless the shape of the malignant tumor is irregular and roughly bounded. This main contravention is utilized to categorize the benign tumor and malignant tumor. The next 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). MalignantProposed ModelMost of the medical image processing applications used fractal analysis and which is focused in divers(a) 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 nearThe structure of this study is described as given below, section-III discussed about the loanblend 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. Sect ion-VI described about our experiment and results. Section-VI provides the conclusion about this study and suggestion for further enhancement work.Hybrid FilterThe 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 tribulationed while experimenting to impro ve the appearance of the contour. The morphological functions are specify as (1)Where denotes the opening operation and denotes the dilation and denotes the morphological erosion operation. Devices 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)Th e 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 vivacious 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 kinetics 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 fit 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 applyin g 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)W here 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 etcetera 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 southward 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 acc usations are calculated and plot in the form of log-log magnitude plot for classifying the tumors.From the centroid to all directions, the magnitude variance 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 stellate 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 ResultsTo experiment Fractal based fourier transform analysis method the matlab software is choosen to implement, due to its capability in image processin g. 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 apply into hybrid filters. The result of the hybrid filter is separated into small segments with dissimilar radius continuance 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 compositors case 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 di stance 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 h omogeneous 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 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 EnhancementThe 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, FF T 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.References1.James W. Baish and Rakesh K. 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