International Journal of Pure and Applied Mathematics Volume 118 No. 18 2018, 781-789 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue
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CLASSIFICATION OF POSITRON EMISSION TOMOGRAPHY IMAGES USING OTSU’S AND NEUTROSOPHIC METHOD Vijayan T1, Sridhar raja 2 ,kalaiselvi B 3 Asst. Professor School of Electrical Sciences, BIST, BIHER, Bharath University tvij16@gmail.com, sridharraja.eie@bharathuniv.ac.in, kalaiselvi.eie@bharathuniv.ac.in 1,2,3
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Abstract The segmentation is used to simplify or to change the representation of an image into something that is more meaningful and easier to analyze. Many foreground segmentation methods are available to increase the efficiency of the image. The foreground segmentation can be improved by the classification performance on weakly annotated datasets – those with no additional annotation other than class labels. A new co-segmentation algorithm called triclass that looks at all training images jointly and automatically segments out the most classdiscriminative foregrounds for each image. Ultimately, those foreground segmentations are used to train a classification system. Triclass solves the co-segmentation problem by minimizing losses at three different levels: the category level for foreground/background consistency across images belonging to the same category, the image level for spatial continuity within each image, and the dataset level for discrimination between classes. The segmentation is based on Otsu’s thresholding but iteratively searches for sub regions of the image for segmentation, instead of treating the full image as a whole region for processing. And further the Neutrosophic thresholding is applied to improve the segmentation result. These methods are combined together and implemented in a new advanced scanning technique called as Positron Emission Tomography (PET). Tests on synthetic and real images showed that the new iterative method and neutrosophic method can achieve better performance than the standard Otsu’s method in many challenging cases, such as
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Identifying weak objects and revealing fine structures of complex objects and also improves the segmentation score. Keywords: Otsu’s thresholding, Triclass, Neutrosophic technique, Segmentation score. 1. Introduction Image segmentation is the process of partitioning a digital image into multiple segments or set of pixels called super pixels. There is various foreground segmentation methods are available to improve classification performance on weakly annotated datasets – those with no additional annotation other than class labels. (1-2) The existing segmentation method is based on Otsu’s iterative tri-class thresholding. Triclass was a new co-segmentation algorithm along with Otsu’s method that looks at all training images jointly and automatically segments out the most class-discriminative foregrounds for each image. It solves the cosegmentation problem by minimizing losses at three different levels.(3) This method is applied only for microscopic images and it is less efficient to noisy images and it also has less segmentation score. The proposed segmentation method has two techniques such as iterative triclass thresholding and Neutrosophic algorithm. This algorithm considers the whole image for processing. (4-5) The objective of the proposed method is to apply segmentation techniques in the scans (Ex: PET) and to make it efficient to operate in various noisy images and also to improve the segmentation score.Matrix Laboratory (MATLAB) is the software used for the convenient extraction of the image which is faster than other computational software.(6-11)
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2. Block Diagram
Fig: Overall operation and analysis of PET image. 3. Input Image Positron emission tomography (PET) is a nuclear medicine exam that produces a three dimensional image of functional processes in the body. It is a highly sensitive non-invasive technology that is ideally suited for pre-clinical and clinical imaging of cancer biology, in contrast to anatomical approaches. (12-17) By using radio labeled tracers, which are injected in non-pharmacological doses, threedimensional images can be reconstructed by a computer to show the concentration and location(s) of the tracer of interest.With the recent advances in molecular/cell biology that have led to target discovery, it is now possible to design specific tracers to image events noninvasively in small animals and humans with positron emission tomography (PET). (18-21) PET is ideally suited for monitoring cell/molecular events early in the course of a disease, as well as during pharmacological or radiation therapy. Furthermore, it can be used for prognostic information and to image for disease recurrence. PET should become increasingly important in cancer imaging in the next decade.(22-27)
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Some common uses of PET To detect cancer To evaluate the heart for blood flow, signs of coronary artery disease or heart function To evaluate the brain for memory disorders, brain tumors or seizure disorders To provide valuable information to physicians in many neurological diseases such as Alzheimer's disease, dementias, Parkinson's disease, Huntington's disease, and Down's Syndrome. Used in Psychiatry, because PET is very sensitive to biological brain alterations during episodes of schizophrenia, depression and other disorders. To provide unique information— including details on both function and anatomic structure of the body that is often unattainable using other imaging procedures. For many diseases, nuclear medicine scans yield the most useful informationneeded to make a diagnosis or to determine appropriate treatment, if any.
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T= arg
σw2(T)
Where σw2(T)=q0(T) σ02(T)+ q1(T) σ12(T) where the subscript 0 and 1 denote the two classes, background and foreground, respectively, and qi and σi , i = [0,1] are the estimated class probabilities and class variances, respectively. These quantities are calculated as q0=
Fig No. 1 A PET image of brain with parkinson’s disease
q1= and the individual class variances are given as Fig No. 2 A PET image of brain with tumor
σ02 σ12
4. Method 4.1 Otsu’s Thresholding The simplest method of image segmentation is called the thresholding method. This method is based on a clip-level (or a threshold value) to turn a gray-scale image into a binary image. There is also a balanced histogram thresholding. (28-31) The key of this method is to select the threshold value (or values when multiple-levels are selected). Several popular methods are used in industry including the maximum entropy method, Otsu's method (maximum variance), and k-means clustering. Recently, methods have been developed for thresholding computed tomography (CT) images. The key idea is that, unlike Otsu's method, the thresholds are derived from the radiographs instead of the (reconstructed) image. Otsu’s method searches the histogram of an image to find a threshold that binarizes the image into two classes, the background with a mean of μ0 and the foreground with a mean of μ1, as shown in the top of Fig. 1. Without loss of generality, here we assume that the foreground is brighter than the background, i.e., μ1 > μ0. The calculation of threshold T is as follows:
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0(T)]
2
1(T)]
2
Where we assume that the pixel values of the image are from0 to K. So from the above equations we can see that T is function of the pixel values of both the foreground and the background. If the signal intensity changes, it may affect Tin such a way that the segmentation result may become less optimal.(32-36) 4.2Triclass Thresholding For an image u, at the first iteration, Otsu’s method is applied to find a threshold T [1] where the superscript denotes the number of iteration. We then find and denote the means of the two classes separated by T [1]as μ0[1] and μ1[1] for the background and foreground, respectively. Then we classify regions whose pixel values are greater than μ1[1] as foreground F[1]and regions whose pixel values are less than μ0[1] as background B[1].For the remaining pixels u(x, y) such that μ0[1] ≤ u(x, y) ≤μ1[1] .we denote them as the TBD class Ω[1]. So our iterative process assumes that the pixels that are greater than the mean of the “tentatively” determined foreground are the true foreground. Similarly, pixels with values less than μ0 are for certain the background. But the
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pixels in the TBD class, which are the ones that typically cause mis-classifications in the standard Otsu’s method, are not decided at once and will be further processed. By our definition, we have U = F[1]
B[1]
Ω[1
where ∪ is the logical union operation. At the second iteration, we apply Otsu’s method to find threshold T [2] on region Ω[1]only. We then calculate the two class means in Ω[1]separated by T [2]as μ0[2]and μ1[2] . Similarly, the second iteration will generate a new F[2], B[2], and Ω[2]such that Ω[1] = F[2] B[2] Ω[2] where F[2]is defined as the region in Ω[1]with pixel values greater than μ1[2], B[2]as the region in Ω[1]with pixel values less than μ0[2] and Ω[2]are the new TBD region. The iteration stops when the difference between two consecutive threshold |T [n+1] − T [n]| is less than a preset threshold. At the last iteration Ω[n +1], Ω[n+1]is separated into two instead of three classes, i.e., foreground F[n+1] is defined as the region of Ω[n] that is greater than T [n+1]instead of μ[n+1] and background B[n+1]is defined as the regions with pixel value less than T [n+1]. The innovation of the new method is to iteratively define the TBD regions to gain a high distance ratio, which will result in better segmentation by applying Otsu’s method.
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artificial images with different levels of noise and real images demonstrate that the proposed approach can reduce the indeterminate of the images and perform thresholding with better result especially, in noisy cases. Let U be a universe of discourse, and W be a set included in U , which is composed by bright pixels. A neutrosophic image Ns P is characterized by three subset T , I and F . A pixel P in the image is described as P(T, I, F) and belongs to W in the following way: it is t% true in the bright pixel set, i% indeterminate, and f % false, where t varies in T , i varies in I , and f varies in F . The pixel P(i, j) in the image domain is transformed into neutrosophic domain PNS( i, j) = {T (i, j) I( i, j) F( i, j)} . T(i, j) , I (i, j) and F(i, j) are the probabilities belong to white set, indeterminate set and non-white set, respectively, which are defined as: T(i.j)= I( i, j)= F(i, j) = 1−T(i, j) Ho(i, j) = abs(e(i, j)) Where HO(i, j) is the homogeneity value of T at (i, j) ,which is described by the local gradient value e(i, j). A λ-mean operation for PNS, PNS(λ ) is defined as:
4.3Neutrosophic Method Neutrosophy, a branch of philosophy, introduced by Florentin Smarandacheas a generalization of dialectics, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. First, the image is transformed into neutrosophic set and a new operation, λ-mean, is employed to reduce the indetermination degree of the image, which is evaluated by the entropy of the indeterminate subset. Then, the image becomes more uniform and homogenous, and more suitable for thresholding. Finally, the image in Ns is thresholded using a histogram thresholding method. The experiments on
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NS
= P ( (λ), (λ),
(λ)
λ
λ
λ
λ
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I( i, j) = References Where (i, j) is the homogeneity value of T(λ) at (i, j) with the local window size. After a λ-mean operation is performed on neutrosophic set PNS, the entropy of the indeterminate subset I is decreased and the distribution of the elements in I becomes more non-uniform. It leads to the decrease of the indetermination of the neutrosophic set PNS. Otsu's method reduces the interclass variance defined by the following equation: σ (t)=c1 (t)σ1 (t)+c2 (t)σ2 (t) where σ (t) is the sum of variances of the two classes as a function of threshold t. σi(t)and ci(t)are the respective variance and probability of class i , i = 1,2. Threshold t that results in the minimization of σ (t) separates the two classes as the foreground and background, respectively. 5. Segmentation Score Segmentation score is nothing but the efficiency of the segmentation algorithm used. In our method, we use the neutrosophic method inorder to increase the efficiency of the scanning images. By using this technique, the score has been improved from 4.1885 to 49.9939 for our input PET image. 6. Conclusion The proposed segmentation algorithm is based on iterative triclass thresholding and Neutrosophic algorithm. These methods are implemented in new scanning technique called Positron Emission Tomography (PET) and it was finely segmented to obtain the high segmentation score than the existing method. In future, noisy images can be segmented using the proposed method.
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