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\title{Supervised Content based image Retrieval using Fuzzy Texton and Shearlet Transform}
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             \author[1]{Sudhakar  Putheti}

             \author[2]{Mohan Krishna  Kotha}

             \author[3]{Srinivasa Reddy  Edara}

             \affil[1]{  Acharya Nagarjuna University}

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\date{\small \em Received: 12 December 2014 Accepted: 1 January 2015 Published: 15 January 2015}

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\begin{abstract}
        


In this paper we proposed, a novel framework to assist and automate the diagnosis of diseases from computer-based image analysis method using Content-based image retrieval (CBIR). CBIR is the process of retrieving related images from large database collections by using low level image features such as color, texture and shape etc. we have used fuzzy texton and discrete shearlet transform to extract texture and shape features. The aim is to support decision making by retrieving and displaying relevant past cases visually similar to the one under examination with relevance feedback using Support Vector Machines.

\end{abstract}


\keywords{content based medical image retrieval, fuzzy texton, texels, and support vector machines.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
he digital imaging revolution in the medical domain over the past three decades has changed the way that the present-day physicians diagnose and treat diseases. These images of various modalities are playing an important role in detecting the anatomical and functional information about different body parts for the diagnosis, medical research, and education. Modern medical information systems need to handle these valuable resources effectively and efficiently. Currently, the utilization of medical images is limited due to the lack of effective search methods; text-based searches have been the dominating approach for medical image database management \hyperref[b0]{[1,}\hyperref[b1]{2]}.\par
Content-based image retrieval (CBIR), also known as query by image content (QBIC) and content based visual information retrieval (CBVIR) is the application of computer vision to the image retrieval problem. Research in content-based image retrieval (CBIR) today is an extremely active discipline. There are already review articles containing references to a large number of systems and description of the technology implemented \hyperref[b0]{[1,}\hyperref[b1]{2]}. A more recent review \hyperref[b2]{[3]} reports a tremendous growth in publications on this topic. Applications of CBIR systems to medical domains already exist \hyperref[b3]{[4]}, although most of the systems currently available are based on radiological images.\par
When referred to text retrieval based on keyword, current technique has already met the demand of the users expectation. As to the demand of digital multimedia retrieval in the network, for instance image, video and many other digital multimedia retrieval. Nowadays there also have some digital multimedia format's search engines which are special for image and mp3 format, for example Google image search engine, but the retrieval methods of these search engines still use the techniques based on text and keywords match. The goal is to retrieve the images based on visual features such as color, texture and shape.\par
Formerly developed commercial content-based image retrieval systems characterized images by global features such as color histogram, texture values and shape parameters, however, for medical images, the systems using global image features failed to capture the relevant information \hyperref[b4]{[5]}.\par
Color is one of the most widely used low-level visual features and is invariant to image size and orientation \hyperref[b5]{[6]}. Various texture representations have been investigated in pattern recognition and computer vision. Basically, texture representation methods can be classified into two categories: structural and statistical. Structural methods, including morphological operator and adjacency graph, describe texture by identifying structural primitives and their placement rules \hyperref[b6]{[7]}. They tend to be most effective when applied to textures that are very regular. Statistical methods, including Fourier power spectra, co-occurrence matrices, Zernike moments, shift-invariant principal component analysis (SPCA), Markov random field, fractal model, and multiresolution filtering techniques such as Gabor and wavelet transform, characterize texture by the statistical distribution of the image intensity \hyperref[b7]{[8]}.\par
Shape has been one of the most important and effective low level visual features in characterizing much pathology identified by medical experts \hyperref[b8]{[9]}. The use of shape as a feature is less developed than the use of color or texture, mainly because of the inherent complexity of representing it \hyperref[b9]{[10]}. Yet, retrieval by shape has the potential of being the most effective search technique in many application fields \hyperref[b10]{[11]}.\par
Support Vector Machines (SVM) \hyperref[b11]{[12]} is an approximate implementation of the structural risk minimization (SRM) principle. It creates a classifier with minimized Vapnik-Chervonenkis (VC) dimension. SVM minimizes an upper bound on the generalization error rate. The SVM can provide a good generalization performance on pattern classification problems without incorporating problem domain knowledge. One key design task, when constructing image databases is the creation of an elective relevance feedback component. While it is sometimes possible to arrange images within an image database by creating a hierarchy, or by handlabeling each image with descriptive words, it is of-ten time-consuming, costly and subjective. Alternatively, requiring the end-user to specify an image query in terms of low level features (such as color and spatial relationships) is challenging to the end-user, because an image query is hard to articulate, and articulation can again be subjective.\par
Recent trials for content-based medical image retrieval were ASSERT system \hyperref[b12]{[13]} for high resolution computed tomography (CT) images of the lung and image retrieval for medical applications (IRMA) system \hyperref[b13]{[14]} for the classification of images into anatomical areas, modalities and viewpoints. Flexible image retrieval engine (FIRE) system handles different kinds of medical data as well as non-medical data like photographic databases  {\ref [15]}.\par
The rest of the paper is organized as follows. In Section II, the proposed image retrieval method steps fuzzy texton detection, shear wavelet transform and support vector machines (SVM) for relevance feedback and texels calculation are discussed. Section III, Experiments, performance evaluations, and discussions are given. 
\section[{II.}]{II.} 
\section[{Proposed Method}]{Proposed Method}\par
An efficient image retrieval technique is required to improve the success rate with the rapid increase in the usage of digital media. The block diagram of the proposed CBIR system is shown in Figure \hyperref[fig_0]{1}.  
\section[{a) Extraction of Fuzzy Texton Images}]{a) Extraction of Fuzzy Texton Images}\par
Fuzzy Texton is a way to describe the texture property further better than the Texton since Fuzzy texton uses the fuzzy texture unit (FTU) instead of texture unit (TU). By including fuzzy concept to the texton will generates all ranges of the values including '2' in the FTU \hyperref[b16]{[16,}\hyperref[b17]{17]}. Then, it helps to generates different textures are 5 8 instead of 4 8 . The main idea of the proposed method (TFT) is, Texton images are obtained by applying the 12 types of 3 x3 texton templates \hyperref[b18]{[18]}.\par
As per Julesz description a texton is a pattern which is shared by an image as a common property \hyperref[b19]{[19]}. Textures which can be decomposed into elementary units, the texton are formed only if the adjacent elements lie within the neighborhood. The critical distances between texture elements which depend on the texture element size are used to incline the texton. Textons are classes of colors, elongated blobs of specific width, orientation, aspect ratios and terminators of elongated blobs. If texture elements are greatly expanded in one orientation, discrimination reduces. If the elongated elements are not jittered in orientation, texture gradients increase at boundaries. Thus with a small sub image of size 3 x 3 is used to obtain texton gradient. In the previous proposed technique TFT \hyperref[b18]{[18]}, we have proposed 12 textons of 3 x 3 grids. The computational complexity for using the 
\section[{Global Journal of C omp uter S cience and T echnology}]{Global Journal of C omp uter S cience and T echnology}\par
Volume XV Issue I Version I Year ( ) overlapped components of 12 textons is also less to obtain final texton image.\par
The basic unit of the method is defined by a central pixel and its eight neighbors, forming a 3x3 pixel square. This minimal square image has the local texture information of the central pixel in all the directions.\par
In our case the size of the neighborhood is 3x3 pixels. This pattern of the image, consisting by 9 pixels, is denoted by a set V of nine elements, V= \{V 0 , V 1 , V 2 ? V 8 \}, where V 0 represents the intensity value of the central pixel and V i (1?i?8) the intensity value of each neighboring pixel. The smallest complete unit which best characterizes the local texture aspect of a given pixel and its neighborhoods, in all eight directions of a square raster, is Texture Unit (TU) that is defined, by TU=\{E 1 , E 2 , ?,E 8 \}, where:E i = ? ? ? ? ? 0 if V i < V 0 and V i < ?? 1 if V i < V 0 and V i > ?? 2 if V i = V 0 ; 3 if V i > V 0 and V i < ?? 4 if V i > V 0 and V i > ?? 1 ? i ? 8 (1)\par
here p and q are user defined values and each element E i occupies the same position as pixel i. An example is shown in Figure \hyperref[fig_0]{1}. As to each element of the TU can be assigned one of three possible values 0, 1,2,3 or 4, the total number of Texture Units is 5 8 = 16777216. These Units can be labeled and ordered in different ways; here we will label each TU as a 5-base number, named Texture Unit Number, N TU according to next formula:N TU = ? E i ? 5 i?1 2 8 i=1 (2)\par
Where the position of the Texture Unit box and E i is the value of the box (0, 1, 2, 3 or 4). Moreover, the 8 elements can be ordered differently. If they are ordered clockwise, as shown in Figure \hyperref[fig_0]{1}(c), the first element can take eight possible positions, from the top left a to the middle left h, and then the 16777216 texture units can be labeled by the abode formula under eight different ordering ways (from a to h).\par
A more detail study of texture unit indicates that the absent TU's involve two's in their texture unit. This is the case when neighbors and central pixels have the same values. If there is a lack of two's then TU will take only 0,1,3 and 4 which means that the possible real number of different textures are 4 8 instead of 5 8 , that is 65536 and 390625 the spectrum will be never totally covered, thus the power of the method is misused. It impacts on texture Unit number also. To overcome this, fuzzy texture is used in the proposed method. Fuzzy Texton is a way to describe the texture property further better than Texton.\par
Fuzzy Texton is a way to describe the texture property further better than the Texton since Fuzzy texton uses the fuzzy texture unit (FTU) instead of texture unit (TU). By including fuzzy concept to the texton will generates all ranges of the values including '2' in the FTU \hyperref[b20]{[20]}. Then, it helps to generates different textures are 5 8 instead of 4 8 . It covers total spectrum which is not possible by texton only (means without fuzzy) \hyperref[b21]{[21]}. The main idea of the proposed method (TFT) is, Texton images are obtained by applying the 12 types of 3 x3 texton templates \hyperref[b22]{[22]} as shown in figure \hyperref[fig_3]{4} on HSV planes as shown in figure \hyperref[fig_2]{3}.\par
We used the Fuzzy Texture unit boxes (FTUB) and Fuzzy Texture Unit Numbers (FTUN) which are used by Aina Barceló. et. al \hyperref[b20]{[20]}. In this proposed work, FTUB and FTUN are used during the period of quantifying the texton images. Then, the resultant textons are called as fuzzy texton images. Using fuzzy techniques provide a more flexible way of assigning values (E i ) to the TU boxes. From now on E i will not be a unique value 0, 1, 2, 3 or 4, but it will have the five values associated at the same time, each one to its own degree. Each particular degree will be calculated with the aid of a membership function that has to be defined. Therefore, we will consider Fuzzy Texture Unit Boxes (FTUB) FE i that are defined as follows:???? ?? = \{?? 0 (?? ?? ), ?? 1 (?? ?? ), ?? 2 (?? ?? ), ?? 3 (?? ?? ), ?? 4 (?? ?? )\}, 1 ? ?? ? 8\textbf{(3)}\par
Where in ? 0 (V i ),? 1 (V i ),? 2 ( Vi ), ? 3 (V i ) and ? 4 (V i ) are the membership degrees of V i \hyperref[b20]{[20]} to the fuzzy sets 0, 1, 2, 3 and 4 respectively. In a similar way to the TU, the Fuzzy Texture Unit (FTU) is defined by: Global Journal of C omp uter S cience and T echnology Volume XV Issue I Version I Year ( )?????? = \{???? 1 , ???? 2 , ???? 3 , ???? 4 , ???? 5 , ???? 6 , ???? 7 , ???? 8 \} (4)\par
As part of the detection process of fuzzy texton, our 3 x 3 grids can detects the textons in all directions and also corners of the textures. If three pixels are highlighted and have the same value then grid will form a fuzzy texton as shown in Figure \hyperref[fig_5]{5}. 
\section[{b) Edge Orientation using Discrete Shearlet Transform}]{b) Edge Orientation using Discrete Shearlet Transform}\par
The approach used in this paper is based on a new multiscale transform called the shearlet transform. It is multidimensional version of the traditional wavelet transform, and is especially designed to address anisotropic and directional information at various scales. Indeed, the traditional wavelet approach, which is based on isotropic dilations, has a very limited capability to account for the geometry of multidimensional functions. In contrast, the analyzing functions associated to the shearlet transform are highly anisotropic, and, unlike traditional wavelets, are defined at various scales, locations and orientations. As a consequence, this transform provides an optimally efficient representation of images with edges \hyperref[b23]{[23]}. The shearlet transform has similarities to the curvelet transform, Shearlets and curvelets, in fact, are the only two systems which were mathematically known to provide optimally sparse representations of images with edges and the implementations of the curvelet transform correspond to essentially the same tiling as that of the shearlet transform. Both systems are related to contourlets \hyperref[b26]{[26]}, \hyperref[b27]{[27]} and steerable filters \hyperref[b28]{[28]}, \hyperref[b29]{[29]}. We refer to \hyperref[b30]{[30]} for more details about the comparison of shearlet and other orientable multiscale transforms.\par
In this paper, we combine the shearlet framework with several well established ideas from the image processing literature to obtain improved and computationally efficient algorithms for edge analysis and detection. Our approach may be viewed as a truly multidimensional refinement of the approach of Mallat et al., where the isotropic wavelet transform is replaced by an anisotropic directional multiscale transform. As a result, the shearlet transform acts as a multiscale directional difference operator and provides a number of very useful features: Improved accuracy in the detection of edge orientation. Using anisotropic dilations and multiple orientations, the shearlet transform precisely captures the geometry of edges. It is a multiscale transform, based on the same affine mathematical structure of traditional wavelets. The discretization of the shearlet transform provides a stable and computationally efficient decomposition and reconstruction algorithm for images. An algorithm for edge detection based on shearlets was introduced in \hyperref[b24]{[24,}\hyperref[b25]{25]}, where a discrete shearlet transform was described with properties specifically designed for this task. In fact, the discrete shearlet transform which was presented above for image denoising, produces large side lobes around prominent edges which interfere with the detection of the edge location. By contrast, the special discrete shearlet transform introduced in \hyperref[b24]{[24,}\hyperref[b25]{25]} is not affected by this issue since the analysis filters are chosen to be consistent with the theoretical results in \hyperref[b31]{[31,}\hyperref[b32]{32]}, which require that the shearlet generating function ? satisfies certain specific symmetry properties in the Fourier domain.\par
The first step of the shearlet edge detector algorithm consists in selecting the edge point candidates of a digital image u[m1,m2]. They are identified as those points (?? 1 ????, ?? 2 ????) which, at fine scales j, are local maxima of the function?? ?? ??[?? 1 , ?? 2 ] 2 = ? ???????[??, ??, ?? 1 , ?? 2 ] ? 2 ?? (5)\par
Here ??????[??, ??, ?? 1 , ?? 2 ] denotes the discrete shearlet transform. According to the properties of the continuous shearlet transform summarized above, we expect that, if (?? 1 ????, ?? 2 ????)is an edge point, the discrete shearlet transform of u will behave as|??????[??, ??, ?? 1 ????, ?? 2 ????]|\textasciitilde ??2 ????? (6)\par
Where ? ? 0. If, however, ? < 0 (in which case the size of |SHu| increases at finer scales), then (?? 1 ????, ?? 2 ????)will be recognized as a spike singularity and the point will be classified as noise. Using this procedure, edge point candidates for each of the oriented components are found by identifying the points for which ? ? 0. Next, a non-maximal suppression routine is applied to these points to trace along the edge in the edge direction and suppress any pixel value that is not considered to be an edge. At each edge point candidate, the magnitude of the shearlet transform is compared with the values of its neighbors along the gradient direction (this is obtained from the orientation map of the shearlet decomposition). If the magnitude is smaller, the point is discarded; if it is the largest, it is kept. Extensive numerical experiments have shown that the shearlet edge detector is very competitive against other classical or state-of-the-art edge detectors, and its performance is very robust in the presence of noise. An 
\section[{Global Journal of C omp uter S cience and T echnology}]{Global Journal of C omp uter S cience and T echnology}\par
Volume XV Issue I Version I Year ( ) example is displayed in Figure \hyperref[fig_4]{12}, where the shearlet edge detector is compared against the wavelet edge detector (which is essentially equivalent to the Canny edge detector) and the Sobel and Prewitt edge detectors. Notice that both the Sobel and Prewitt filters are 2D discrete approximations of the gradient operator. The performance of the edge detectors is assessed using the Pratt's Figure of Merit, which is a fidelity function ranging from 0 to 1, where 1 is a perfect edge detector. This is defined as?????? = 1 ?????? (?? ?? ,?? ?? ) ? 1 1+???? (??) 2\par
?? ?? ??=1 \hyperref[b6]{(7)} where ?? ?? is the number of actual edge points, ?? ?? is the number of detected edge points, d(k) is the distance from the k-th actual edge point to the detected edge point and ? is a scaling constant typically set to 1/9. The numerical test reported in the figures show that the shearlet edge detector consistently yields the best value for FOM.\par
These properties lead directly to a very effective algorithm for the estimation of the edge orientation, which was originally introduced in \hyperref[b25]{[25]}. Specifically, by taking advantage of the parameter associated with the orientation variable in the shearlet transform, the edge orientations of an image u, can be estimated by searching for the value of the shearing variable s which maximizes ???? ? ??(??, ??, ??) at an edge point p, when a is sufficiently small. Discretely, this is obtained by fixing a sufficiently fine scales (i.e.,?? = 2 ?2?? sufficiently "small") and computing the index ?? ?which maximizes the magnitude of the discrete shearlet transform ??????[??, ??, ??] as?? ?(??, ??) = ???????????? ?? |??????[??, ??, ??]|\textbf{(8)}\par
Once this is found, the corresponding angle of orientation ?? ?? ?(??, ??) associated with the index ?? ?(??, ??)can be easily computed. As illustrated in \hyperref[b25]{[25]}, this approach leads to a very accurate and robust estimation for the local orientation of the edge curves. To illustrate the general principle, consider the simple image in Figure \hyperref[fig_4]{13} consisting of large smooth regions separated by piecewise smooth curves. The junction point A, where three edges intersect, is certainly the most prominent object in the image, and this can be easily identified by looking at values of the shearlet transform. In fact, if one examines the discrete shearlet transform ??????[?? 0 , ??, ?? 0 ], at a fixed (fine) scale ?? 0 and locations?? 0 , as a function of the shearing parameter l, the plot immediately identifies the local geometric properties of the image. Specifically, as illustrated in Figure \hyperref[fig_4]{13}(b), one can recognize the following four classes of points inside the image. At the junction point ?? 0 = ??, the function |??????[?? 0 , ??, ?? 0 ]| exhibits three peaks corresponding to the orientations of the three edge segments converging into A; at the point ?? 0 = ??, located on a smooth edge, |??????[?? 0 , ??, ?? 0 ]| has a single peak; at a point ?? 0 = ??, inside a smooth region, |??????[?? 0 , ??, ?? 0 ]| is essentially flat; finally, at a point ?? 0 = ??"close" to an edge,|??????[?? 0 , ??, ?? 0 ]| exhibit two peaks, but they are much smaller in amplitude than those for the points A and B. A similar behaviour was observed, as expected, for more general images, even in the presence of noise. Based on these observations, a simple and effective algorithm for classifying smooth regions, edges, corners and junction points of an image was proposed and validated in  {\ref [52]}. 
\section[{c) Support Vector Machine for Relevance Feedback}]{c) Support Vector Machine for Relevance Feedback}\par
Consider the binary classification problem \{(xi, yi)\}, for i=1 to N, where xi are the labeled patterns and yi? \{?1, +1\} the corresponding labels. Based on this training set, we want to train an SVM classifier. The SVM classifier maps the patterns to a new space, called kernel space, using a transformation x ? ?(x), in order to get a potentially better representation of them. This new space can be nonlinear and of much higher dimension than the initial one. After the mapping, a linear decision boundary is computed in the kernel space. In the context of SVM methodology, the problem of classification is addressed by maximizing the margin, which is defined as the smallest distance, in the kernel space, between the decision boundary and any of the training patterns. This can be achieved by solving the following quadratic programming problem:?????? ?? ?? ?? ?? ??=1 ? 1 2 ? ? ?? ?? ?? ?? =1 ?? ??=1\par
?? ?? ?? ?? ?? ?? ????? ?? , ?? ?? ?? over ?? ?? , i=1,?,N\par
Such that 0 ? ?? ?? ? ?? and? ?? ?? ?? ??=1 ?? ?? = 0\textbf{(10)}\par
Where????? ?? , ?? ?? ? = ??(?? ?? ) ?? ????? ?? ?\textbf{(11)}\par
is the kernel function and C is a parameter controlling the trade-off between training error and model complexity. The most popular non-linear kernel functions used for SVMs belong to the class of Radial Basis Functions (RBFs). From all RBF functions, the most commonly used is the Gaussian RBF, which is defined by:????? ?? , ?? ?? ? = ?????? ??????? ?? ? ?? ?? ? 2 ?\par
After the training of the classifier, the value of the decision function for a new pattern x is computed by:??(??) = ? ?? ?? ?? ??=1 ?? ?? ??(?? ?? , ??) + ??\par
Where b is a bias parameter the value of which can be easily determined after the solution of the Year ( ) optimization problem \hyperref[b33]{[33]}. The value |y(x)| is proportional to the distance of the input pattern x from the decision boundary. Thus, the value y(x) can be regarded as a measure of confidence about the class of x, with large positive values (small negative values) strongly indicating that x belongs to the class denoted by +1 (?1). On the contrary, values of y(x) around zero provide little information about the class of x. 
\section[{d) Extraction of Texels}]{d) Extraction of Texels}\par
After the extraction of fuzzy texton images need to extract the texels from them. The local properties \hyperref[b18]{[18]} used to extract the feature vectors used here come under two categories: one is regarding color information and other is about texture. Some of the important features of texture properties (cluster properties) are Local Homogeneity, Cluster Shade and Cluster Prominence. \par
ii) Color Variance?? ?? = ( 1 ?? ? (?? ???? ?? ?? ) 2 ?? ?? =1 ) 1 2\textbf{(17b)}\par
iii) Skewness?? ?? = ( 1 ?? ? (?? ???? ?? ?? ) 3 ?? ?? =1 )\textbf{1 3}\par
(18) In the framework of CBIR with RF, in each round of RF we have to solve a classification problem as the one described above, where a number of images, represented as feature vectors, correspond to the feedback examples provided by the user so far, and each image is labeled by ?1 or +1 corresponding to irrelevant or relevant, respectively. The initial query is considered to be one of the relevant images and is labeled by +1. From the above, it is obvious that we can train an SVM classifier based on the feedback examples and use it to distinguish between the classes of relevant and irrelevant images. Each image in the database will be presented to the trained classifier and the value of the decision function (Eq. (  {\ref 5})) will be used as the ranking criterion. The higher the value of the decision function for an image, the more relevant this image is considered by the system. III. 
\section[{Results and Discussion}]{Results and Discussion}\par
The effectiveness of the proposed retrieval system is evaluated on fundus image database, Skin cancer image database and Endoscopy image database. The sample images from the fundus image database are shown in the figure \hyperref[fig_5]{5}.   We can use different distance metrics for matching such as an N-dimensional feature vector F = [F1, F2...FN]. It is extracted from every image of database and stored in database. Let Q = [Q1, Q2, Q3,?,QN] be the feature vector of query image. A simple distance measure \hyperref[b34]{[34]} whose time complexity is very less when compared with others like Euclidean (no square or square root operations) when we consider large databases, is given by(F, Q) = ? |F i ?Q i | 1+F i +Q i N i=0\textbf{(19)} 
\section[{b) Performance Measure}]{b) Performance Measure}\par
Most common measurements are used to evaluate the performance of image retrieval methods are Precision, Recall and Accuracy curves \hyperref[b35]{[35]}.\par
Precision ??(??) = ?? ?? ?? \hyperref[b20]{(20)} Recall ??(??) = ?? ?? ?? \hyperref[b21]{(21)} Accuracy ??(??) = (??(??)+??(??)) 2 \hyperref[b22]{(22)} Where I N is the number of images retrieved in the top N positions that are similar to the query image and M is the total number of images in the database similar to the query image. In all cases the framework provides higher precision, recall and accuracy. 
\section[{Global Journal of C omp uter S cience and T echnology}]{Global Journal of C omp uter S cience and T echnology}\par
Volume XV Issue I Version I Year ( )\begin{figure}[htbp]
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