An Efficient CT Image Reconstruction with Parallel Modeling for Superior Quantitative Measures

An Efficient CT Image Reconstruction with Parallel Modeling for Superior Quantitative Measures

S.Asif Hussain1 K. Lokeswara Reddy2

Associate professor M.Tech (E.S) student Department of ECE, A.I.T.S, Department of ECE, Rajampet, Andhra Pradesh, India A.I.T.S Rajampet, A.P, India e-mail: sah.ssk@gmail.com e -mail: lokes9@gmail.com

ABSTRACT

Image segmentation algorithms based on ROI typically rely on the homogeneity of image intensities. CT scanner is dedicated as research Scanner which has been developed in view of imaging applications. A key Feature of the work is to use Empirical system to achieve resolution recovery with novel region based method. This method identifies local intensity cluster with local clustering criterion function with respect to neighborhood center. Reconstruction quality is analyzed quantitatively in terms bias field correction for intensity inhomogenity correction. This method is valid on synthetic images of various imaging modalities. A significant improvement in reconstruction quality can be realized by faster and more accurate visual quality quantitative measures where Reconstruction quality is analyzed quantitatively in terms of bias-variance measures (bar phantom) and mean square error (lesion phantom). However, with the inclusion of the empirical kernel, the iterative algorithms provide superior reconstructions compared to FBP, both in terms of visual quality and quantitative measures. Simulated results show improved tumor bias and variance characteristics with the proposed algorithm.

Keywords: Intensity inhomogeneities, Empirical system kernel, Bias-variance, Iterative algorithms

1. INTRODUCTION

   Image segmentation is often an essential step before further image-processing of three-dimensional medical images canbe done. An object can be segmented based on shape and/or intensity characteristics. The task of image segmentation can be simplified with initialized parameters to guide accurate segmentation. Semi-automated and interactive methods [1] have been relatively successful, but require varying degrees of human input. Segmentation is often an important step in US B-mode image analysis .we consider the problem of correcting for attenuation-related intensity inhomogenieties i.e., those that cause a slowly changing (low-frequency) intensity contrast and are not due to speckle-mode imaging artifacts include speckle noise, attenuation(absorption and scattering), etc. The statistical analysis and reduction of speckle noise has been studied extensively in the literature [1][7]. Other artifacts, particularly those caused by non uniform beam attenuation within the body that are not accounted for by time gain compensation (TGC), also decrease the image signal-to-noise ratio (SNR).Existing level set methods for image segmentation can be categorized into two major classes: region-based models [4], [10], and edge- based models [3], [7], [8], [12]. Region-based models aim to identify each region of interest by using a certain region descriptor to guide the motion of the active contour. However, it is very difficult to define a region descriptor for images with

   intensity inhomogeneities. Most of region-based models [4],

   [16] are based on the assumption of intensity homogeneity. Edge-based models use edge information for image segmentation. These models do not assume homogeneity of image intensities, and thus can be applied to images with intensity inhomogeneities. A novel region-based method for image segmentation. From a generally accepted model of images with intensity inhomogeneities, we derive a local intensity clustering property, and therefore define a local clustering criterion function for the intensities in a neighbourhood of each point. This local clustering criterion is integrated over the neighbourhood center to define an energy functional, which is converted to a level set formulation. Minimization of this energy is achieved by an interleaved process of level set evolution and estimation of the bias field. As an important application, our method can be used for segmentation and bias correction of magnetic resonance(MR) images.

2. Methods:

   BACKGROUND:

   In this section, we review the method proposed by Zhang for estimating the field distortion and simultaneously segmenting an MR image and provide implementation details on how it has been adapted to work with US images. This method essentially estimates the low (spatial)-frequency multiplicative degradation field while at the same time identifying regions of similar intensity inhomogeneity using an MRF-MAP frame work. As we will explain in Section III, although developed for another imaging modality, under simplified assumptions, we can justify using the same approach on displayed US images.

   1. Model Specification:

      Let S be a lattice indexing the pixels in the given image. Further,

      let and be the observed and the ideal (that is, without intensity inhomogeneity distortion) intensities of the given image respectively, being the number of pixels in the image. We assume that the distortion at pixel can be expressed by a multiplicative model of the form

      Whererepresents the gain of the intensity due to the intensity inhomogeneity at pixel . A logarithmic transformation of this equation yields an addition. Let anddenote, respectively ,the observed and the ideal log- transformed intensities, then

      Where denotes the log-transformed intensity distortion field. Segmentation can be considered as a problem of statistical classification, which is to assign every pixel a class label from a label set. Let denote the label set. A labeling

      of will be denoted by in is the corresponding class label of Given the class label , it is assumed that the intensity value at follows a Gaussian distribution(this assumption will be justified in

      Section III) with parameter being the mean and the variance of class respectively

      where

      With the distortion field taken into account, the above distribution can be written in terms of the observed intensity as

      (4)

      and, hence, a class-independent intensity distribution

      (5)

      Thus, the intensity distribution at is modeled as a Gaussian mixture, given the distortion field. Assuming that the pixel intensities are statistically independent, the probability density for the entire image, given the distortion field,

      (6)

      Bayes rule can be used to obtain the posterior probability of the distortion field, given the observed intensity values

      (7)

      Where is a normalization constant. The prior probability density of the distortion is modeled as a Gaussian with zero mean to capture its smoothness property. The maximum a posteriori (MAP) principle can be employed to obtain the optimal estimate of the distortion field , given the observed intensity values

      . (8)

      The optimum satisfies the following condition

      . (9)

      Solving this equation leads to the update equations (see [12] for detail)

      , with I= (1,1,,1 . (11)

      Here, is the posterior probability that belongs to class given the distortion field is a low-pass filter, is the mean residual in which for pixel

      (12)

      And is the mean inverse covariance, in which if otherwise.

      (13)

   2. Bayesian criterion for filtering edge information:

      It is assumed that interpolated boundaries will partially overlap with the true edges found using edge detection. The probability of edges overlapping with shape-interpolated boundaries may be modeled using Bayes probability. It is assumed that the probability of overlap at interpolated slces is greater than or equal to that at user-initialized contours. Edges are divided into edge components based on their connectivity. To retain edges with higher saliency, the edge components are sorted in descending order relative to the amount of overlap with the boundary. When the cumulative probability of overlap exceeds that obtained from user initialized contours, the remaining edge components are discarded. The Bayes classification is thus not employed for training, but rather as a guide to how well boundaries can be defined based on edge detection.

3. Proposed Algorithms:

   1. The 3-D Case:

      The algorithm can be applied to 3-D volumes reconstructed from a sequence of parallel, closely spaced 2-D images. We assume that in such a sequence neighbouring slices resemble each other, that is, overlapping pixels in neighbouring slices tend to have the same class labels. Intensity in homogeneity field estimation is performed within each 2-D image, while the energy function in the MRF prior model involves a 3-D neighbourhood system, which includes, for each pixel in a 2- D scan, the eight nearest neighbours in the same scan and the two direct neighbours in the previous and the next scan. This 3-D constraint helps to strengthen ambiguous boundaries that are easily mislocated in2-D processing.

   2. Boundary-edge correspondence:

      Ideally, the match between boundary and edge should be one- to-one. However, deviations in the interpolated shape will not initialize Bi well. To prevent many-to-one snapping of boundary points, a minimum snapping-distance map is stored for every edge point. Subsequent boundary points will only be allowed to snap to the edge point if the snapping distance is less than or equal to the value in the minimum snapping- distance map. Therefore, boundary points will not arbitrarily snap to false edges if there are no edges to be found. During

      the first iteration, the search window has not been adaptively altered to match the edge proximity for the image slice. There is a possibility that a false edge will be included in the Bayesian criterion. To prevent this, an inverse weighted distance transform, M, is multiplied to Fi,k, where M is a square matrix. Denoting pq M as an element in M and any two points on the Bi as bp and bq.,pq M is defined in Eq. 1.

      (1)

   3. Local Intensity Clustering Property:

      Region-based image segmentation methods typically relies on a specific region descriptor (e.g. intensity mean or a Gaussian distribution) of the intensities in each region to be segmented. However, it is difficult to give such a region descriptor for images with intensity inhomogeneities. Moreover, intensity inhomogeneities often lead to overlap between the distributions of the intensities in the Therefore, it is impossible to segment these regions directly based on the pixel intensities

      .Nevertheless, the property of local intensities is simple

      ,which can be effectively exploited in the formulation of our method for image segmentation with simultaneous estimation of the bias field based on the image model in (3) and the assumptions A1and A2, we are able to derive a useful property of local intensities, which is referred to as a local intensity clustering property as described and justified below. To be specific, we consider a circular neighbourhood with a radius centered at each point defined by .The of the entire

      domain induces a partition of the neighbourhood

      , i.e., forms a partition of . For as lowly varying bias field the values for all in the circular Neighbourhood are close to i.e. for

      (4)

      Thus, the intensities in each sub are close to the constant i.e.

      (5)

      Then, in view of the image model in (3), we have

      Where is additive zero-mean Gaussian noise. Therefore, the intensities in the set

      form a cluster with cluster which can be considered as samples drawn from a Gaussian distribution with mean . Obviously , the clusters ,, , are well-separated ,with distinct cluster centers

      , (because the constants

      are distinct and the variance of the Gaussian noise is assumed to be relatively small). This local intensity clustering property is used to formulate the proposed method for image

      segmentation and bias field estimation as follows.

   4. Energy Formulation:

      The above described local intensity clustering property indicates that the intensities in the neighbourhood can be classified in to clusters with centers

      , This allows us to apply the standard K-means clustering to classify these local intensities. Specifically, for the in the neighbourhood

      , the K-means algorithm is an iterative process to minimize the clustering criterion [19], which can be written in a continuous form as

      (6)

      Where is the cluster center of the cluster, is the

      mem and for Since is the membership function of the region , we can rewrite as

      dx. (7)

      In view of the clustering criterion in (7) and the approximation of the cluster center by

      we define a clustering criterion for classifying

      the intensities in as (8)

      Where is introduced as a nonnegative window

      function, also called kernel function, such that for .With the window function, the clustering criterion function can be rewritten as

      (9)

      This local clustering criterion function is a basic element in the formulation of our method.

   5. Multiphase Level Set Formulation:

      For the case of we can use two or more level set functions to define membership functions of the regions , such that

      .

      For example, in the case of , we use two level set functions to define

      And to give a three-phase level set formulation of our method. For the four-phase case ,

      the definition of can be defined as

      functional in our multiphase level set formulation is defined by

      . (25)

      The minimization of the energy in (25) with respect tto the variable can be performed by solving the following gradient flow equations:

      and

      For notational simplicity, we denote these level set functions by a vector valued function .

      Thus, the membership functions can ) be written as . The energy in (10) can be converted

      to a multiphase level set formulation .

      With given by .

      (16). For the function .

      This defines the regularization Terms and ,

      Where and are defined by (19) and (20) for

      each level set function , respectively. The energy .

4. IMPLEMENTATION AND SIMULATION RESULTS:

   Fig 3. Iterations are Performed to the Input Image

   Fig 1. showsInput Of CT Image of bones

   Fig 2. gives Histogram of CT Image With Density

   50 iterations

   Fig 4. CT image with 50 Iterations

   Fig 5. Blurring Of Input Image for Checking from Initial Point of the Image

   Bias corrected image

   Fig 6. Input Image Of Bias Corrected Image

   Histogram of Bias corrected image

   200

   180

   160

   Author Profile:

   Lokeswar Reddy.Kokatam received B.Tech Degree in Electronics& Communication Engg. from JNT University, Annanthapur, India. Presently he is with Annamacharya Institute of Technology & Sciences,

   Rajampet, A.P., India in Dept. of ECE and pursuing his M.Tech. His research interests include Signal Processing, Time Series Analysis and Image Processing.

   Asif Hussian.Shaik received B.Tech & M.Tech Degree in Electronics & Communication Engg. from JNT University, Hyderabad, India. He is currently working towards PhD Degree in Biomedical Image

   Processing at JNTU University, Annantapur, India. Presently he is with Annamacharya Institute of Technology & Sciences, Rajampet, A.P., India. He is working as Assistant Professor in Dept. of ECE. He presented many research papers in National & International Conferences & journals. He is a member of Professional societies like ISTE (India), BMESI (India), IACSIT (Singapore), IAENG (Hongkong) and WASE (Hongkog).His research interests include Signal Processing, Time Series Analysis and Image Processing.

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      Fig 7. Image describes Histogram of Bias Corrected Image

5. Conclusion:

   This work presents a variational level set framework for segmentation and bias correction of images with intensity inhomogeneities. Based on a generally accepted model of images with intensity inhomogeneities and a derived local intensity clustering property, the work defines an energy of the level set functions that represent a partition of the image domain and a bias field that accounts for the intensity inhomogeneity. Segmentation and bias field estimation are therefore jointly performed by minimizing the proposed energy functional. The slowly varying property of the bias field derived from the proposed energy is naturally ensured by the data term in our variational framework, without the need to impose an explicit smoothing term on the bias field. The proposed method is much more robust to initialization than the piecewise smooth model. Experimental results have demonstrated superior performance of our method in terms of accuracy, efficiency, and robustness.

6. ACKNOWLEDGMENTS:

The work was supported by my guide S.Asif Hussain from Annamacharya Institute of Technology & Sciences,,Rajampet ,India under Research grants of R.P.S A.I.C.T.E, New delhi.

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