A Level Set Method for Image Segmentation in the Presence of Intensity in homogeneities with Application to MRI(2011)

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INTRODUCTION

We propose a novel region-based method for image segmentation, which is able to deal with intensity inhomogeneities in the segmentation. First, based on the model of images with intensity inhomogeneities, we derive a local intensity clustering property of the image intensities, and de?ne a local clustering criterion function for the image intensities in a neighborhood of each point. This local clustering criterion function is then integrated with respect to the neighborhood center to give a global criterion of image segmentation.In a level set formulation, this criterion de?nes an energy in terms of the level set functions that represent a partition of the image domain and a bias ?eld that accounts for the intensity inhomogeneity of the image.Therefore, by minimizing this energy, our method is able to simultaneously segment the image and estimate the bias ?elds, and the estimated bias ?eld can be used for intensity inhomogeneity correction (or bias correction). Our method has been validated on synthetic images and real images of various modalities, with desirable performance in the presence of intensity inhomogeneities. Experiments show that our method is more robust to initialization, faster and more accurate than the well-known piecewise smooth model. As an application, our method has been used for segmentation and bias correction of magnetic resonance (MR) images with promising results.

OVERVIEW

Intensity inhomogeneity often occurs in real-world images, which presents a considerable challenge in image segmentation. The most widely used image segmentation algorithms are region-based and typically rely on the homogeneity of the image intensities in the regions of interest, which often fail to provide accurate segmentation results due to the intensity in-homogeneity. This paper proposes a novel region-based method for image segmentation, which is able to deal with intensity inhomogeneities in the segmentation. First, based on the model of images with intensity inhomogeneities, we derive a local intensity clustering property of the image intensities, and define a local clustering criterion function for the image intensitiesin a neighborhood of each point. This local clustering criterion function is then integrated with respect to the neighborhood center to give a global criterion of image segmentation. In a level setformulation, this criterion defines an energy in terms of the level setfunctions thatrepresenta partition of the image domain and a bias field that accounts for theintensity inhomogeneity of the image. Therefore, by minimizing this energy, our method is able to simultaneously segment the image and estimate the bias field, and the estimated bias field can be used for intensity inhomogeneity correction (or bias correction). Our method has been validated on synthetic images and real images of various modalities, with desirable performance in the presence of intensity inhomogeneities. Experiments show that our method is more robust toinitialization, faster and more accurate than the well-known piecewise smooth model.As an application, our method has been used for segmentation and bias correction of magnetic resonance (MR) images with promising results.

EXISTING SYSTEM

The level set method, originally used as numerical technique for tracking interfaces and shapes, has been increasingly applied to image segmentation in the past decade. In the level set method, contours or surfaces are represented as the zero level set of a higher dimensional function, usually called a level set function. With the level set representation, the image segmentation problem can be formulated and solved in a principled way based on well-established mathematical theories, including calculus of variations and partial differential equations (PDE).

Existing level set methods for image segmentation can be categorized into two major classes: region-based models and edge-based models.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 are based on the assumption of intensity homogeneity. a typical example is piecewise constant (pc) models proposed.in level set methods are proposed based on a general piecewise smooth (ps) formulation originally proposed by mumford and shah. these methods do not assume homogeneity of image intensities, and therefore are able to segment images with intensity inhomogeneities. however, these methods are computationally too expensive and are quite sensitive to the initialization of the contour which greatly limits their utilities.

Disadvantages

It is very dif?cult to de?ne a region descriptor for images with intensity inhomogeneities in Region-based model.

Existing methods are computationally too expensive and are quite sensitive to the initialization of the contour, which greatly limits their utilities.

Edge based model do not assume homogeneity of image intensities, and thus can be applied to images with intensity inhomogeneities.

PROPOSED SYSTEM

We propose 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 de?ne a local clustering criterion function for the intensities in a neighborhood of each point. This local clustering criterion is integrated over the neighborhood center to de?ne 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 ?eld.

Advantages

Our method can be used for segmentation and bias correction of magnetic resonance (MR) images.

The slowly varying property of the bias ?eld 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 ?eld. Our method is much more robust to initialization than the piecewise smooth model.

MODULES DESCRIPTION

  • Variational framework for joint segmentation and Bias field estimation

  • Level set formulation and Energy minimization

  • Method comparison

VARIATIONAL FRAMEWORK FOR JOINT SEGMENTATION AND BIAS FIELD ESTIMATION

This module deal with intensity inhomogeneities in image segmentation, we formulate our method based on an image model that describes the composition of real-world images, in which intensity inhomogeneity is attributed to a component of an image. Local Intensity Clustering Property and Energy Formulation are other two models in this module.

This part of the code in the application uses the approach to handle the elements like level set spline.

This is representing the image with RGB concentration verification and tracing its curvature property like its weight.Applying the filters by extracting their  and setting their threshold values to make the image identical in intensities it also involves the reading of image  pixel by pixel

filter the images and the storage time and tracing of similar intensity pixel elements .The image is converted  to unique intensity pixel set by using the gradient magnitude  cubic spline method .This process generate the output of the image with the specified properties of unique  or individual bias components by generating the duplicate itemsets of pixels.The pixels that are traced are assigned with a constant coefficient value that increases the magnitude of the pixel which helps easy reference of the intensity for each pixel.The variations in the intensity are mapped to low level values called as level set elements and compared pixel by pixel in generating the differences between the two neighboring pixel collections.The threshold that is set is the maximum level set index to mark the high intensity layers in the image of specified limit this can be activated by increasing or decreasing the image access coefficient level.   This process is supported by the quadratic implicit functions that use the image to morph the intensity by reducing the pixel wise gray scale components in the cluster that is   derivate by the user at the run time.

Image Model and Problem Formulation

In order to deal with intensity in-homogeneities in image segmentation, we formulate our method based on an image model that describes the composition of real-world images, in which intensity in-homogeneity is attributed to a component of an image. In this project, we consider the following multiplicative model of intensity in-homogeneity. From the physics of imaging in a variety of modalities (e.g. camera and MRI), an observed image can be modeled as

 I=bJ+n

where J is the true image, b is the component that accounts for the intensity in-homogeneity, and n is additive noise. The component b is referred to as a bias field (or shading image). The true image J measures an intrinsic physical property of the objects being imaged, which is therefore assumed to be piecewise (approximately) constant. The bias field b is assumed to be slowly varying. The additive noise n can be assumed to be zero-mean Gaussian noise.

Local Intensity Clustering Property

Region-based image segmentation methods typically relies on a specific region descriptor  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 regions . 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.

LEVEL SET FORMULATION AND ENERGY MINIMIZATION

This module consists of Two-Phase Level Set Formulation, Multiphase Level Set Formulation and Numerical Implementation. This is handling the image and comparing them through their contour initialization and stable performance for different scale parameters .In this we segment the image into several parts and apply bias correction on various MR images .It uses the implementation technique of multiple or multiscalelevelset spline which includes the level set handling of the image with its  border segmentation process and intensity verification using the minimum energy level and comparing them with the previous energy level elements .The class cubic spline  mirror space transform the images into spline model  which variates in the energy level making it uniform intensity pixel wise arrangement that helps in implementing the image comparision pixel by pixel rather than in binary format. The conumpion of energy level is reduced by using the energy level process on the images with similar intensity levels.

Applying Binary Threshold Value on the Image

This indicates the level of intensities that are available on the image with the specific value ranges .It starts with the value with a minimum of zero to a maximum of 8 each level the variation of differences between each pixel point on the low rate image. The variation can be adjusted to check the ratio of the threshold elements within the specific maximum threshold value . It also shows the number  of iterations that can be applied in generating  the required threshold identified pixels in the image. Increase the intensity level to view the exact difference between the pixels of the image.

Two- phase level set formulation

In this layer we undertaken the images and implement the transformations using poisson model that implements the image access similarity process which represents the image in matrix format .Where the data that is obtained are stored into linked lists making it a dynamic array collection. The linked list is reffered every time the change occurs in the image to compare the intensity of variations. This class is accompanied with a Select Tool class to handle RGB formatted images in which the images can be duplicated when the mouse is clicked on that respective image this class uses the buffered image class to handle the image input to generate and duplicate copy of that image.

Charged Fluid Algorithm

This is a small implementation of image duplication that is activated when the mouse is pressed on the required image. The process capture the dimensions of the image like width and height which is assigned to a matrix object with the size of the image. The image is red within its dimensions and store into the matrix array. The process uses the class AffineTransform which converts the mouse point co-ordinates to annotation format that helps in converting the matrix content to the image format. It also uses the geomentriccountours that initializes the process by handling the matrix content and tracing the pixels at that location. The image that is obtained is stored as a true copy for that selected image.

Procedure to work with the charged fluid elements

This process handles or uses a plugin for image handling or processing in the form of Jviewbox.jar , plugins.jar. Set the classpath to the respective jar files. The classpath that is set initializes the respective jar files to support the classes that are used in the application. The Jcontrolset represents a panel that can be used to handle the classes that are used to work with the image transactions.

Phase-Two includes transactions like the movements and selection of the images of the required part in and out using mouse interface and mouse motion interface methods. By increasing and decreasing the pixel points within the specified range. It also contains the features of gradients like brightening and contrasting the image grid scale ratio. Duplicate copies of the image can be created on a temporary phase to give the similar features in that image without damaging the original image which uses the features of AWT and Image Processing using mouse interfaces.

Run the runj.bat by placing the folder in required driver. In handling the image featurs the file plugin.jar, jviewbox.jar provides the required package and classes for image rendering . The plugins.jar provides the information about the multi-dimensional array mappings. The file runj.bat on execution prompts for the file name to be selected. It displays an open dialogue window for input file goto the path.

It opens a graphical screen loading on the graphical editor enables the user to handle the transaction respectively. The classes that support the transactions in the application are Zoom Tool thus uses the annotators that handle the pixel formation when the mouse is dragged on the image.

PanTool

This is used to handle the gradient setting of the application or image by increasing and decreasing the gray scale or morphing ratio.

ChargeFluidTool

This is used to increase the pixel collection by referring to the neighbouring pixels of the specified ratio of intensity starting at the specified point in the image. The matrix object helps in storing the content of the image in various matrix arrays of several data types. Place the folder at the required location run the runj.bat to select the required file and apply the pictorial effects on it.

Select the pan control in the displayed menu that enables the user to move the image in the display area. Select the ZoomControl to zoom on and zoom out the selected image by enlarging the copy of the current loaded image to the specified level. Drag the mouse towards up or down to view the change in the zooming factoe.

Click on WindowLevel to apply gradient effect by moving the mouse in all the four directions .Increase or decrease the brightness to the level of gray scale spots in the selected image click on select, click on the image to create a duplicate copy of the currently loaded image. The image that is created is loaded by storing content of it. As pixels these data is stored in the temporary arrays of various data types like byte, int, long and double. Click on level set and select circle or square to select the type of image from the database. While zoom in or out the real image is loaded with the increased dimensions in width and height and the actual image where as while implementing the level set the arrays are used for referring the intensity of similar types.

Numerical Implementation

The implementation of our method is straightforward. The level set evolution can be implemented by using the same finite difference scheme as for the DRLSE provided in. While we use an easy full domain implementation to implement the proposed level set method in this paper, it is worth pointing out that the narrow band implementation of the DRLSE, provided in, can be also used to implement the proposed method, which would greatly reduce the computational cost and make the algorithm significantly faster than the full domain  implementation.

Method Comparison

This module shows the method comparison through the Robustness to Contour Initialization and Stable Performance for Different Scale Parameters and also through the Piecewise Smooth Model.   In this sub module, we focus on the application of  the proposed method to segmentation and bias correction of brain MR images.

Performance Evaluation and Method Comparison

As a level set method, our method provides a contour as the segmentation result. Therefore, we use the following contour- based metric for precise evaluation of the segmentation result. Let C be a contour as a segmentation result, and S be the true object boundary, which is also given as a contour. For each point Pi,i=1,---,N , on the contour C, we can compute the distance from the point Pi to the ground truth contour S , denoted by dist(Pi,S). Then, we define the deviation from the contour C to the ground truth S by

which is referred to as the mean error of the contour C. This contour-based metric can be used to evaluate a subpixel accuracy of a segmentation result given by a contour.

Robustness to Contour Initialization

With the above metrics,we are able to quantitatively evaluate the performance ofour method with different initializations and different settingsof parameters. We applied our method to a synthetic image with 20 different initializations of the contour and theconstants . Despite the great difference of these initialcontours, the corresponding results are almost the same, all accuratelycapturing the object boundaries. The segmentation accuracyis quantitatively verified by evaluating these results interms of mean errors. The mean errors of these results are allbetween 0.21 and 0.24 pixel . These experimentsdemonstrate the robustness of our model to contourinitialization and a desirable accuracy at subpixel level.

Stable Performance for Different Scale Parameters

We also tested the performance of our method with different scale parameters , which is the most important parameter in our model. For this image, we applied our method with 12 different values of from 4 to 15.  While the mean error increases .as increases, it is below 0.5 pixel for all the 12 different values of used in this experiment.

Comparison With Piecewise Smooth Model

We can also quantitatively compare our method with the PS model on synthetic images. We generated 15 different images with the same objects, whose boundaries are known and used as the ground truth. These 15 images are generated by smoothing an ideal binary image, adding intensity inhomogeneities of different profiles and different levels of noise. We use the same initial contour (the circles in the top row) for the two models and all the 15 images. It is obvious that our model produces more accurate segmentation results than the PS model. To quantitatively evaluate the accuracy, we compute the mean errors of both models for all the 15 images,where the x-axes represent 15 different images. On the other hand, our model is much more efficient than the PS model. This can be seen from the CPU times consumed by the two models for the 15 images. In this experiment, our model is remarkably faster than the PS model, with an average speed-up factor 36.43 in our implementation. The CPU times in this experiment were recorded in running our Matlab programs on a Lenovo ThinkPad notebook with Intel (R) Core (TM)2 Duo CPU, 2.40 GHz, 2 GB RAM, with Matlab 7.4 on Windo

Application to MR Image Segmentation and Bias Correction

In this subsection, we focus on the application of the proposedmethod to segmentation and bias correction of brain MRimages. We first show the results for 3T MR images. These images exhibit obvious intensity inhomogeneities. It can be seen that the intensities within each tissue become quite homogeneous in the bias corrected images.The improvement of the image quality in terms of intensity homogeneity can be also demonstrated by comparing the histograms

of the original images and the bias corrected images.

Our method has also been tested on 7T MR images with promising results. At 7T, significant gains in image resolution can be obtained due to the increase in signal-to-noise ratio.

However, susceptibility-induced gradients scale with the main field, while the imaging gradients are currently limited to essentially the same strengths as used at lower field strengths (i.e., 3T). Such effects are most pronounced at air/tissue interfaces, as can be seen at the base of the frontal lobe.This appears as a highly localized and strong bias, which is challenging to traditional methods for bias correction. The result for this image shows the ability of our method to correct such bias.

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