VELAMMAL COLLEGE OF ENGINEERING AND TECHNOLOGY
Madurai-625 009.
Paper Presentation
On
Image Processing
Submitted by,
S.T.Vinotha (B.Tech. – II year I.T.)
B.Aarthy Krishna (B.Tech. – II year I.T.)
Bayesian Region growing Segmentation of Magnetic Resonance Images with Outlier detection for tumor identification
Abstract:
The segmentation of brain tumor from magnetic resonance (MR) images is a vital process for treatment planning and for studying the differences of healthy subjects and subjects with tumor. The process of automatically extracting tumor from MR images is a challenging process due to the lack of reliable ground truth. This paper proposes a new method for generating synthetic multi-modal 3D brain MRI with tumor and edema, along with the ground truth. Tumor mass effect is modeled using a biomechanical model, while tumor and edema infiltration is modeled as a reaction-diffusion process that is guided by a modified diffusion tensor MRI. Warping and geodesic interpolation on the diffusion tensors are used to simulate the displacement and the destruction of the white matter fibers. The principle behind the devised approach is segmenting fiber bundles from diffusion-weighted magnetic resonance images using a Bayesian locally-constrained region based approach. From a pre-computed optimal path, the algorithm propagates outward capturing only those pixels which are locally connected to the fiber bundle. Rather than attempting to find large numbers of open curves or single fibers, which individually have questionable meaning, this method segments the full fiber bundle region. The strengths of this approach include its ease-of-use, computational speed, and applicability to a wide range of fiber bundles. The result is simulated multi-modal MRI with ground truth available as sets of probability maps. The system will be able to generate large sets of simulation images with tumors of varying size, shape and location, and will additionally generate infiltrated and deformed healthy tissue probabilities
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Index terms: MRI Images, Bayesian region growing, Segmentation etc.
Introduction:
Segmentation refers to the process of partitioning a digital image into multiple regions to simplify or change the representation of an image into something that is more meaningful and easier to analyze. image segmentation is typically used to locate objects and boundaries with lines, curves, mathematical expressions etc. in images. The result of image segmentation is a set of regions that collectively cover the entire image, or a set of contours extracted from the image. Each of the pixels in a region is similar with respect to some characteristic or computed property, such as color, intensity, or texture. Adjacent regions are significantly different with respect to the same characteristics.
Medical imaging refers to the techniques and processes used to create images of the human body for clinical purposes like medical procedures seeking to reveal, diagnose or examine disease or medical science including the study of normal anatomy and physiology. It is part of biological imaging and incorporates radiology, radiological sciences, endoscopy, thermography, medical photography and microscopy. Measurement and recording techniques which are not primarily designed to produce images, such as electroencephalography (EEG) and magneto encephalography (MEG) and others, but which produce data susceptible to be represented as maps which contains positional information, that can be seen as forms of medical imaging.
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The process of automatically extracting tumor from MR images is a challenging process, and there is variety of methods found. The typical standard for validation of the different segmentation methods is comparison against the results of manual raters. However, manual segmentation suffers from the lack of reliability and reproducibility, and different sites may have different methods for manually outlining tumors in MRI. The true ground truth may need to be estimated from a collection of manual segmentations. Validation of the segmentation of structures other than brain tumor is typically not done since manual segmentation of edema or of the whole brain is very challenging tasks and might not represent truth very well. Brain MRI with tumor is difficult to segment due to a combination of the following factors:
1. The deformation of non-tumor structures due to tumor mass effect.
2. Infiltration of brain tissue by tumor and edema (swelling).
Edema appears
around the tumor mainly in white matter regions.
3. There is gradual transition from tumor to edema, often it is difficult to
discern the boundary between the two structures.
4. The standard MR modality used to identify tumor, T1w with contrast enhancement (typically using gadolinium), is not always ideal. Blood vessels and cortical cerebrospinal fluid (CSF) tend to be highlighted along with tumor, while parts of tumor that are necrotic tissue do not appear enhanced at all. It is generally impossible to segment tumor by simply thresholding the contrast enhanced image.
Background:
Since the advent of diffusion weighted magnetic resonance imaging, a great deal of research has been devoted to finding and characterizing neural connections between brain structures. Image resolution is typically high enough so that major white matter tracts, or bundles of densely packed axons, are several voxels in cross-sectional diameter. The goal of tractography algorithms is to segment these fiber bundles from the DW-MRI datasets. Early tractography methods were based on streamlines which employed local decision-making based on the principal eigenvector of diffusion tensors. In these techniques, tracts are propagated from a starting point until the tracts reach some termination criterion. Due to the local decision-making process, these methods perform poorly in noise and often stop prematurely. These techniques do not provide a measure of connectivity for the resulting tracts. Despite the shortcomings of this approach, due to its ease-of-use, streamlining has quickly become the most popular method for fiber segmentation. To infer fiber bundles from streamline tractography results, several groups have successfully worked on methods for fiber clustering. The goal of clustering is to capture group behavior of a population of streamlines and to use this group behavior to drive fiber bundle segmentation. The end result of clustering algorithms has been shown to accurately capture many neural fiber bundles. Recently, another line of work has emerged which seeks to avoid the use of the problematic streamlines. Tractography advances have been made which provide full brain optimal connectivity maps from predefined seed regions. These methods are more robust to noise and depending upon the underlying metric, may be able to more fully use the complete DW-MRI data. These approaches can be subdivided into stochastic and energy-minimization approaches. Stochastic approaches produce probability maps of connectivity between a seed region and the rest of the brain.
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Outlier detection for brain tumor:
The automated segmentation method that we have developed is composed of three major stages, as shown in Fig. 1. First, it detects abnormal regions, where the intensity characteristics deviate from the expectation. In the second stage, it determines whether these regions are composed of both tumor and edema. Finally, once the estimates for tumor and edema intensity parameters are obtained, the spatial and geometric properties are used for determining proper sample locations. The details of each stage are discussed in the following subsections.
Detect Abnormality
Detect Abnormality
Test edema presence Detect Abnormality
Figure 1. Three major stages of the segmentation method
Detection of abnormality
Before identifying tumor and edema, it is necessary to first detect regions that have properties that deviate from the expected properties of a normal, healthy brain. In our segmentation method, this involves finding the intensity parameters for healthy classes and the abnormal class. The initial parameters for the healthy brain classes are obtained by sampling specific regions based on the probabilistic brain atlas shown in Fig. 2
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Figure 2.Brain atlas Figure 3. Tumor affected regions
The registration of the medical images is performed using affine transformation with the mutual information image match measure. After alignment, the samples for each healthy class (white matter, gray matter, and cerebrospinal fluid (CSF)) are obtained by randomly selecting the voxels with high atlas probability values. In this paper, the set of training samples is constrained to be the voxels with probabilities higher than a threshold τ = 0:85.
The training data for the healthy classes generally contain unwanted samples due to contamination with samples from other tissue types, particularly tumor and edema. The pathological regions are not accounted for in the brain atlas and they therefore occupy regions that are marked as healthy. The contaminants are data outliers, and they are removed so that the training samples for the healthy classes are not contaminated. The samples are known to be contaminated if their characteristics differ from prior knowledge. The intensities for healthy classes are known to be well clustered and can be approximated using Gaussians theorems.
Handling data outliers is a crucial step for atlas based image segmentation, developed a segmentation method for healthy brains that builds the Minimum Spanning Tree from the training samples and iteratively breaks the edges to remove false positives, a process called pruning and showed that pruning the training samples results in significant improvement of the segmentation quality. We use a robust estimate of the mean and covariance of the training data to determine the outliers to be removed.
The robust estimator that we use is the Minimum Covariance Determinant (MCD) estimator. It is defined to be the mean and covariance of an ellipsoid covering at least half of the data with the lowest determinant of covariance. The method is highly robust, with a high breakdown point. The breakdown point is the fraction of the data that must be moved to infinity so that the estimate also moves to infinity.
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A fast algorithm for computing the MCD estimate is described. The algorithm first creates several initial subsets, where the elements are chosen randomly. From each subset, the algorithm determines different initial estimates of the robust mean and covariance. The estimates are then refined by performing a number of C-step operations on each initial selections. A single C-step operation consists of the following steps:
1. Given a subset of the data, compute the mean and covariance of the elements in the subset.
2. Compute Mahalanobis distances of the data elements in the whole set.
3. Sort points based on distances, smallest to largest.
4. Select a new subset where the distances are minimized like a first half of the sorted data points.
A C-step operation will result in a subset selection that yields a determinant of covariance less or equal to the one obtained from the previous subset. The iterative applications of C-steps yield final estimates with the smallest determinant of covariance. From all the final estimates computed with different initial selections, the mean and covariance estimate with the smallest determinant of covariance is chosen as the robust estimate. Given the robust mean and covariance, samples that are further than three standard deviations are considered as outliers. The inliers of the healthy brain tissue class samples are used as training samples for estimating the corresponding density functions.
The specific aim at this stage is to compute the density estimates and posterior probabilities for the class labels Γ = {white matter, gray matter, csf, abnormal, non-brain}. A parametric density function is not ideal for the case of tumor segmentation. Tumors do not always appear with uniform intensities, particularly in the case where some tissues inside the tumor are necrotic tissues. So, we make no assumption regarding the intensity distributions and use a non-parametric model for the probability density functions. The spatial priors for white matter, gray matter, csf, and non-brain classes are the corresponding atlas probabilities. For the abnormal class, we use a fraction of the sum of white matter and gray matter atlas probabilities since tumor and edema usually appear in these regions and not in the csf regions.
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An issue with MR images is the presence of the image inhomogeneity or the bias field. It is dealt by interleaving the segmentation process with bias correction. The entire process of detecting the abnormal regions consists of a loop that is composed of the following five stages:
1. Threshold the posterior probabilities and sample the high confidence regions. At the first pass, the atlas probabilities are used in place of the posterior probabilities.
2. Remove the samples for normal tissues that exceed a distance threshold based on the MCD estimate.
3. Estimate the non-parametric density for each class labels. The initial density for the abnormal class is set to be uniform, which makes this class act as a rejection class. The brain voxels with intensity features that are different from those of healthy classes or not located in the expected spatial coordinates will be assigned to this class.
4. Compute the posterior probabilities.
5. Estimate bias field from white matter and gray matter probabilities. Apply correction using the estimated bias field.
The first major segmentation stage detects the abnormal regions by executing the loop for several iterations, obtaining the intensity descriptions for each class. The abnormal class density at different iterations for the Tumor data is shown in Fig. 4.
Fig.4. Snapshots of the estimated probability density function of the abnormal class for the Tumor data.
The bias correction method is based on the one developed by the method which uses the posterior probabilities to estimate the homogeneous image. It then computes the bias field estimate, as the log-difference between the homogeneous images and the real subject images. The bias field is modeled as a polynomial, and the coefficients of the polynomial are determined through least squares fitting. The method assumes that the class intensity distributions are approximately Gaussians. So, we use only the white matter and gray matter probabilities for bias correction, as they generally can be approximated by Gaussians without significant errors.
Detection of edema:
The densities and posterior probabilities computed for the abnormal class give us an approximate idea of how likely it is that some voxels are part of tumor or edema. Let us consider that the detected abnormal voxels are composed mostly of tumor and possibly edema. Edema is not always present when tumor is present, therefore it is necessary to specifically test the presence of edema, whose detection is first obtaining the intensity samples for the abnormal region, the posterior probabilities are thresholded and a subset of the region is selected. The samples are clustered and then the determination of whether there exist separate clusters for tumor and edema.
| The T1 image (left) and the T2 image (right) from the Tumor020 data. The tumor and edema on the right part of the brain can be clearly differentiated based on the T2 intensities. As observed in the T2 image, the tumor region (rightmost) is darker than the left side region that is T1 image. |
The T2 channel contains most of the information needed for differentiating tumor and edema. Therefore, we have chosen to measure the overlap for only the T2 data of each cluster. If the amount of overlap is larger than a specified threshold, then the tumor density is set to be the density for the abnormal class and the edema density is set to zero.
Reclassification with spatial and geometric constraints
Once this stage is reached, tumor and edema are already segmented based on atlas priors and intensity characteristics. However, the geometric and spatial properties were not considered and this generally leads to having at least a few false positives. Since there is no model for the intensity distributions of tumor and edema, it is necessary to use geometric and spatial heuristics to prune the samples that are used for estimating the densities, as all the tumors are mostly blobby. For edema, we use the constraint that each edema region is connected to a nearby tumor region. Some edema voxels can be located far away from tumor regions, but they must be connected to a tumor region spatially.
Tumor structures generally appear as blobby lumps, this shape constraint is enforced through region competition. The tumor posterior probabilities are used as the input for the snake, which is represented as the zero level set of some scalar function say φ. The propagation term is represented by α. It is modulated by the difference of the posterior probabilities for the tumor class and the non-tumor class, so that the direction of the propagation is determined by the sign of the difference. The probability that a voxel is part of brain and not part of tumor is represented by , more explicitly P(tumor
| |
Each segmented edema object must have a voxel that is no further than some small distance from tumor regions. This test can be done efficiently by using the connected component algorithm and mathematical morphology. We first generate a binary image representing the segmented edema region. Then, we use this image as an input for the connected component algorithm to determine the individual edema objects. Each object is then dilated with a small structuring element, and then compared against the segmented tumor regions. The objects that share at least a voxel with a tumor region is considered valid. Edema samples from these regions are kept, while other edema samples are discarded. This way, the segmentation for these locations can be determined.
Conclusion:
We have proposed a method for generating synthetic multi-modal MR images with brain tumors that present similar difficulties as real brain tumor MR images. Using sets of such images with variations of tumor size, location, extent of surrounding edema, and enhancing regions, segmentation methods can be tested on images that include most of the challenges for segmentation. The synthetic MRI allows for the validation of the segmentation of the whole brain, which includes white matter, gray matter, csf, tumor, and edema. This capability is novel as most validations done so far were focused on tumor only but not on infiltrated tissue and on deformed healthy tissue. A possible extension to the method we proposed is the inclusion of vessel information to determine additional regions where contrast agent tends to accumulate. Blood vessel information can also be combined together with deformation and infiltration to generate more precise simulation of the tumor growth and the development of necrosis. This could lead to development of a texture model for the tumor and edema regions. We also focus on the generation of test images that empirically simulate pathology as seen in real images, with the main purpose to use simulated images and ground truth for validation and cross-comparison. The method presented here may also be applied for multi-focal lesions in which the local deformation and the tissue infiltration can be generated using our framework.
