外文翻译-- Approximating Major Cerebrospinal Fluid Space in a Distance Transformation Based Bayesian Framework from Clinical Non-enhanced Computed

Approximating Major Cerebrospinal Fluid Space in a Distance Transformation Based Bayesian Framework from Clinical Non-enhanced Computed Tomography Images Liang Zhang1,2,Qingmao Hu2,Yonghong Li2 1Institute of Computer and Applications,Chinese Academy of Sciences Chengdu,China 2Shenzhen Institute of Advanced Integration Technology Chinese Academy of Sciences/The Chinese University of Hong Kong Shenzhen,China AbstractAutomatically detecting the abnormality within cerebrospinal fluid space(CSF)from clinical non-enhanced computed tomography(NCT)images is significant since it can help diagnosis of many neurological diseases such as hydrocephalus and subarachnoid hemorrhage(SAH).However,extracting CSF space from NCT images is not easy,due to such factors as small size of CSF,partial volume effect due to large slice spacing,varied grayscale of CSF especially when hemorrhage appears in CSF space.In this paper a method is proposed to approximate major CSF space for detecting hemorrhage.The tissues with good contrast in the brain are extracted as anatomical landmarks,followed by extraction of features using distance transformation with respect to the landmarks.By combining kernel density estimation(KDE)and mutual information(MI),discriminative features are selected for Bayesian decision based classification.Experiments show that the proposed method can locate the major CSF space.Keywords-cerebrospinal fluid space;subarachnoid hemorrhage;kernel density estimation;Bayesian decision;distance transformation I.INTRODUCTION CSF space constitutes the subarachnoid space and the ventricular system around and inside the brain.With the development of the medical imaging technologies,CSF can be examined for the diagnosis of a variety of neurological diseases such as hydrocephalus and SAH.In the light of clinical requirement,to design a computer-assisted diagnosis(CAD)system for detecting SAH from NCT images is of great urgency.For this purpose,it is essential to extract CSF space as region of interest(ROI)for further analysis，which is the very focus of this article.Although magnetic resonance imaging(MRI)is superior to CT in terms of tissue discrimination,CT is preferred in case of detecting acute intracranial hemorrhage for its sensitivity to hemorrhage 1,widespread availability and short imaging time.The latter is crucial for the emergency patients with intracranial hemorrhage.Research on locating the CSF space from NCT images for detecting hemorrhage is challenging and scarce.The difficulties include:low contrast between soft tissues,large voxel size in Z direction(5mm to 10mm),CSF space being isointense to parenchyma when hemorrhage is not acute or when the amount of hemorrhage is not large due to the circulation of CSF.Methods relying only on intensity information to segment CSF space from CT 2,3 are not suitable under the circumstances.Anatomical atlas 4 will not work well due to the large slice spacing which makes it hard to extract Talairach landmarks for registration.In this article,we propose a method to approximate the main CSF space,which includes Sylvian fissures,front interhemispheric cisterns and basilar cisterns.The proposed method constructs the probability model of the spatial relation with respect to anatomical landmarks,and then locates the main CSF space in a Bayesian framework.In the training stage,we select a certain number of data sets with ground truth delineated by radiologist as samples.Then,tissues with good contrast are extracted as landmarks,with respect to which,features are extracted using distance transformation.To reduce the redundancy,features are selected through mutual information based feature selection(MIFS)algorithm 5.The class-conditional PDFs are learned using KDE to construct the classifier.In the test stage,after the specified features are extracted,pixels in the test NCT images are classified according to Bayesian decision theory.978-1-4244-4713-8/10/$25.00 2010 IEEEII.METHOD A.Preprocessing for Landmarks Extraction Skull and lateral ventricles can be segmented from brain NCT images by thresholding and mathematical morphology 6.Only the pixels inside the skull will be processed.We adopt local symmetry and outlier removal 7 to extract the midsagittal plane(MSP).Anterior and posterior intersection points of MSP with skull boundary can be obtained and will be used as landmarks subsequently.In order to get the location information in axial direction,we define the first slice with lateral ventricles presented(it is supposed that the subject is scanned in such a way that superior-inferior direction has increasing slice numbers)as reference.B.Feature Extraction and Representation Distance transformation is also known as distance map or distance field.It supplies each pixel with the distance to the nearest object pixels hence implicitly represents spatial relations of each pixel relative to different objects in the image.In brain NCT images,taking landmarks as objects,distance transformationfmaps each pixelx to the smallest distance fromx to landmarkT:()min(,)|Tfxd x ppT=(1)Typically,the distance metric()dis taken as Euclidean distance.Fig.1 illustrates the result of distance transformations with respect to landmarks.Particularly,we define the distance fromx to the plane of reference slice as()Zfx,which is the interval from slice containingx to the reference slice.Combining all the distance transformations together,each pixelx in original CT images can be mapped to a high dimensional feature space:(),(),(),(),(),()SVMAPZfxfxfxfxfxfx=x(2)where,S V M A P Zdenote skull boundary,lateral ventricles,MSP,anterior intersection point,posterior intersection point and reference slice respectively.As the scale of brain from NCT images varies among individuals and image resolution,all the features are normalized by a scale factor()max()Sfx=,which generally indicates the size of the brain.This feature representation has several advantages:1)the features naturally contain the spatial relations to landmarks,according to which we judge the position of the main CSF space;2)the features include only the spatial information,thus less sensitive to gray level variability owing to pathology,individual or radiation dose difference;3)since all the features are taking from a frame of reference determined by the subject itself,the feature space is invariant to orientation,scale and translation.(a)(b)(c)(d)(e)Figure 1.Distance transformations with respect to:(a)skull boundary,(b)lateral ventricles,(c)MSP,(d)anterior intersection point and(e)posterior intersection point C.Feature Selection by Mutual Information In information theory,the mutual information(MI)measures the mutual dependence of two variables X and Y which is defined by:(,)(;)(,)log()()YXp x yI X Yp x ydxdyp x p y=(3)MI between features and class labels can measure the amount of classification information contained in a set of features.According to Hellman and Raviv 8,an upper bound of Bayes error can be derived from MI between features and class labels.Therefore it is reasonable to use MI to evaluate the dependability of the features.Furthermore,MI among features should be minimized to reduce the redundancy.The proposed method uses MIFS algorithm to select discriminating features by taking both the feature-class MI and feature-feature MI into account.To select0MMfeatures from the original set of0M features,the process of the algorithm can be described as follows:1)Select the feature with highest MI with respect to class labels:(;)I X C 2)Within the remained features,calculate through the formula(4):(;)(;)SS SelectedI X CI X X(4)and select the next feature with the highest value.The parameterregulates the relative importance of the two types of MI.Typically is set to 1 or 0.5.3)Repeat until M features are selected.Using brain NCT samples described in Section 3,MI can be calculated by estimating the PDFs in formula(3)using KDE technology.From Table 1,we can see that as the features are selected sequentially,MI between features and class labels increases while upper bound of Bayes error declines.As to feature selection,except for error rate,the computational complexity and the robustness of features must be taken into account.As shown in the bottom of Table 1,when the sixth featureVf is selected,MI and upper bound of Bayes error change very little.This can be explained from Table 2.The dependencies between Vf and other features is rarely large.Furthermore,the lateral ventricles on whichVf depend are relatively unstable in NCT images comparing with other landmarks.We thus select all the features exceptVf for the following classification task.D.Classification Based on Bayesian Decision In the proposed method,Bayesian decision is used to approximate the main CSF space.Let1c and2c represent two categories:pixels in the main CSF space and that out of the main CSF space.Using multivariable KDE,the class-conditional probabilities1(|)pcxand 2(|)pcxare learned from brain NCT samples with ground truth.Given an arbitrary pixel P within the skull,the selected features Pxcan be observed in the feature extraction stage.Fig.2 illustrates that PDFs estimated by KDE are projected onto selected features.For the task of hemorrhage detection,it is preferred to limit the false negative rate to a minor value and minimize the false positive as much as possible.Then the pixel P can be classified appropriately by comparing the likelihood ratio:12(|)/(|)PPpcpcxxto a certain threshold according to Neyman-Pearson lemma.From Fig.3,we can see that the map of likelihood ratio indicates the location of main CSF space.III.EXPERIMENTAL RESULTS AND VALIDATION All the data sets are from clinical NCT images.There were 10 data sets from Beijing Tiantan Hospital(resolution is 512512 with thickness 9mm)and 10 data sets from Shenzhen Sekou Hospital(512512 with thickness 10mm).Each data set includes 10 to 14 axial scanning slices.All the data sets are used to calculate MI to verify and select the features.The experiments use leave-one-out cross validation on the data sets to validate the accuracy of the method.Fig.4 illustrates that,as the threshold value increases from 1 to 3.5,the sensitivity declines and the specificity increases.For detecting hemorrhage,the sensitivity is concerned to be more important than specificity.It is because the increasing false positive area will not influence much the diagnosis of hemorrhage until it is extended to the area with great variation in grayscales.Whereas the increasing false negative can cause the approximating area fail to enclose the main CSF space thus miss the hemorrhage.In the experiments,we tuneto 2 hence limit the sensitivity to 94.78%and the specificity to 89.82%.The algorithm was implemented in Matlab and C+on Pentium 4(2.8 GHz CPU,512MB RAM),the main CSF space in each slice was located within 2 minutes.We are not able to compare the performance with other method,as we have not found similar work on locating CSF space for detecting hemorrhage from NCT images.In Fig.5,(a),(b)and(c)are 3 axial slices from 3 subjects respectively(c)with SAH).After rotation and translation,(a)is transformed to(d).The radiologist needs to rely on TABLE I.COMPARISON OF MI AND UPPER BOUND OF BAYES ERROR WHEN FEATURES ARE SELECTED SEQUENTIALLY BY MIFS.THE RESULTS ARE THE SAME WHEN IS SET TO 1 AND 0.5.Selected features(;)I X C Upper bound of error rate Af 0.0778 19.70%,AZff 0.1689 15.14%,MAZfff 0.2667 10.25%,MAPZffff 0.2871 9.23%,SMAPZfffff 0.3169 7.74%,SVMAPZffffff 0.3276 7.20%TABLE II.THE MI AMONG FEATURES CALCULATED IN PAIRS.THE MI BETWEEN FEATURE AND ITSELF IS IGNORED.(a)(b)(c)(d)(e)Figure 2.PDFs projected onto:(a)Sf,(b)Mf,(c)Af,(d)Pf,(e)Zf (a)(b)Figure 3.(a):NCT slice.(b):likelihood ratio map of(a)experience to delineate the ground truth(green).Even so,the approximating results locate the main CSF space properly(red).IV.DISCUSSION AND CONCLUSIONS Some knowledge based methods use spatial relations to Sf Vf Mf Af Pf Zf Sf 0.8009 0.7361 0.6146 0.6328 0.3050 Vf 0.8009 0.8807 0.8283 0.8872 0.5369 Mf 0.7361 0.8807 0.4144 0.4256 0.1869 Af 0.6146 0.8283 0.4144 1.1108 0.0223 Pf 0.6328 0.8872 0.4256 1.1108 0.0204 Zf 0.3050 0.5369 0.1869 0.0223 0.0204 Figure 4.Plot of sensitivity and specificity with respect to threshold.(a)(e)(b)(f)(c)(g)(d)(h)Figure 5.Result of approximating Sylvian fissures,front interhemispheric cisterns and basilar cisterns.(a),(b):normal NCT slice.(c):NCT slice with SAH presenting in the right Sylvian fissure.(d):transformed image of(a).(e)-(h):the contour of approximated result(red)and the ground truth(green)corresponding to the upper row.segment brain structure from MRI images 9,10.From this point of view,our method is similar to them.However,they have some essential differences.Firstly,in our method,the spatial relations are represented as PDFs rather than fuzzy sets.Secondly,except the landmarks extraction,the proposed method avoid low level image processing based on gray level,which is required in those knowledge based methods and not suitable for segmenting CSF space from NCT images.Individual differences are the main source of classification error.The shape of brain tissues varies widely among different age,gender and ethnic groups.To resolve this issue,different probability models should be constructed according to different populations.The scan baseline tilt to the orbitomeatal line can result in deviant of the spatial relations between brain tissues from the 2D projection point of view.In the future work,the 3D distance transformation will be explored to circumvent nonstandard scan baseline.The discriminability of the features is finite,which is another source of classification error.In the future,we will explore feature transformation in addition to feature selection.To conclude,a method is proposed to approximate the main CSF space from NCT images using the spatial relations with respect to anatomical landmarks.We verify the dependability of the 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