Phương pháp chẩn đoán hình ảnh (Phần 3)

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2 Medical-Image Processing and Analysis for CAD Systems

Athanassios N Papadopoulos, Marina E Plissiti, and Dimitrios I Fotiadis

CONTENTS

2.1 Introduction2.2 Basics of a CAD System2.2.1 Computer-Aided Methodologies in Mammography2.2.2 Historical Overview

2.2.3 CAD Architecture2.2.4 Preprocessing2.2.5 Segmentation2.2.6 Feature Analysis (Extraction, Selection, and Validation)2.2.7 Classification System (Reduction of False Positives orCharacterization of Lesions)

2.2.7.1 Conventional Classifiers2.2.7.2 Artificial Neural Networks (ANNs)2.2.7.3 Fuzzy-Logic Systems

2.2.7.4 Support-Vector Machines2.2.8 Evaluation Methodologies

2.2.9 Integrated CAD Systems2.3 Computer-Aided Methodologies for Three-Dimensional Reconstruction

of an Artery2.3.1 IVUS Image Interpretation2.3.2 Automated Methods for IVUS ROI Detection2.3.2.1 IVUS Image Preprocessing

2.3.2.2 IVUS Image Segmentation2.3.3 Limitations in Quantitative IVUS Image Analysis2.3.4 Plaque Characterization in IVUS Images

2.3.5 Three-Dimensional Reconstruction2.4 Conclusions

References

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52 Medical Image Analysis

2.1 INTRODUCTION

Over the last 15 years, several research groups have focused on the development ofcomputerized systems that can analyze different types of medical images and extractuseful information for the medical professional Most of the proposed methods useimages acquired during a diagnostic procedure Such images are acquired using avariety of techniques and devices, including conventional radiography, computerizedtomography, magnetic resonance imaging, ultrasound, and nuclear medicine Com-puterized schemes have been widely used in the analysis of one-dimensional medicalsignals such as Electrocardiogram (ECG), Electromyogram (EMG), Electroenceph-alogram (EEG), etc However, the majority of medical signals are two-dimensionalrepresentations Computerized systems designed for the automated detection andcharacterization of abnormalities in these images can provide medical experts withuseful information Such systems are commonly referred to as computer-aideddetection/diagnosis systems (CAD)

A computer-aided detection procedure does not provide a medical diagnosis.Rather, the computerized system is developed to detect signs of pathology in medicalimages by extracting features that are highly correlated with the type and thecharacteristics of the abnormality or the disease under investigation If a specificarea in a radiological image meets the requirements, the computerized schemeidentifies it, and the radiologist can review it to improve the accuracy of the detectionprocedure On the other hand, computer-aided diagnosis schemes, based on the same

or additional features, characterize the identified region according to its pathology

A CAD system is defined as a combination of image-processing techniques andintelligent methods that can be used to enhance the medical interpretation process,resulting in the development of more efficient diagnosis The computer outcomeassists radiologists in image analysis and diagnostic decision making In addition,

a CAD system could direct the radiologist’s attention to regions where the probability

of an indication of disease is greatest A CAD system provides reproducible andquite realistic outcomes

In this chapter, we review two of the most common procedures in CAD systems.The first is related to microcalcification detection and classification in mammograms

In this procedure, features of microcalcifications are extracted, and intelligent ods are then used to classify these features The second procedure is based on thefusion of intravascular ultrasound and biplane angiographies aiming at the three-dimensional (3-D) reconstruction of an artery

meth-2.2 BASICS OF A CAD SYSTEM

Most of the automated CAD approaches include feature-extraction procedures ever, several studies of semi-automated approaches have been reported whereinradiologists manually perform feature-mining procedures by employing variousfeature-extraction modules [1, 2] CAD systems can be classified in two categoriesaccording to their objectives: (a) those that are used to detect regions of pathologyand (b) those that are used to classify the findings based on their features, whichindicate their histological nature

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Medical-Image Processing and Analysis for CAD Systems 53

The role of these computerized systems is to improve the sensitivity of thediagnostic process and not to make decisions about the health status of the patient.However, the “D” in CAD should stand for “diagnosis” [3], although several reports

in literature utilize the word “detection” [4], which is undoubtedly an essential part

of the diagnostic procedure

For the design and development of an automated CAD system, several issuesmust be considered, including the quality of the digitized images, the sequence ofthe processing steps, and the evaluation methodology Most of the studies use film-screen images that are digitized using high-performance film digitizers Recentstudies employ high-quality medical images obtained directly in digital format usingadvanced imaging systems (filmless technology) The specific characteristics of thefilm digitizer significantly influence the quality of the image In the case of film-screen technology, the maximum optical density of the film is a critical parameter

in the quality of the final digitized image In cases where the upper limit of theoptical density is low, an estimation of noise is possible during the digitizationprocedure, especially on the background area (air) of the image Utilization of film-screen systems with higher optical densities might lead to the reduction of suchnoise due to digitization

2.2.1 C OMPUTER -A IDED M ETHODOLOGIES IN M AMMOGRAPHY

Mammography is one of the radiological fields where CAD systems have beenwidely applied because the demand for accurate and efficient diagnosis is so high.The presence of abnormalities of specific appearance could indicate cancerous cir-cumstances, and their early detection improves the prognosis of the disease, thuscontributing to mortality reduction [5] However, diagnostic process is complicated

by the superimposed anatomical structures, the multiple tissue background, the lowsignal-to-noise ratio, and variations in the patterns of pathology Thus, the analysis

of medical images is a complicated procedure, and it is not unusual for indications

of pathology, such as small or low-contrast microcalcifications, to be missed ormisinterpreted by radiologists On the other hand, clinical applications require real-time processing and accuracy in diagnosis Based on these high standards in diag-nostic interpretation, numerous intelligent systems have been developed to providereliable automated CAD systems that can be very helpful, providing a valuable''second opinion'' to the radiologist [6, 7]

2.2.2 H ISTORICAL O VERVIEW

Computerized analysis of radiological images first appeared in the early 1960s [8,9] One of the first studies employing computers in the area of mammography waspublished by Winsberg et al in 1967 [10] In this approach, the right- and left-breastshapes were compared to detect symmetry differences Computation of local imagecharacteristics from corresponding locations with high variations indicated the pres-ence of a disease Ackerman et al [11] defined four computer-extracted features forthe categorization of mammographic lesions as benign or malignant Another study2089_book.fm Page 53 Tuesday, May 10, 2005 3:38 PM

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by the same research group [12] proposed a computational procedure for the cessing of a feature set with 30 characteristics that are obtained by radiologists forthe classification of lesions according to their malignancy At the same time, severalother works targeting detection and characterization of microcalcification clustersappeared in the literature Wee et al [13] classified microcalcification clusters asbenign or malignant using the approximate horizontal length,the average internalgray level, and the contrast of individual microcalcifications The cluster patterntogether with features such as size, density, and morphological characteristics of thecluster were also used for microcalcification characterization [14] In the late 1970s,Spiesberger [15] was the first to propose an automated system for the detection ofmicrocalcifications

pro-At the end of the 1980s, the literature was enriched by studies reporting severalimage-processing algorithms and computational processes that provided satisfactorydescriptions and efficient procedures for the detection of microcalcifications [16–18]

In 1990, Chan et al reported that under controlled circumstances, a CAD systemcan significantly improve radiologists' accuracy in detecting clustered microcalcifi-cations [19]

2.2.3 CAD A RCHITECTURE

CAD systems proposed in the literature are based on techniques from the field ofcomputer vision, image processing, and artificial intelligence The main stagesof atypical CAD scheme are: preprocessing, segmentation, feature analysis (extraction,selection, and validation), and classification utilized either to reduce false positives(FPs) or to characterize abnormalities (Figure 2.1) A description of the methodsemployed in each stage is given in the following sections

2.2.4 P REPROCESSING

In this stage, the subtle features of interest are enhanced and the unwanted teristics of the image are de-emphasized The enhancement procedure results in abetter description of the objects of interest, thus improving the sensitivity of thedetection system and leading to better characterization in the case of diagnosis Theenhancement of the contrast of the regions of interest, the sharpening of the abnor-malities’ boundaries, and the suppression of noise is performed in this stage Severalmethodologies have been reported in the literature based on conventional image-processing techniques, region-based algorithms, and enhancement through the trans-formation of original image into another feature space Global processing can beperformed, or local adjusting enhancement parameters can be used to accommodatethe particularity of different image areas

charac-Morphological, edge-detection, and band-pass filters have been utilized Anenhanced representation can be obtained using subtraction procedures on the pro-cessed image [18] One of the earliest contrast-enhancement methodologies was themodification of image histogram [20] and its equalization [21] The resulting imagecontains equally distributed brightness levels over the gray-level scale Because themammogram contains areas of different intensity, a global modification is poor.2089_book.fm Page 54 Tuesday, May 10, 2005 3:38 PM

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Performance can be improved utilizing local adjustments of the processing eters (adaptive histogram equalization) [22] Another technique restricts the meth-odology to certain contrast values to increase the effective range of contrast in thespecific areas (contrast-limited adaptive histogram equalization) [23]

param-Unsharp masking is a routinely used procedure to enhance the fine-detail tures A high-spatial-frequency component multiplied by a weight factor is added

struc-on the original image In the case of linear unsharp filtering, the above parametersare constant throughout the entire image In nonlinear methodologies, the weightingfactor depends on the intensity of the examined region (background/foreground), or itcan be applied differently in different resolution levels in multiscale approaches [24].Contrast stretch is a rescaling of image gray levels based on linear or nonlineartransformations In linear transformations, the difference between the backgroundand foreground areas is increased to improve the contrast of both areas Introducing

a nonlinear transformation, the contrast of the different parts of the image is modified,selectively enhancing the desired gray levels In most medical images, objects ofinterest have nonstandard intensities, thus the selection of a proper “intensity win-dow” is not sufficient for contrast enhancement

The adaptive neighborhood contrast-enhancement method improves the contrast

of objects or structures by modifying the gray levels of the neighborhood (contextualregion) of each pixel from which the object is composed After the identification ofhomogeneous areas (using, for example, a growing technique) several conditionsare imposed to downgrade unconventional high-contrast areas or low-level noise and

to enhance regions surrounded by variable background [25] Techniques that enhanceregions of interest by estimating their difference from their background areas are

FIGURE 2.1 CAD architecture.

Digital mammogram

Preprocessing

Classification module - reduction

of FP findings Feature extraction - selection Segmentation

Classification module - likelihood

of malignancy Feature extraction - selection

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called region-based enhancement techniques Typical region growing techniques,which employ contrast and statistical conditions, result in the definition of the extentand the shape of the objects [26]

Multiresolution methods, based mainly on wavelet analysis, are used to enhancethe features of mammographic images [27] A multiscale analysis of the originalmammogram to several subband images provides the advantage of studying eachsubband independently using scale characteristics Each subband provides informa-tion based on different scales resulting in the representation of high- or low-fre-quency elements on separate images Thus, noise or similar type components of theimage can be described in high resolution (small scale), while subtle objects withdefined extent or large masses are described in medium-resolution and low-resolutionlevels (medium and coarse scales), respectively Hence, the significant image featurescan be selectively enhanced or degraded in different resolution levels [28] Further-more, adaptive approaches in wavelet enhancement techniques that ensure the avoid-ance of the utilization of global parameters have been reported [29]

Fuzzy-logic techniques are also used for contrast enhancement of cations [30] Global information (brightness) is employed to transform an image to

microcalcifi-a fuzzified version using microcalcifi-a function, while locmicrocalcifi-al informmicrocalcifi-ation (geometricmicrocalcifi-al stmicrocalcifi-atistics)

is employed to compute the nonuniformity

Methods that are based on deterministic fractal geometry have been used toenhance mammograms [31–33] A fractal-image model was developed to describemammographic parenchymal and ductal patterns using a set of parameters of affinetransformations Microcalcification areas were enhanced by taking the differencebetween the original image and the modeled image

2.2.5 S EGMENTATION

In this stage, the original mammographic image is segregated into separate parts,each of which has similar properties The image background, the tissue area, andthe muscle or other areas can be separated because they are characterized usinggeneric features Moreover, apart from the generic classification of image regions,

a CAD segmentation procedure can identify regions containing small bright spotsthat appeared in groups and that correspond to probable microcalcifications and theirclusters The complexity of a segmentation procedure depends on the nature of theoriginal image and the characteristics of the objects that have to be identified Amammographic image contains several regions having different attenuation coeffi-cients and optical densities, resulting in intensity variations In addition, because amammogram is a two-dimensional (2-D) representation of a 3-D object, the over-lying areas develop a complex mosaic composed of bright regions that may or maynot be a real object Thus, the implementation of a global single threshold or a set

of fixed thresholds that defines intensity ranges is not an efficient segmentationprocedure Moreover, the employment of a global intensity threshold usuallyincreases the number or the size of the selected regions introducing noise, whichmakes the procedure inefficient because noise removal requires further treatment

In any case, after the first partitioning has been achieved, region-growing techniques,following specific homogeneity and differentiation criteria, can be utilized to definethe real extent and the exact borders of the segmented region

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To overcome the limitations of a global thresholding methodology, local oldingcriteria must be utilized from the beginning The definition of the parametersthat satisfy the demands of the segmentation algorithm increase the efficiency of thetechnique The corresponding measures were calculated for a specific window size.Some of the local thresholding criteria are:

thresh-The mean intensity values plus/minus a number of standard deviation (SD)values of intensity [16]

The difference of the intensity value of a seed pixel from the maximum andminimum intensity values of pixels that belong to a specific neighborhoodaround a seed pixel [34]

A contrast measure equal to the difference of intensity between object andbackground region [35]

An object is selected only if the feature value belongs to the highest 2% of the valuesobtained

In a similar but more flexible way, adaptive filtering methodologies have beenproposed, defining parameters or measures adjusted to a specific area A featurecalled prediction error (PE) is the difference between the actual pixel value and theweighted sum of the eight nearest-neighbor pixels [36] If PE follows a Gaussiandistribution, calcifications are not present Functions using first, second, and thirdmoments of the PE are used to generate a threshold value that reveals the presence ofthe microcalcifications In another study [37], given a local maximum pixel value x0,y0,

an edge pixel is given by the value of x,y that maximizes the difference in pixel valuesbetween pixels at x,y and x0,y0, divided by the distance between the two pixels.Mathematical morphology filtrationhas been used to segment the microcalcifi-cations Classical erosion and dilation transformations, as well as their combinationssuch as open, close, and top-hat transformations, are employed [38]

In statistical approaches,several histogram-based analysis and Markov randomfield models are used [39, 40] Markov random fields have been used to classifypixels to background, calcification, line/edge, and film-emulsion errors [41] Multi-scale analysis based on several wavelet transformations has been used to enable thesegmentation process to be performed using the different scales-levels [42, 43].Furthermore, as in the preprocessing module, techniques have been applied exploit-ing fractal [44] and fuzzy-logic methodologies [45]

2.2.6 F EATURE A NALYSIS (E XTRACTION , S ELECTION , AND V ALIDATION )

In this stage, several features from the probable microcalcification candidates areextracted to reduce false positives In any segmentation approach, a considerablenumber of normal objects are recognized as pathological, which results in reducedefficiency of the detection system To improve the performance of the scheme, severalimage features are calculated in an effort to describe the specific properties orcharacteristics of each object The most descriptive of these features are processed

by a classification system to make an initial characterization of the segmentedsamples

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Although the number of calculated features derived from different feature spaces

is quite large, it is difficult to identify the specific discriminative power of each one.Thus, a primary problem is the selection of an effective feature set that has highability to provide a satisfactory description of the segmented regions Early studiesutilized features that were similar to the features that radiologists employ duringtheir diagnosis However, as mentioned previously, additional features not employed

by the doctors also have high discrimination power Table 2.1 provides a list oftypical morphological features of individual microcalcification and their clusters.Specific features could be extracted, such as the surround region dependencematrix (SRDM), gray-level run length (GLRL), and gray-level difference (GLD)[46] Laplacian or Gaussian filtration can be used in the validation of features [47].Using wavelet analysis, features such as energy, entropy, and norms of differencesamong local orientations can be extracted [48]

The use of a large number of features does not improve the classificationperformance Indeed, the use of features without discriminative power increases thecomplexity of the characterization process In addition, the probability of misclas-sification increases with the number of features Moreover, the prediction variability

TABLE 2.1 Features for the Detection and Characterization

of Microcalcifications and Their Clusters

Microcalcification (MC) Cluster Classification Features

Radiologists’

Characterization Features

Mean MC background intensity Density of calcifications

Mean distance from cluster centroid Calcification distribution Neighboring with a larger cluster Cluster distribution

Spreading of MCs in cluster Calcification distribution

SD of distances from cluster centroid Calcification distribution Area of the cluster convex hull Shape of cluster Length of the cluster convex hull Shape of cluster

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is larger, and the classifier is sensitive to outliers Finally, the more features included

in a given classifier, the greater is the dimension of a training set needed for thesame degree of reliability [49] The selection of the optimal feature subset is alaborious problem Only an exhaustive search over all subsets of features can providethe system with a reliable subset Usually, the criterion of selecting an efficientsubset of features is the minimization of misclassification probability (classificationerror) However, for the testing of a subset, a classifier must be chosen, and it isimportant to consider that different classifiers and different methods for the estima-tion of error rate could lead to the selection of a different feature subset

One of the most important issues of a mammographic CAD system is theselection of a standard feature set and the classification method that is used to extractregions of pathological interest while minimizing false-positive findings The selec-tion of the appropriate features can be based on “weighting factors” proposed byradiologists [50–53] or on algorithmic procedures that identify the most discriminantfeatures

The feature space can be a transformed space that has lower dimension than theoriginal, although its discriminating power could be higher To achieve this, PCA(principal component analysis), which is based on the elimination of features thatcontribute less, can be used [54, 55]

Alternatively, the most discriminative features can be selected, reducing in thisway the size of the feature set Several methods have been proposed, such as:Stepwise discriminant analysis [56]

Sequential Forward Selection (SFS) and Sequential Backward Selection(SBS) [57]

Genetic algorithms [58]

Stepwise discriminant analysis is based on the sequential trial of different featuresubsets The one that results in the smallest error rate is chosen as the most convenient[59–61] Sequential forward selection is a bottom-up search procedure where onefeature at a time is added to the feature set At each stage, the feature to be included

in the feature set is selected from among the remaining features [57, 62, 63] Geneticalgorithms have been used to select features that could enhance the performance of

a classifier (for distinguishing malignant and benign masses) In the same way,genetic algorithms have been used to optimize the feature set for the characterization

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circumscribed masses, or calcifications) [66] to techniques that produce binarydiagnosis, characterizing the findings as malignant or benign

The classifiers that are utilized in the area of the detection of mammographicmicrocalcification are those employed in most of the medical image-analysis pro-cedures They could be categorized in the following classes:

2.2.7.1.1 Rule-Based Systems (Decision Trees)

The decision tree is one of the most widely used techniques for the extraction ofinductive inference As a learning method, it aims at the definition of an approxi-mating discrete-value target function in which the acquired knowledge is represented

as a decision tree The architecture of the classifier includes a set of “if-then” rules

A decision-tree scheme includes a main root node, from where the classificationprocedure starts, and several leaf nodes where the classification of the instance isgiven Each node in the tree specifies a check of an attribute of the instance, andeach branch descending from that node corresponds to one of the possible valuesfor this specific attribute An instance is categorized beginning from the root nodeand, by checking the attribute specified by this node, moving down to the specifictree branch that is responsible for the value of this attribute A similar procedure isreplicated if a new tree is rooted at the new node

From the early studies of microcalcification detection and characterization inmammography, rule-based systems provide a remarkable assistance in the simulation

of the diagnosis process carried out by a radiologist [67, 68] Although, the sion of medical rules to “if-then” rules is a feasible task, the development of a high-performance system has not been achieved This is due to the absence of attribute-value pair representations in medical data and the lack of disjunctive descriptions

conver-or large data sets fconver-or system training that include all the specific disease cases

2.2.7.1.2 Bayesian Quadratic and Linear Classifiers (Statistical)

A Bayesian classifier is based on the approximation of the class-conditional bilistic density functions (PDFs) Each PDF expresses the frequency of occurrence

proba-of each sample in the feature space Typically, an unknown sample is classified to

a class with the highest value of its PDF The problem is that the precise mation of the PDFs has to be defined [62]

approxi-Quadratic and linear classifiers are statistical (parametric) methods that utilizeGaussian distributions for the PDFs The mean vector and the covariance matrix areestimated from the training set of each class In the case of a Bayesian quadraticclassifier (BQC), the classification boundary forms a quadratic curve In the case of

a Bayesian linear quadratic (BLQ) classifier, instead of using different covariancematrices for the individual classes, one unified covariance matrix is used for allclasses, and the classification border is a straight line

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2.2.7.1.3 Nonparametric

When the underlying distributions of the samples are quite complex, additionaltechniques can be employed to approximate the PDFs The K-nearest neighbor andthe Parzen estimate belong to this category In the K-nearest-neighbor technique,the classification boundary is directly constructed instead of calculating the PDFs[69] For an unknown sample, distances to the individual training samples arecalculated, and the major class in the nearest K samples is selected The Parzenestimate method is used if the distribution is complex, and its generation is quitedifficult Numerous kernel functions that describe the individual training samplesare summed up to calculate the complex PDF [70]

2.2.7.2 Artificial Neural Networks (ANNs)

A neural network is a structure that can be adjusted to produce a mapping ofrelationships among the data from a given set of features For a given set of data

, the unknown function, y = f(x), is estimated utilizing numerical algorithms.The main steps in using ANNs are: First, a neural-network structure is chosen in away that should be considered suitable for the type of the specific data and theunderlying process to be modeled The neural network is trained using a trainingalgorithm and a sufficiently representative set of data (training data set) Finally, thetrained network is evaluated with different data (test data set), from the same orrelated sources, to validate that the acquired mapping is of acceptable quality.Several types of neural networks have been reported, such as feedforward [12,

20, 36, 43, 48, 55, 57], radial basis function [71], Hopfield [72], vector quantization,and unsupervised types such as self-organizing maps [73] A review of the role ofthe neural networks in image analysis is reported by Egmont et al [74] Becausefeedforward back-propagation and radial basis function neural networks are the mostcommon, a brief description of these network architectures can be meaningful.Typically, a neural network is a structure involving weighted interconnections amongneurons (nodes), which are typically nonlinear scalar transformations Figure 2.2shows an example of a two-hidden-layer neural network with three inputs, x = {x1,

x2, x3}, that feed each of the five neurons composing the first hidden layer The fiveoutputs from this layer feed each of the three neurons that compose the secondhidden layer, which, in a similar way, are fed into the single-output-layer neuron,yielding the scalar output, The layers of neurons are called hidden because theiroutputs are not directly seen in the data The inputs to the neural network are featurevectors with dimensions equal to the amount of the most significant features Severaltraining algorithms are implemented before selecting the one that is “most suitable”for the network training Gradient descent, resilient back-propagation, conjugategradient, quasi-Newton, and Levenberg-Marquardt are some of the most commontraining methods [75]

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develop more reliable classification approaches Fuzzy set theory is an approach toresolve this problem Initially, fuzzy sets are integrated into rule-based expert sys-tems to improve the performance of decision-support systems Fuzzy procedurescan also be used to automatically generate and tune the membership functions onthe definition of different classes Image-processing techniques have been reportedemploying different feature sets defined in a fuzzy way Intelligent methodologiesand pattern-recognition techniques have been used to introduce fuzzy clustering andfuzzy neural-network approaches [76]

However, fuzzy sets can be utilized in more than one stage of a classifier design.Fuzzy inputs can also be used, wherein the original input values are converted to amore “blurry” version For instance, instead of using the exact values of the featurevector, a new vector consisting of feature values expressing the degree of member-ship of the specific value to the fuzzy sets (e.g., small, medium, large) can be used.Fuzzy reasoning can be utilized in classification processes in which the inferencesare not strictly defined The categories in a medical classification procedure areexclusive Thus, every sample belongs to a specific category However, in somecases, an unknown sample belongs to more than one class, but with a different degree

of membership In such cases, the classification scheme is based on the utilization

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definition of an optimal hyperplane that separates the training data to achieve a

minimum expected risk In contrast to other classification schemes, an SVM aims

to minimize the empirical risk Remp while maximizing the distances (geometric

margin) of the data points from the corresponding linear decision boundary (Figure

2.3) Remp is defined as

(2.1)

where

x i∈R N, i = 1, …, l, is the training vector belonging to one of two classes

l is the number of training points

y i∈ {−1, 1} indicates the class of x i

ƒ is the decision function

The training points in the space R N are mapped nonlinearly into a higher

dimen-sional space F by the function (a priori selected) : R N→F It is in this space (feature

space) where the decision hyperplane is computed The training algorithm uses only

the dot products ((x i)⋅(x j)) in F If there exists a “kernel function” K such that K(x i ,x j)

= (x i)⋅(x j ), then only the knowledge of K is required by the training algorithm The

decision function is defined as

(2.2)

where a i represents the weighting factors and b denotes the bias After training, the

condition a i > 0 is valid for only a few examples, while for the others a i = 0 Thus,

the final discriminant function depends only on a small subset of the training vectors,

which are called support vectors Several types of kernels have been reported in the

literature, such as the polynomial type of degree p

FIGURE 2.3 A nonlinear SVM maps the data from the feature space D to the

high-dimen-sional feature space F using a nonlinear function.

Data space Feature space

Nonlinear Function

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(2.3)and the Gaussian kernel

(2.4)where σ is the kernel width

2.2.8 E VALUATION M ETHODOLOGIES

The evaluation of a classification system is one of the major issues in measuringthe system’s performance From the early beginning, researchers have utilized sev-eral performance indexes to estimate the diagnostic system’s ability to distinguishaccurately the samples in their classes True-positive (TP) rate and false-positive(FP) rate are indexes that partially indicate the classification performance of a system.The TP rate represents the percentage of “diseased” samples that are correctlyclassified as “diseased,” and the FP rate represents the percentage of normal samplesthat are incorrectly classified as “diseased.” However, in most of the statisticalclassification systems, the adjustment of certain algorithmic parameters can modifytheir operating points, resulting in the achievement of different pairs of TP and FPrates Such behavior introduces questions about the selection of the appropriatetraining parameters of the system and results in difficulties in evaluating the system’sactual performance for different degrees of confidence

The receiver operating characteristic (ROC) methodology is the most widelyused scheme for evaluating the performance of a CAD system ROC analysis over-comes the problem of a fixed selection of the classification parameters A 2-Dgraphical representation of all corresponding single points, expressing each pair of

TP and FP rates, gives the overall performance of the system It is generated byplotting the true-positive rate (sensitivity) against the false-positive rate (1-specific-ity) for various threshold values (Figure 2.4) The ROC curve represents the trade-off between the TP/FP values and changes in the criterion for positivity [81] The

area under curve (AUC, Az) is a measure of the diagnostic performance of the

classifier The Az value defines the probability that the classifier will rank a randomlychosen positive instance higher than a randomly chosen negative instance It is

possible for a classifier with a lower Az value to have higher classification ability,

in a specific point, than another having higher Az value Nevertheless, the Az value

is an efficient measure of the classification performance

Alternative evaluation methodologies are the free ROC (FROC) [82] and thelocation-specific ROC (LROC) [83] In the FROC technique, the detection outcome

of a CAD system, for each image, contains normal or abnormal objects that arecharacterized as TP or FP findings if they are in the area of real or fake detections,respectively The FROC curve is created by a plot of TP rate vs the number of falsepositive samples per image In the case of the LROC methodology, only one object

is contained in each image or, in the case of a normal exam, none The annotation

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of the database is performed by radiologists, who localize the abnormalities on eachimage A simpler version of the FROC method is the alternative free-ROC (AFROC)technique [84] ROC methodologies impose limitations in their application to dif-ferent medical diagnostic systems such as limited data sets, independence of samples,the lack of categorical rating in the characterization, and the absence of indexes thatcan characterize the detection difficulty of a specific sample[85, 86] A unified ROCmethodology that can be used efficiently for all CAD systems does not exist

2.2.9 I NTEGRATED CAD S YSTEMS

The research tasks that have been proposed for more than 15 years in the area ofcomputer-aided detection in mammography have been integrated into efficient clin-ical devices that can provide useful information to radiologists To date, three CADsystems have been approved by the U.S Food and Drug Administration as clinicaldevices valuable in detection of pathological areas/objects in mammography Thesesystems are the ImageChecker (R2 Technology) [87], the Second Look Digital/AD(CADx Medical Systems) [88], and MammoReader (Intelligent Systems Software)[89]

FIGURE 2.4 ROC curves indicating the performance of three different classification systems.

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However, other systems have also been developed and are being clinicallyevaluated Some of these systems are: Mammex TR (Scanis Inc.) [90], the Promam(DBA Systems Inc.) [91], and the MedDetect (LMA & RBDC) [92] The perfor-mances of the clinically approved systems have been evaluated by several researchgroups or organizations [93–96]

2.3 COMPUTER-AIDED METHODOLOGIES FOR

THREE-DIMENSIONAL RECONSTRUCTION OF AN ARTERY

The modules of a CAD system for the detection and characterization of abnormalities

in mammography have been described in Section 2.2 Those systems take advantage

of the specific appearance of the breast tissue depicted utilizing X-rays However,similar image-analysis and artificial-intelligence techniques can be applied in med-ical images obtained by different imaging modalities One such case is intravascularultrasound (IVUS) images, which are acquired using ultrasonic signals to depict theinner structure of arteries Detection of the actual borders of the lumen and plaque

in vessels is crucial in defining the severity of arterial disease Diagnostic ultrasoundhas become the most common imaging modality, and the number of clinical appli-cations for ultrasound continues to grow

Coronary artery disease is the most common type of heart disease and the leadingcause of death both in men and women in Europe and the U.S The main cause ofcoronary artery disease is atherosclerosis, which results in hardening and thickening

of the inner lining of arteries Deposits of fatty substances, cholesterol, cellular wasteproducts, calcium, and other substances build up in the arterial wall, resulting in thedevelopment of atheromatic plaque As a consequence, partial or total obstruction

of blood flow in the artery can occur, which can lead to heart attack

Early diagnosis and accurate assessment of plaque position and volume areessential for the selection of the appropriate treatment Biplane coronary angiographyhas been used as the “gold standard” for the diagnosis of coronary narrowings andguiding coronary interventions On the other hand, intravascular ultrasound (IVUS)

is an interventional technique that produces tomographic images of the arterialsegments These techniques are considered to be complementary because the firstprovides information about the lumen width and the vessel topology, while thesecond permits direct visualization of the arterial wall morphology

Today, IVUS is used extensively as a routine clinical examination that assists

in selecting and evaluating therapeutic intervention such as angioplasty, atherectomy,and stent placement The aim of IVUS and angiographical image processing is theextraction of valuable diagnostic information about the nature of alternations oflining of arteries and the three-dimensional vessel morphology Quantitative estima-tions of plaque thickness, volume, and position in the arterial wall are obtained fromthe processing of the acquired images Sophisticated modeling techniques combiningimages from both modalities allow the three-dimensional (3-D) reconstruction ofthe arterial segment and provide useful geometrical and positional information aboutthe shape of the lumen in 3-D space The following sections describe several auto-mated methods for quantitative analysis of IVUS images and techniques for the

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extraction of three-dimensional vessel models with fusion of IVUS and ical data

angiograph-2.3.1 IVUS I MAGE I NTERPRETATION

IVUS is an invasive catheter-based imaging technique that provides 360° radial

images in a plane orthogonal to the long axis of the catheter IVUS image sequencesconsist of cross-sectional images of the arterial segment and are acquired with theinsertion of a catheter in the vessel The reflection of the ultrasound beam as it passesthrough the different layers and the scattering of the material give rise to a typicalimage pattern that can then be used to identify different regions in IVUS images.Figure 2.5 shows a schematic diagram of the cross-sectional anatomy of an artery

as well as an original depiction in IVUS images

There are two key landmarks in IVUS images that assist in the correct tation of arterial structure: the lumen/intima border and the media/adventitia border.Each one is recognized in IVUS images by its location and its characteristic appear-ance As seen in Figure 2.5(b), the first bright interface beyond the catheter itself isthe lumen/intima border Moreover, the media is usually a discrete thin layer that isgenerally darker than intima and adventitia The appearance of intima, media, andadventitia follows a double-echo pattern showing a circumferentially oriented par-allel bright-dark-bright echo pattern that is referred to as the “typical” three-layeredappearance In IVUS images of normal arteries, the three-layered appearance maynot be visible because the intima may be too thin or there may be sufficient collagenand elastin in the media of some arterial segments for it to blend with the surroundinglayers In addition, in highly diseased vessels, the media may be very thin to register

interpre-as a separate layer on ultrinterpre-asound images It is more likely that the media is clearlydefined over only a part of the vessel circumference In such cases or in noisy images,the identification of the media/adventitia border is obtained by the transition in

FIGURE 2.5 (a) Cross-sectional pattern appearance of IVUS images; (b) borders of interest

calcium

media

distal

shadowing

lumen /intima border

media /adventitia border

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“texture” of regions corresponding to plaque and adventitia In sequential IVUSframes, plaque can be distinguished from blood flowing in the lumen, because plaqueechoes exhibit a constant pattern, while blood has a highly speckled and changingpattern over time

Besides the information about the amount and distribution of the plaque, IVUSimages provide a detailed description of plaque composition The ultrasonic appear-ance of atherosclerotic plaque depends on its composition, and several components

of plaque can be identified in IVUS images

During clinical imaging, several practical methods are used to enhance theappearance of the different parts of the vessel Saline injections help real-timevisualization of luminal border [97] Injection of echo-contrast is another usefultechnique for the detection of vessel borders [98] Although these injections assist

in the better visualization of the arterial segment, they can also interrupt continuousrecording or even increase intracoronary pressure, which will result in erroneousgeometric measurements of the vessel components

2.3.2 A UTOMATED M ETHODS FOR IVUS ROI D ETECTION

The vast amount of data obtained by a single IVUS sequence renders manualprocessing a tedious and time-consuming procedure Furthermore, manually deriveddata are difficult to reproduce because interobserver and intraobserver variabilitycan reach up to 20% [99] Accurate automated methods for the detection of theregions of interest in IVUS images improve the reproducibility and the reliability

of quantitative measures of coronary artery disease Those methodologies usuallytake advantage of the characteristic appearance of the arterial anatomy in two-dimensional IVUS images and the connectivity of frames in the entire IVUSsequence

2.3.2.1 IVUS Image Preprocessing

IVUS frames contain noise, and the actual boundaries of regions of interest (ROIs)are difficult to identify in many cases A preprocessing step is essential in removingspeckles and artifacts that can interfere with the detection of desired boundaries.Usually, in IVUS images, calibration marks are included for quantitative measure-ments because they provide useful information about the real dimensions of the vessel

To remove all of the bright pixels constituting the calibration markers, substitution oftheir gray-level value by the average or the median value evaluated in the neighborhood

of each pixel must be carried out [100, 101] This operation may be preceded byautomated identification of the mark location based on the expected position andisolation of the corresponding pixels using thresholding techniques [100]

Furthermore, the detection of regions of interest in IVUS images is restricted

by the existence of weak edges, and image enhancement is required To enhanceimage features, common image-processing techniques are used: median filtering [99,101–103], Gaussian smoothing [101, 102], and nonlinear diffusion filtering based

on Euclidean shortening [102] Repeated application of these filtering techniques isacceptable for noise reduction For contrast enhancement, a local columnwise his-togram stretching can also be used [99]

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