## Difference in Average Separation Measure

This measure is defined as the difference in average separation (AVS) 23 between the original and corresponding enhanced image. The average separation is a measure of intergroup dissimilarity and is defined as the average Euclidean distance d between confused pixels, that is, pixels with the same gray scales found in both target and background regions. The AVS measure is defined as for all pairs of points such that a single point is drawn from each region, target & > i and background m2...

## Af

We define the height measure of the multiscale filter response as the peak response hM(ar) Mline lline(0, 0, 2 ar) . Since the filter response is normalized, hM(ar) is constant regardless of ar. That is, where hMc 0.25 (see the Brain Storming Question at the end of this chapter for the derivation). We define the width measure wM(ar) of the multiscale filter response as the distance Jxfi + y from the z-axis to the circular locus where Mline lline(x0, y0, z ar) gives half of the peak response,...

## The Complete Adaptive Knowledge Based Model Framework

A schematic low-level representation of the adaptive knowledge-based model is shown in Fig. 11.2. Each component identified in Fig. 11.2 is discussed now to show how the complete model comprising a knowledge-based framework is to be implemented. Each blocked level in Fig. 11.2 is described in further detail in each part of this chapter and summarized below Image preprocessing component The following image preprocessing is performed. Firstly, mammograms are grouped on the basis of their breast...

## Measures of Contrast Enhancement 11311 Distribution Separation Measure

Using the method for labeling the Target (T) and Background (B) regions, it is possible to plot the overlap of the density functions for the gray scales comprising these two regions. In mammography, this is representative of the overlap found between a breast cancer lesion and its background border. A good enhancement technique should ideally reduce the overlap. In particular, it is anticipated that the enhancement technique should help reduce the spread of the target distribution and shift its...

## Conclusion and Perspectives

In this chapter, we have seen different ways of computer assistance to the diagnosis of diabetic retinopathy, which is a very frequent and severe eye-disease image enhancement, mass screening, and monitoring. Different algorithms within this framework have been presented and evaluated with encouraging results. However, there are still improvements to be made. The first one is to use high-resolution images. We worked on images already used in centers of ophthalmology, but it is clear that...

## Conclusion

The model-based brain tissue classification framework presented here was setup to analyze MR signal abnormalities in neuropathological disorders in large sets of multispectral MR data in a reproducible and fully automatic way. The overall strategy adopted was to build statistical models for normal brain MR images, with emphasis on accurate intensity models. Signal abnormalities are detected as model outliers, i.e., voxels that cannot be well explained by the model. Special attention has been...

## Key Observations

The above discussion has described an approach to the reduction of false-positive region from segmented images containing suspicious ROI. The following key observations can be drawn 1. Region prefiltering prefiltering regions based on their area is a quick and simple method to reducing false-positive regions while maintaining similar levels of sensitivity prior to filtering. The area threshold Tarea is defined for a circular region with a diameter of 5 mm. This is a similar value to that used...

## Image Segmentation

Image segmentation can be defined as separating the image into similar constituent parts. Given an image I, segmentation of I is a partition P of I into a set of N regions Rn, n 1, , N, such that (JN1 Rn I. The separated regions should be homogeneous and meaningful to the application intended. According to Pham et al. 1 image segmentation techniques can be classified into several categories, such as thresholding, region growing, classifiers, clustering, Markov random field, artificial neural...

## Multidimensional MRFBased Segmentation

In this section, we provide a multispectral image-segmentation solution based on mMRF model. Similar to MRF model discussed in section 8.2.1, our introduction of mMRF model is also based on MAP criterion. Assume the input images I1 I2, , Id Figure 8.14 Illustration of d-dimensional image space. are observed in d channels as illustrated in Fig. 8.14 and the label matrix of segmentation result is X. Then a posterior probability can be expressed in Eq. (8.39). Another way to express the input data...

## Detection Segmentation Stage

The terms segmentation and detection may be confusing for the reader not so familiar with the medical imaging vernacular. In some instances these terms may be used interchangeably, but other times not. We might consider segmentation as being a more refined or specialized type of detection. For instance, we may gate a receiver for some time increment and make a decision as to whether or not a signal of interest was present within the total time duration, but not care about exactly where the...

## Bibliography

F., A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell., Vol. 8, pp. 679-698, 1986. 2 Gonzalez, R. C. and Woods, R. E., Digital Image Processing, Addison-Wesley, Reading, MA, 1992. 3 Kass, M., Witkin, A., and Terzopoulos, D., Snakes Active contour models, Int. J. Computer Vision, Vol. 1, pp. 321-331, 1988. 4 Cohen, L. D., On active contour models and balloons, CVGIP Image Understanding, Vol. 53, pp. 211-218, 1991. 5 Geman, D., Geman, S., Graffigne,...

## Ada Boost Procedure

Adaptative Boosting (AdaBoost) is an arcing method that allows the designer to continue adding weak classifiers until some desired low-training error has been achieved 40,41 . A weight is assignedto each of the feature points, these weights measure how accurate the feature point is being classified. If it is accurately classified, then its probability of being used in subsequent learners is reduced or emphasized otherwise. This way, AdaBoost focuses on difficult training points. Figure 2.16...

## Analysis for Sheet Width Quantification Accuracy

In this section, we present a systematic approach to the accuracy validation of width quantification. Especially, we investigate inherent limits on the accuracy of sheet width measurement described in the previous section arising from finite resolution. We focus on MR imaged structure, and especially address the question as to how the accuracy depends on the orientation of sheet structures when a voxel shape is anisotropic in MR imaging. In the following, a theoretical procedure for...

## Artificial Neural Network Classification

Using a labelled training set, an ANN classifier can be trained using supervised learning algorithms to discriminate between normal and abnormal regions. Features from representative training samples are provided during supervised learning and the weights of the ANN are updated until the generalization ability of the classifier starts to decrease measured on a separate validation set. Implementation in the adaptive knowledge-based model results in the construction of a separate ANN classifier...

## Atherosclerotic Blood Vessel Tracking and Lumen Segmentation

Most existing active contour model based algorithms require the topology of the object to be known before the tracking action starts. Unfortunately, this requirement is difficult to be satisfied in some practical scenarios since the topography is often difficult to be predicted in advance. For example, in our study of carotid artery, the lumen bifurcates from one common carotid artery into internal and external carotid arteries at certain location along the image

## Application to Analysis of fMRI Data

Functional MRI is a powerful modality for determining neural correlates of cognitive processes. It can be used to monitor changes of physiological parameters such as regional cerebral blood flow, regional cerebral blood volume, and blood oxygenation during cognitive tasks 126 . To extract functional information and detect activated regions using fMRI, the most widely adopted procedures are generally based on statistics theory and are paradigm dependent 65,127,128 . Cluster analysis has recently...

## D

Figure 8.12 An example of the MRF-based active contour framework. (a) The original image of T1W MR image on carotid artery lumen. (b) Edge map by Canny edge detector. (c) Segmentation result of QHCF algorithm with Trc 10, p1 400, p2 1000, Tmin 20. (d) Lumen contour based on the QHCF algorithm. (e) Six selected control points. (f) Fine-tuned contour by applying MPA. Figure 8.12 An example of the MRF-based active contour framework. (a) The original image of T1W MR image on carotid artery lumen....

## Improving Human Computer Interaction 1461 Background

Extensive research has been invested in recent years into improving interactive segmentation algorithms. It is, however, striking that the human-computer interface, a substantial part of an interactive setup, is usually not investigated. Although the need for understanding the influence of human-computer interaction on interactive segmentation is recognized, only very little research has been done in this direction. In order to improve information flow and to achieve optimal cooperation between...

## Effects of Voxel Anisotropy in MR Imaging

Figure 10.20(a) shows the effects of sheet normal orientation 0 and voxel anisotropy Az on measured thickness T. The relations between measured thickness T and sheet normal orientation 0 for six values of true thickness t (1, 2, 3, 4, 5, 6) were plotted when three different values of voxel anisotropy Az (1, 2, 4) were used. The relations were regarded as ideal when T t for any 0, which is the horizontal in the plots of Fig. 10.20(a). When Az 1, the relations were highly close to the ideal for t...

## Evaluation on DDSM Mammograms

This section presents the results obtained from the segmentation of 200 mam-mograms from the DDSM. The aim of the experiment is to identify the optimal contrast enhancement expert for each of the 200 abnormal mammograms. Each mammogram image has been grouped according to its target breast type. There are 50 images per breast type grouping and results will be presented on a per breast type basis. Each mammogram is contrast enhanced using each enhancement method identified in section 11.3.2.1.1...

## Markovian Based Segmentation Method

The algorithm consisted of running the pixel classification approach using Markov random field with mean field (see Zhang 149 ). Here, the image segmentation was posed as a classification problem where each pixel is assigned to one of K image classes. Suppose the input image was y (yij j, (i, j) e L , where yi,j is a pixel, i.e., a 3-D vector, and L was a square lattice. Denote the segmentation as z zi,j, (i, j) e L . Here, zi, j is a binary indicator vector of dimension K, with only one...

## Fuzzy Clustering

A cluster or a class may be defined as a set of objects with similar characteristics (features) and different from other objects outside the group. When data are clustered, a condition is chosen for measuring the similarity of an object to that cluster. There are three types of clustering techniques crisp, also known as hard or classical clustering, fuzzy, and probabilistic clustering 43, 48 . Crisp or classical clustering algorithms classify objects as part of a cluster or not part of a...

## Model Based Initialization

The previously described model-based approaches employing statistical encoding of large organ populations can also be successfully applied to efficient initialization of interactive methods 61 . The underlying idea is to apply statistical shape analysis for examining the remaining variability of shape due to interactive point-wise subtraction of variation. The key element is the optimal selection of principal landmarks that carry as much shape information as possible. The goal is to remove as...

## Analytic Kernel Based Methods 2221 Derivatives of Gaussian

In order to handle image structures at different scales in a consistent manner, a linear scale-space representation is proposed in 24,34 . The basic idea is to embed the original signal into an one-parameter family of gradually smoothed signals, in which fine scale details are successively suppressed. It can be shown that the Gaussian kernel and its derivatives are one of the possible smoothing kernels for such scale-space. The Gaussian kernel is well-suited for defining a space-scale because...

## Knowledge Representation with Multistage Neural Networks

An alternative to a hard bounded grouping scheme such as those proposed above is in the use of soft decision boundaries. These knowledge-based components utilize a mixture-of-experts paradigm. Lai and Fang 11, 12 proposed the use of a hierarchical neural network to model the optical transformation of a 12-bit magnetic resonance image (MRI) into an 8-bit representation for display on a computer monitor. This optimal optical transformation is crucial if the expert radiologist is to effectively...

## KNearest Neighbors

Voting k-nearest neighbors classification procedure is a very popular classification scheme that does not rely on any assumption concerning the structure of the underlying density function. As any nonparametric technique, the resulting classification error is the smallest achievable error given a set of data. This is true because this technique implicitly estimates the density function of the data, and therefore, the classifier becomes the Bayes classifier if the density estimates converge to...

## Introduction

The importance of plaque component classification and vessel wall quantification has been well established by several research groups (see Refs. 1-30 ). Following are the two main reasons for this research 1. Regression and progression of atherosclerosis Direct plaque imaging is of potential use not only for diagnosis but also for monitoring response to treatment. Angiographic studies of progression and regression of atherosclerosis have been notoriusly poor in demonstrating changes in plaque...

## Modeling a Sheet Structure

The Fourier transform of 3-D sheet structure orthogonal to the x-axis, s0(x t), is given by S0(& > t) F Bar(x t) 8(a> y) 8(uz), (10.60) where F represents the Fourier transform, 8(w) denotes the unit impulse, and x (wx, rny, mz). Note that F Bar(x t) t Sinc( x t) when L + L_ 0 and L0 1 in Bar(x t). The Fourier transform of 3-D sheet structure whose normal is s(x t, rg ), is given by S(X t, re4) S00' t), (10.61) where a> ' Re cx, in which denotes a 3 x 3 matrix representing rotation...

## B us t

Figure 10.1 Weight functions in measures of similarity to local structures. (a) (Xs Xt), representing the condition Xt Xs, where Xt < Xs. (Xs Xt) 1 when Xt Xs. (Xs Xt) 0 when Xs 0. (b) w(Xs Xt), representing the condition Xt Xs 0. w(Xs Xt) 1 when Xs 0. w(Xs Xt) 0 when Xt Xs 0 or Xs(> in which 0 < a < 1 (Fig. 10.1(b)). a is introduced in order to give m(Xs Xt) an asymmetrical characteristic in the negative and positive regions of Xs. Figure 10.2(a) shows the roles of weight functions in...

## Detection of Focal Contour Abnormality

A focal contour abnormality is said to occur when the local curvature is large compared to the average lumen curvature. The curvature, is calculated for a small segment of the lumen and its ratio to the average curvature for the whole lumen is assigned to the point in the center of that segment. In order to obtain gradient and curvature parameters for the same point, the TOF contour and BB contour are brought into correspondence by registering the centroids of their convex hulls. With this...

## Effects of Gaussian Standard Deviation in Postprocessing

Figure 10.19 shows the effects of the standardg deviation (SD), a, in Gaussian blurring. In Fig. 10.19(a), the relations between true thickness t and measured thickness T are shown for three a values (1, 1) when Az is equal to 1, i.e. in the case of isotropic voxel. The relation is regarded as ideal when T t , which is the diagonal in the plots of Fig. 10.19(a). For each a value, the relations were plotted using two values of sheet normal orientation 0 (0 , 45 ), while was fixed to 0 . Strictly...

## Ooo

Figure 12.14 Computer graphic display of a sphere using different grids (reproduced from 19 ). (a) Display based on a sc grid with voxels of the same volume as the display based on a fcc used for (b). The image (c) corresponds to a display based on a sc grid with voxels of volume equal to one eighth of the voxel volume in the other two images. grid, grid points whose Voronoi neighborhoods share a face can be at one of two distances from each other, depending on the kind of face they share (see...

## Modeling MR Image Acquisition

The Fourier transform of MR PSF is given by M(T Ax, Ay, Az) 1 Rect M -1, -1, -M . (10.64) where Rect(x ax, ay, az) Rect(x ax) Rect(y ay) Rect(z az) (Fig. 10.18(b)), and By substituting Eq. (10.62) for T in Eq. (10.64) to obtain 1-D frequency component affecting S(ts), the following is derived M(Ms) M(Ms rM Ax, Ay, Az). (10.66) Thus, the Fourier transform of MR image of the sheet structure, F(a> s) is given by F (Ms) F( F_1 S( s)M (Ms ) , (10.67) where F-1 represents the inverse Fourier...

## Overlap Analysis of Segmentation Results

The results in the previous section show that the performance obtained following ROC analysis of the knowledge-based segmentation component is greater than that obtained from the best performing segmentation expert. By thresholding each probability image using a ROC operating point following optimal expert combination, region boundaries can be identified. In general, the ROC operating point 40 can be selected for each individual mammogram by associating a cost for a false positive, CFp, and a...

## Parameterizing the Vasodilation Response

In the last few years there has been a growing interest in understanding the link between endothelial function and several aspects of cardiovascular diseases (CVD). It is known that impaired endothelial function is associated with a number of disease states, including CVD and its major risk factors 28-31 . Also, endothelial dysfunction seems to precede by many years other more manifest symptoms and may itself be a potentially modifiable CVD risk factor. Therefore, it promises to have not only...

## Ef

Figure 2.23 Tissue characterization results (b), (d), and (f) White labels soft plaque, dark gray areas are displayed where calcium plaques are located, and light gray areas labels hard plaque. (a), (c), and (e) Original images. accumulation local moments are good descriptors of the different kind of plaque tissues. However, local binary patterns and accumulation local moments are also fast, in terms of low-time processing. On the other hand, the classification of the feature data is a critical...

## Questions

What are the physical characteristics of helical CT scans that may impact CAD algorithm design and performance 2. What are the clinical characteristics of pancreatic cancer that may impact CAD algorithm design 3. What is the general approach for image segmentation of medical images 4. Advantages and disadvantages of unsupervised, supervised, and semi-supervised clustering methodologies for image segmentation. 5. What is FCM and when is it used for image segmentation List any advantages over...

## Identification of Fibrous Cap Status by MRI

Several image weightings (T1, T2, PD, 3D TOF) are used together by a radiologist to make the diagnosis of a FC 97 . A dark rim on 3D TOF is associated with a thick cap and a thin cap is associated with its absence. A ruptured cap is indicated by the absence of a dark rim in the presence of other markers like a focal contour abnormality or a bright gray region near the lumen 97 usually best seen in flow suppressed black blood images. Figures 8.22-8.24 show typical appearances of thick, thin, and...

## Portal Vein Segmentation from 3D CT Data

Multiscale line filtering was applied to abdominal CT images taken by a helical CT scanner so as to segment the portal veins to localize a tumor with the relation to them for surgical planning. The CT dataset consisted of 43 slices of 512 x 512 pixels the pixel dimensions were 0.59 mm2. The beam width was 3 mm and the reconstruction pitch was 2.5 mm. The CT data were imaged using CTAP Figure 10.5 Liver vessel (portal vein) segmentation from abdominal CT images. (a) Original cross-sectional...

## Region Based Segmentation

Region-based segmentation approaches examine pixels in an image and form disjoint regions by merging neighborhood pixels with homogeneity properties based on a predefined similarity criterion. Suppose that I represents an image that is segmented into N regions, each of which is denoted as R where i 1, 2, , N, the regions must satisfy the following properties where ( ) is a logical predicate. The original image can be exactly assembled by putting all regions together (Eq. 3.9) and there should...

## RGB Representation

These considerations explain why the use of green light is very advantageous for the analysis of the retina, particularly for the visualization and analysis of blood containing elements. The RGB representation of the color image allows (c) The green channel (d) The blue channel Figure 7.4 A RGB representation of a color image. (c) The green channel (d) The blue channel Figure 7.4 A RGB representation of a color image. one to exploit this interpretation of the reflected spectrum. A color image...

## Results and Conclusions

The goal of automatic tissue characterization is to identify the different kind of plaques in IVUS images. This process requires two tasks identification of what the plaque is and labelling of the different areas of the plaque. Figure 2.18 illustrates roughly the procedure of supervised tissue characterization. The IVUS image (see Fig. 2.18(a)) is preprocessed and sent to the automatic tissue characterization system. Figure 2.18(b) illustrates the physicians-assisted segmentation of IVUS, which...

## Dataset and Adaptive Knowledge Based Model Configuration

In this section, the adaptive knowledge-based model is evaluated using the same configuration as described in the previous section and using exactly the same strategy for determining the segmentation operating point from an independent Table 11.17 Frequency of normal and abnormal images Table 11.17 Frequency of normal and abnormal images training set. The dataset is extended to include 200 normal images from four different breast types, 50 normal images drawn from each. The use of normal...

## Results of Synthetic System Boundary Estimation

Figure 9.31 shows in the FCM classification system all the steps for the left and right lumen detection, identification, and boundary estimation process in the synthetic images. We look at large noise protocol as an example below with noise level a2 500. In the first row the left image shows the synthetically generated image. In the first row the right image shows the image after it has been smoothed by the Perona-Malik smoothing function. In the second row the left image shows the classified...

## FMD Response Eigen Parameterization

As can be concluded from Table 5.7, a weak but significant correlation was found between AFMDc and LDL cholesterol in a damaging way and between AFMDc and HDL cholesterol in a protective way. This had been previously reported when studying dyslipidemic populations with a similar correlation magnitude, association that could be slightly attenuated in our population due to a narrower range of lipids variation. For instance, Kuvin et al. 38 found a correlation coefficient of HDL cholesterol and...

## Results

3.6.4.1 Simulated 11C Thymidine PET Study Figure 3.9 shows the segmentation results using different numbers of clusters, k, in the clustering algorithm. The number of clusters is actually varied from 3 to 13 but only some representative samples are shown. In each of the images in Figs. 3.9(a)-3.9(f), different gray levels are used to represent the cluster locations. Figure 3.9 shows that when the number of clusters is small, segmentation Figure 3.9 Tissue segmentation obtained with different...

## MRFBased Active Contour Model 831 Introduction

As discussed in section 8.1, most segmentation algorithms can perform well only on certain types of practical images because of the applicability limitation of each modeling or ease of use. In this section, we will introduce a flexible and powerful framework for general-purpose image segmentation. In the course of our investigation, we use the following assumption A successful segmentation is an optimal local contour detection based on an accurate global understanding of the whole image. This...

## Multivariate Segmentation

The main aim of dynamic imaging is to study the physiology (function) of the organ in vivo. Typically the image sequence has constant morphologic structures of the imaged organs but the regional voxel intensity varies from one frame to another, depending on the local tissue response to the administered contrast agent or radiopharmaceutical. In the past, analysis of such dynamic images involved only visual analysis of differences between the early and delayed images from which qualitative...

## Supervised and Unsupervised Test Image Segmentation

A test image to be segmented is represented in the same way as the training image by a 1-D array X. In the case oftest image, a 1-D array Y y , y2, , yN) is the estimate of the segmentation. We can now adopt one of the two strategies for test image segmentation. 1. Supervised segmentation with GMM Using the ML estimate of the parameter values obtained from the training images, a segmentation of the test images is performed. This is achieved by substituting the learnt model parameters 0 from...

## Knowledge Based Framework

The CAD scheme detailed in this chapter is based on an adaptive framework. An adaptive framework is capable of modifying itself such that it is more suitable to the environment within which it operates. Within the context of CAD, an adaptable component or a framework, attempts to automatically optimize the lesion detection process for a given mammogram. Broadly speaking, an adaptive characteristic can be built into CAD in three different ways (1) Using a deterministic component (2)...

## Contributors

University of Zaragoza, Zaragoza, Spain Anand Manhoar, M.S. University of South Florida, Tampa, FL, USA University of Pennsylvania, Philadelphia, USA University of Washington, Seattle, WA, USA Case Western Reserve University, Cleveland, OH, USA Katholieke Universiteit Leuven, Leuven, Belgium Katholieke Universiteit Leuven, Leuven, Belgium Katholieke Universiteit Leuven, Leuven, Belgium Swiss Federal Institute of Technology, Zurich Case Western Reserve University, Cleveland, OH, USA Ecole des...

## Deformable Surface Models

The basic concepts of Snakes minimization of an energy term through optimization can easily be generalized to three dimensions. Additional effort is required only to handle the parameterization problem adherent to 2-D manifolds. In contrast to 2-D active contour models, where arc length provides a natural parameterization, 2-D manifolds as used for 3-D deformable models pose a complex, topology, and shape-dependent parameterization problem. Parameterizing a surface effectively is difficult...

## Cluster Validation

As mentioned earlier, the optimum number of clusters for a given dataset is usually not known a priori. It is advantageous if this number can be determined Figure 3.8 Simulated noisy 18F fluorodeoxyglucose (FDG) kinetics in different regions. Figure 3.8 Simulated noisy 18F fluorodeoxyglucose (FDG) kinetics in different regions. based on the given dataset. In this study, a model-based approach was adopted to cluster validation based on two information-theoretic criteria, namely, Akaike...

## Real Data Analysis Circular Vs Elliptical 961 Circular Binarization

Select class is used for binarization of the classified image. The frequency of each pixel value in the ROI is determined. The core class C0 is the class with the greatest number of pixels. The number of pixels is equivalent to the area of the core. The average area of the entire lumen core is determined from the ground truth boundaries, and this area is compared to the area of the C0 area. A threshold function is used to determine whether to binarize the C0 region, or to merge C0 with C1 and...

## Survey of Active Contour Model

The active contour model, also known as Snake, was first introduced by Kass et al. 61 in 1988. In computer vision and image video processing, it has been used as a very effective approach to implement contour tracking and shape feature extraction of interested object, and is also regarded as a successful de-formable model in applications ranging from medical image analysis to video object manipulation. Basically, the development of active contour models has the following phases classical Snake,...

## Challenges in Lumen Wall Boundary Estimation

Following are the challenges for lumen wall (inner) and vessel wall (outer) estimation processes (see also Fig. 9.4) 1. Mulitple classes in the lumen region due to laminar blood flow The lumen region consists of multiple classes core class (central part of the lumen), adjoining class (due to slow moving blood flow as seen in Fig. 9.4), and some times border pixels in the fibrous cap region giving different classes. So, the lumen region can be C1, C1 + C2, or C1 + C2 + C3 class regions. 2. Lumen...

## Ab

Figure 2.4 Accumulation local moments response. (a) Original image. (b) Accumulation local moment of order (3,1). throughout the region of interest. The parameter a controls the shape of the logistic function. Therefore each textural feature will be the result of the application of the nonlinear operator to the computed moments. If n k l moments are computed over the image, then the dimension of the feature vector will be n. Hence, a n-dimensional point is associated with each pixel of the...

## Processing Classification

Very few methodologies have been developed for the classification of pancreatic tumors, e.g., the differentiation between benign and malignant disease or even the differentiation between normal and abnormal pancreas or pancreatic areas reported. One application used several classification schemes to differentiate between pancreatic ductal adenocarcinoma and mass-forming pancreatitis. The methods included artificial neural network classifiers, Bayesian analysis, and Hayashi's quantification...

## Adaptive Fuzzy Leader Clustering

AFLC is an integrated neural-fuzzy clustering algorithm that can be used to learn cluster structure embedded in complex datasets in a self-organizing manner. The algorithm has a two-layer structure as illustrated in Fig. 6.1. The first layer uses a self-organizing neural network similar to ART1 26-28 to find hard clusters. Let C be the current number of centroids and v i 1, ,C) representing the centroids. When a new sample xk comes in, it is normalized and then initially classified into the...

## Sheet Case Medial Surface Detection

We assume that the direction of the surface normal is given by e1 at the voxel around the medial surface. The 1-D intensity function, c(v), which is the profile of f (X af) along e3, should have its peak on the medial surface. The second-order approximation of c(v) is given by c(v) f (X0 a f) + vc0 + 1 v2cl (10.36) where ve3 x e, c'0 Vf e3, and c X3. c(v) should have its peak on the medial surface of the sheet. The peak is located at the position satisfying By solving Eq. (10.37), we have the...

## Fuzzy CMeans

Fuzzy C-means 16 is a fuzzy version of k-means to include the possibility of having membership of the samples in more than one cluster. The goal is to find an optimal fuzzy c-partition that minimizes the objective function Jm(U, V X) J2I> ij)mHxj - v. 2 (6.18) where vi is the centroid of the ith cluster uij is the membership value vector of the ith class for the jth sample dj is the Euclidean distance between the ith class and sample xj c and n denote the number of classes to be clustered and...

## Interactive Segmentation

In spite of the considerable success of knowledge-based automatic segmentation, generic algorithms capable to analyze and understand complex anatomical scenes cannot be expected to be available in the near future. The major reason for the slow progress is that current methods can cover only a very limited fragment of the whole spectrum of prior knowledge, which clinicians use when analyzing radiological images. Accordingly, available solutions can be applied only on very limited problem domains...

## External Signal Segmentation

The approach that was implemented was based on edge detection, line tracing, and histogram thresholding techniques 43 . The requirements for this process do not differ significantly from those followed in standard chest radiography (CXR) and several of the concepts described in CXR literature are applicable to CT as well 62 . One primary issue in this module was the desired level of accuracy in the removal of the external signals, i.e., signals from the rib cage and spine. Increasing the...

## Histological Description of the Lumen

Figure 9.1 shows the 3-D view of the cross section of the lumen. Figure 9.2 shows the histological cross section of the artery. There are three layers in the walls of both arteries and veins Figure 9.2 Histology image of the arterial cross section. Figure 9.2 Histology image of the arterial cross section. 1. Tunica intima It is the innermost layer which consists of the endothelium (a simple squamous epithelium) and a small amount of underlying connective tissue. In arteries it also includes the...

## Clustering Methods

Clustering is a natural way for image segmentation since partitions of similar intensity or texture can be seen as different clusters, the same way human beings perceive objects. Let Xj, i 1, , N, be a sample of the input space, and let Cj c C, j 1, , M, be one class of a total of M classes. A clustering algorithm determines the classes C and assigns every sample x into one of the classes. For hard clustering, a sample belongs to only one class, meaning 0 Cj Vk j. For fuzzy clustering, a sample...

## Ground Truth Tracing and Data Collection

Figures 9.5-9.9 show abnormal images of the left and right carotid arteries overlayed with the ground truth tracing. In each pair of rows, the top row is the left carotid arteries and the bottom row is the right carotid arteries. The ground truth tracing is the boundary of the inner lumen wall. Figure 9.9 shows the normal images of the same left and right carotid arteries. The normal images show Figure 9.6 Abnormal ground truth overlays. The top row in each row pair is the left carotid artery...

## J2 f x

The color We have already seen in the section 5.2 that the green channel contains the most important information about blood-containing elements in the retina and this is why it is used for the detection of microaneurysms. However, there is also some information in the red, and sometimes in the blue channel. We have studied a lot of color features the most efficient are the following two 1. Color Contrast in the Luv color space In the Luv color space, the euclidean distance can be seen as the...

## Knowledge Based Automatic Segmentation

Even the most sophisticated pre- and postprocessing techniques cannot, however, overcome the inherent limitation of the basically intensity-based methods, namely the assumption that segmentation can be carried out solely based on information provided by the actual image. This assumption is fundamentally Figure 14.3 Brain segmentation based on morphological postprocessing. Image (a) shows the result of thresholding, which has been eroded (b) in order to break up unwanted connections between...

## Image Enhancement

This step is usually done to increase the contrast or reduce the noise in an image to allow for more accurate segmentation in the steps that follow. It usually precedes organ segmentation or registration because it offers the potential of redistributing and rescaling pixel values in order to obtain more successful results in the clustering and classification of pixels. Techniques reported in the literature are designed for the spatial or the frequency domain. Spatial domain methods include...

## Mean Error eNp

Using the definition of the polyline distance between two polygons, we can now compute the mean error of the overall system. It is denoted by eNFp and defined by poly _ 2 x J2t J2n 1 Ds(Gnt, Cnt) ,Q where Ds(Gnt, Cnt) is the polyline distance between the ground truth Gnt and computer-estimated polygons Cnt for patient study n and slice number t. Using the definition of the polyline distance between two polygons, the standard deviation can be computed as Ht 1 v g vertices Gvi (db (v, Cnt) - ej...

## Maximum Likelihood

The maximum likelihood (ML) classifier is one of the most popular methods of classification 42 . The goal is to assign the most likely class Wj, from a set of N classes wi, , wN, to each feature vector. The most likely class w j from a given feature vector x is the one with maximum posterior probability of belonging to the class P(w j x). Using the Bayes' theorem, we have On the left side of the equation, there is the a posteriori probability of a feature vector x to belong to the class wj. On...

## Attenuation Correction in PET

Accurate attenuation correction (AC) is essential to emission computed tomography such as PET and SPECT, for both quantitative and qualitative interpretation of the results (Chapter 2 of Handbook of Biomedical Image Analysis Segmentation, Volume I). In PET, for instance, AC factors are most often determined by calculating the pixel-wise ratio of a blank scan acquired before positioning the patient in the gantry of the scanner, and a transmission scan performed with the patient in the gantry....

## Advanced Segmentation Techniques

Functional imaging with PET, SPECT, and or dynamic MRI provides in vivo quantitative measurements of physiologic parameters of biochemical pathways and physiology in a noninvasive manner. A critical component is the extraction of physiological data, which requires accurate localization segmentation of the appropriate ROIs. A common approach is to identify the anatomic structures by placing ROIs directly on the functional images, and the underlying tissue TACs are then extracted for subsequent...

## Analysis of Multiscale Line Filter Responses

The measures of similarity to the local structures have been introduced based on the ideal local structures with an isotropic Gaussian cross section shown in Eqs. (10.12)-(10.14). To examine the effects of parameters involved in the Figure 10.7 Visualization of lung nodule and vessel from CT data (Color Slide). (a) Original CT slice image. (b) Volume rendered images of nodules (green), vessels (red), lung (violet), and bone (white) tissues. Left Using only original images. Right Using original,...

## Performance Evaluation of Three Techniques

Figure 9.44 shows the mean error bar charts for the three pipelines (i.e., using three classification systems MRF, FCM, and GSM methods).5 The charts can be seen in the Tables 9.1-9.3. Table 9.1 shows the error between the computer-estimated boundary and ground truth boundary using FCM-based 5 We ran the system using each of the three different classifying methods on real patient data. Ground truth boundaries of the walls of the carotid artery were traced for 15 patients. Overall the number of...

## Region Prefiltering

Feature extraction is computationally expensive. A common strategy 6, 7,36 to reduce the number of regions considered for false-positive reduction is achieved by applying a size test. By eliminating suspicious regions smaller than a predefined threshold 71area, the number of false-positive regions can be reduced. For the expert radiologist interpreting a film mammogram during screening, it is common to disregard any suspicious ROI less than 8 mm in diameter 37 . In mammographic CAD with...

## Accuracy and Robustness

Because all affinities (and consequently the segmentations) shown in the last section are based on seeds selected manually by a user, the practical usefulness and performance of the multiseeded fuzzy segmentation algorithm need to be experimentally evaluated, both for accuracy and for robustness. The experiments used the top-left images of Figs. 12.3-12.7. We chose these images because they were based on mathematically defined objects to which we assigned gray values that were then corrupted by...

## Conclusions

This chapter presents a new method to assess brachial artery vasodilation in US sequences. This method, based on image registration, minimizes the effect of low-level artifacts. It also incorporates a motion compensation phase, which relieves the operator of manually tracking a region of interest. The method is accurate (bias +0.05 , and limits of agreement 2.05 FMD), has better reproducibility (CV 0.40 ) than manual measurements (CV 1.04 ), and is robust, yielding clinically relevant...

## Characterization of Tissue Kinetics

Kinetic modeling of radiotracer (or radiopharmaceutical) is the core of dynamic PET SPECT imaging. The aim of modeling is to interpret kinetic data quantitatively in terms of physiological and pharmacological parameters of a mathematical model, which describes the exchanges (e.g. delivery and uptake) of radiotracer by the tissue. Statistical inferences can then be made regarding the distribution and circulation of tracers within different tissues regions, which are quantitatively represented by...

## Fuzzy Based Segmentation Method

In this step, we classified each pixel. Usually, the classification algorithm expects one to know how many classes (roughly) the image would have. The number of classes in the image would be the same as the number of tissue types. A pixel could belong to more than one class, and therefore we used the fuzzy membership function to associate with each pixel in the image. There are several algorithms for computing membership functions, and one of the most efficient ones is Fuzzy C means (FCM) based...

## Simulational Evaluation of Medial Axis Detection

We evaluated the medial axis detection performance using synthesized 3-D images of lines with pill-box cross-sections. A simulated partial volume effect was incorporated when synthesizing the images. We focused on the effects of the filter scale af used in medial axis detection on the detection various widths of line structures. Synthesized 3-D images of a line with a circular axis were generated. The diameter of the line, D, was varied between 2.0 and 11.3) voxels. The radius of the circular...

## Annex Algorithm Evaluation

Whenever objects are detected automatically, the performance of the algorithm has to be evaluated. In the medical domain, results are normally compared to the results obtained by one or more specialists. Let us consider a medical examination (diagnostic test). Often, such a test can only be positive or negative (the patient suffers from the disease or not). In order to evaluate the efficiency of this diagnostic test, its result is compared to reality the truth is found by other diagnostic...

## Knowledge Representation Learnt from User Interactions

A novel method of implementing an adaptable characteristic in a knowledge-based component has been suggested by capturing user interactions with a CAD tool. Fenster and Kender 15 proposed the use of a diagnostic tool for the interpretation of computed tomography (CT) images. The authors utilize a boundary-based segmentation technique termed the live wire paradigm. The motivation for the scheme is based on an attempt to utilize the interaction with an expert clinician during segmentation,...

## Challenges in Identification of the Fibrous

Fibrous cap thickness is in the order of a few tenths of a mm while the maximum resolution by MRI by the current protocol used is 250 m x 250 m (interpolated by zero filling) while the native MR resolution is around 500 m. In spite of this resolution, 3D TOF seems to be able to detect the cap status 7, 97, 98 . When using multicontrast MR images for segmentation, registration accuracy becomes very important. Since the characteristics for FC detection by MRI occupy a few pixels around the...

## Single Scale Filter Responses to Mathematical Line Models

The line measure generalizes X 23 in Eq. (10.5) and Xg mean23 in Eq. (10.6). An alternative measure is to use the arithmetic mean of X2 and X3, which is given by Xa mean 23 2 * (1 .20) To compare these three measures, let us consider a 3-D line image with elliptic (nonisotropic Gaussian) cross sections given by elliptic(x ax, ay) exp j 2- + IL J * (10.21) When ax ay, lelliptic(x ax,ay) can be regarded as an ideal line, that is, line(x ax). Figure 10.8 shows the plots of the three measures and...

## Color Cervix Image Segmentation

Cervical cancer is the second most common cancer among women worldwide. In developing countries, cervical cancer is the leading cause of death from cancer. About 370,000 new cases of cervical cancer occur worldwide, resulting (a) Fundus image (left stereo (b) Manually segmented optic image) disk cup by an ophthalmologist (d) DA-segmented optic disk (e) DA-segmented optic cup (f) DA-segmented blood vessels (d) DA-segmented optic disk (e) DA-segmented optic cup (f) DA-segmented blood vessels (g)...

## Feature Extraction

Features are extracted to characterise a segmented region in the mammogram. Feature vectors from masses are assumed to be considered different from normal tissue, and based on a collection of their examples from several subjects, a system can be trained to differentiate between them. The main aim is that features should be sensitive and accurate for reducing false positives. Typically a set or vector of features is extracted for a given segmented region. From the pixels that comprise each...

## Feature Data Dimensionality Reduction 2331 Principal Component Analysis

This method is also known as Karhunen-Loeve method 38 . Component analysis seeks directions or axes in the feature space that provide an improved, lower dimensional representation of the full data space. The method chooses a dimensionality reducing linear projection that maximizes the scatter of all projected samples. Let us consider a set of M samples x , x, ,xM in an n-dimensional space. We also consider a linear transformation that maps the original space in a lower dimensional space (of...

## Discussion and Conclusions

In this section, even though experimental results demonstrate that the QHCF leads to better segmentation results over other approaches, including UGHCF and adaptive ICM, same as what occurred in other random field based solutions, the determination of parameters including Tc, P1,P2, and Tnin is also a difficult part of implementing the QHCF into real applications. This is mainly because the evaluation of segmentation result is usually application oriented, which highly depends on the...

## Erosion and Dilation

Many operators in mathematical morphology are based on the use of a small test-set B called structuring element (SE). Its shape and size can be chosen in accordance with the segmentation or filtering task. In order to calculate the morphological erosion of a binary image A, we test for each point x if the structuring element centered in x fits completely into A. If this is the case, x belongs to the eroded set e A. The dilation can be seen as an erosion of the background. (a) Original (b)...

## Ensemble Based Combination Rules

Kittler 33 proposed a set of very popular rules for combining probability outputs from a number of experts. These rules are stated as follows i D rt r- I q ct nR 1 p(y mi Xn,Or) (Prod) p(y mi Xn,01 Or) 1R- (Sum) p(y mi xn,Oi Or) r p(y 1 I xn, Or) (Max) p(y mi Xn,Oi Or) max R 1 (y mi Xn, Or) Min (Min) p(y mi xn,Oi Or) min R 1 (y mi xn, Or) max r i p(y mi xn, 0j) 0 otherwise The above combination rules have been used in several studies and form the basis of our baseline comparison.

## Snakes

The second class of algorithms presented intends to overcome some of the limitations of the graph-based approaches. The former allows the segmentation line, respectively surface, to have individual properties that are not related to the image, but rather to physical properties of some material. The segmentation process is no longer solely based on the image, but regularized by the constraineds imposed by the physical model. This model introduces some generic knowledge of general organ's shape...

## Biomedical Image Analysis

Handbook of Biomedical Image Analysis TOPICS IN BIOMEDICAL ENGINEERING INTERNATIONAL BOOK SERIES Series Editor Evangelia Micheli-Tzanakou Rutgers University Piscataway, New Jersey Signals and Systems in Biomedical Engineering Signal Processing and Physiological Systems Modeling Suresh R. Devasahayam Edited by George K. Hung and Kenneth J. Ciuffreda PDE and Level Sets Algorithmic Approaches to Static and Motion Imagery Edited by Jasjit S. Suri and Swamy Laxminarayan Frontiers in Biomedical...

## The Detection of the Vascular Tree by Means of the Watershed Transformation

In this section, we present a method for the detection of the vascular tree in color images of the human retina. This algorithm is quite general only few information specific for retinal images is used. It can therefore be used for the extraction of elongated features in other types of images. Detecting the vascular tree is essential for the analysis of fundus images. The structure of the vascular tree gives useful information for other feature or lesion detection algorithms (e.g., optic disk,...

## Classification Process

Once completed the feature extraction process, we have a set of features disposed in feature vectors. Each feature vector is composed of all the feature measures computed at each pixel. Therefore, for each pixel we have an n-dimensional point in the feature space, where n is the number of features. This set of data is the input to the classification process. The classification process is divided in two main categories supervised and unsupervised learning. While supervised learning is based on a...

## Graph Based Segmentation Method

The graph segmentation method (GSM) segments an image by treating it as a graph G (V, E) where V the set of vertices are the pixels and E the set of edges are pairs of pixels. Using a weight function w(e), where e is an edge (vi, Vj), the weights of the edges are computed and the edges are sorted by weight in a nondecreasing order. Initially, each pixel vi is segmented into its own component Ci. For each edge (vi, v j) in the list, a decision criterion D is applied and a decision is made...

## Guidelines for Parameter Value Selection

The multiscale enhancement filter includes several parameters. In defining the similarity measures to local structures, yst and a in Eqs. (10.3) and (10.4) need to be specified, while in the multiscale integration, the smallest scale a1, the scale factor s, and the number of scale levels n in Eq. (10.17) need to be specified. With regard to the parameters in the line measure, if there are strong sheet structures to be removed from an image, y23 should be 1.0. If the cross sections of line...

## 1 2c

Figure 6.2 Adaptive fuzzy leader clustering (AFLC) implementation flow chart. Figure 6.2 Adaptive fuzzy leader clustering (AFLC) implementation flow chart. The above nonlinear relationships between the ith centroid and the membership value of the jth sample to the ith cluster are obtained by minimizing the fuzzy objective function in Eq. (6.18). Figure 6.2 shows the flow chart for AFLC implementation. AFLC has been successfully applied to image restoration, image noise removal, image...

## Acknowledgments

This work has been partially supported by funds from the Advanced Technology Program (ATP) (Grant No. 003644-0280-1999), Technology Development and Transfer Program (TDT) (Grant No. 003644-0217-2001) of the state of Texas, Kestrel Corporation, the NEI Grant No. 1R43 EY14090-01 and the NSF Grant EIA-9980296. We acknowledge Young I. Kim, M.D., and Mary Lucy M. Pereira, M.D., of Young H. Kwon's (M.D., Ph.D.) team from University of Iowa Hospitals and Clinics for their contributions to manual...

## K

Figure 10.17 Thickness determination procedure using zero-crossings of the second directional derivatives along sheet normal direction. (a) Basic concept of thickness determination procedure. (b) Interpolation of discrete MR data. (c) Zero-crossing search procedure. (( 2004 IEEE) Figure 10.17 Thickness determination procedure using zero-crossings of the second directional derivatives along sheet normal direction. (a) Basic concept of thickness determination procedure. (b) Interpolation of...