## Statistical Methods for Brain Segmentation

The performance and limitations of many supervised and unsupervised statistical methods for MR segmentation are discussed in a review by Bezdek et al. 6 . Kapur et al. 19 segment the brain in 3D gradient-echo MR images by combining the statistical classification of Wells et al. 34 with image processing methods. A single channel, non-parametric, multiclass implementation of Well's classifier based on tissue type training points is used to classify brain tissues. Further morphological processing...

## References

Daubechies I., Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., Vol. 41, pp. 909-996, 1988. 2. Mallat S. G. A theory for multiresolution signal decomposition the wavelet representation, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, pp. 674-693, 1989. 3. Wang J., Huang H. K., Three-dimensional medical image compression using wavelet transformation, IEEE Trans. on Medical Imaging, Vol. 15, No. 4, pp. 547-554, 1996. 4. Wang J.,...

## N

Where FLE is the error for each point and N is the number of points in three dimensions (a different adjustment is used for two-dimensional registration). Using perturbation analysis, Fitzpatrick et al. 1 have shown that the error at some arbitrary target location can be approximated using FLE, N, the distance from the target location to each of the three principal axes of the fiducials (dx , dy, and dz,), and the RMS distance of the fiducials to each of the three principal axes of the...

## Interpolation Method

When using an intensity-based cost function, it is necessary to repeatedly resample one of the images to match the other. This resampling process necessarily requires selection of an interpolation model to be used within the registration algorithm. It is important to understand that the interpolation method used for registration does not have to be the same interpolation method used when applying the optimal registration parameters to compute a final image (see Fig. 1). Because speed is...

## Interpolation Constraint

Consider the evaluation of (1) in the specific case when all coordinates of x k0 are integer ko E k int(ko - k) Vko eZq. (2) This equation is known as the interpolation constraint. Perhaps the single most important point of this whole chapter about interpolation is to recognize that (2) is a discrete convolution. Then, we can rewrite Eq. (2) as where we have introduced the notation pk nt(k) to put a heavy emphasis on the fact that we only discuss convolution between sequences that have the...

## ICP on Frames

When images are close enough, one can use still another algorithm the Iterative Closest Point 5,41 The basic principle is the following. For each scene point, we look for the closest point in the model with the current transformation, compute a new rigid transformation with these matches, and iterate the process until convergence. Of course, since we have more geometric information than just the point position, we use a generalization the Iterative Closest Feature 30 . The idea is to use a...

## Volumetric Radiosity

The ray tracing algorithm described in the previous section can be used to capture spectacular interactions between objects in a scene. In reality, most scenes are dominated by diffuse interactions, which are not accounted for in the standard ray tracing illumination model, but are accounted for by a radiosity algorithm for volumetric data 63 . In volumetric radiosity, the basic patch element of classical radiosity is replaced by a voxel. As opposed to previous methods that use participating...

## FMRI Artifacts

Magnetic resonance imaging has recently found application in mapping human brain function. The contrast mechanism used is the dependence of the signal intensity on the local tissue concentration of deoxyhemoglobin. The relationship is approximately logc S S0 oc deoxyHb . During neuronal activity, the brain locally consumes more oxygen, but because of an even greater increase in local blood flow the venous blood becomes less deoxygenated and the signal increases. These subtle changes in signal...

## Cerebral Anatomy at the Macroscopic Level

Although first described by the ancient Egyptians, the cerebral cortex was considered functionless until the beginning of the 19th century. For centuries, observers of the brain believed that this convoluted surface was unlikely to be the seat of any important function and localized mental activity within the ventricular structures, now known to contain only physiological fluid 1 . The gyri were compared to macaroni, or drawn like small intestines, without any precise pattern or organization....

## Symmetry of Projection in the Quantitative Analysis of Mammographic Images

An important practical question in the analysis of mammo-graphic density is the extent to which information about mammographic pattern is carried by any one of the four views of a typical mammographic exam. This applies to both symmetry between the right (R) and left (L) breast in a given projection, and to symmetry of projection, i.e., between cranial-caudal (CC) and medial-lateral oblique (MLO) projections of the same breast. If the information available from a single image is representative,...

## Radiation Treatment Planning

Figure 29 shows application of 3D visualization to radiation treatment planning. Using CT and MRI fused scans, 3D dosimetry can be computed for simulated treatment beams FIGURE 29 3D visualization used in radiation treatment planning. Dosimetry from several simulated treatment beams can be fused with 3D images to shape dose to tumor site. Critical structures such as the spinal cord and optic nerves can be segmented and examined individually to evaluate local dose and determine whether the plan...

## Level Set Methods Incorporating Generic Constraints

We have developed a coupled surfaces approach for automatically segmenting a volumetric layer from a 3D image 43-45 . This approach uses a set of coupled differential equations, with each equation determining the evolution or propagation of a surface within a level set framework. In the case of the cortex, one surface attempts to localize the white matter gray matter (WM GM) inner cortical boundary and the other the gray matter cerebrospinal fluid (GM CSF) outer boundary. Coupling between the...

## Nonlinear Spatial Transformation Models

Once linear constraints are abandoned, many different spatial transformation models are possible. In certain instances, nonlinear models are used to correct for nonlinear distortions imparted by the equipment used for image acquisition (see the chapters entitled Physical Basis of Spatial Distortions in Magnetic Resonance Images and Physical and Biological Bases of Spatial Distortions in Positron Emission Tomography Images). In these instances, the mathematical form of the nonlinear spatial...

## Medical Image Archive Retrieval and Communication

Lou 2 Medical Image Information 772 Umscisity of Cclifornic 3 Medical Image Archive 772 3.1 Archive Server 3.2 Database Management Subsystem 3.3 Storage Subsystem 4 DICOM Image Communication Standard 773 4.1 Information Objects 4.2 Service Classes 4.3 Example of C-STORE DIMSE Service 5.1 Image Receiving 5.2 Image Routing 5.3 Image Stacking 5.4 Image Archiving 5.5 Database Updating 5.6 Image Retrieving 6 HIS RIS Interfacing and Image 777 6.1 Health Level Seven (HL7) Communication Standard...

## Dynamic Analysis of Myocardial Contraction

The methods described earlier for the evaluation of the left ventricular function are based on the analysis of changes in the shape of the ventricular cavity. There is, however, a need to evaluate the myocardial function more directly by analyzing the rate and extent of contraction and relaxation of the FIGURE 7 Phase analysis of dynamic cine-MRI images. See also Plate 54. myocardial muscle. Echocardiography is the preferred imaging modality for the evaluation of myocardial wall thickening and...

## Definition and Properties

Differential Geometry of 3D Surfaces Let us first recall briefly some results of differential geometry about surface curvatures (a good introduction to these notions can be found in 8 or in 20 ). In this paper, we call a smooth surface a 3D surface that is continuously differentiable up to the third order. At any point P of such a 3D surface, we can define one curvature per direction t in the tangent plane of the surface. This directional curvature kt is the curvature of the 3D curve defined by...

## Comparison with Other Risk Factors

The importance of breast density as a risk factor for breast cancer is particularly evident when comparing it with other breast cancer risk factors. For North American women, the strongest risk factor is age. Some other well-known risk factors for breast cancer are summarized in Table 2 (adapted from Kelsey and Gammon 11 ). Many of the factors listed carry a risk prediction less than 2.0. Family history of breast cancer, which is commonly considered to be one of the most important risk factors...

## Intramodality Coregistration

One of the most obvious clinical applications of coregistration is the area of serial imaging. Comparison of scans from a given patient acquired over various time intervals can be routinely performed to follow disease progression and response to treatment. Unfortunately, diagnostic imaging scans are not routinely registered in most radiology departments in contrast, the common practice for an examiner is to do one's best to look at film montages of slices that do not match and try to assess...

## Experimental Results and Comparison

In this section, we present samples of experimental results and compare the dyadic wavelet analysis with other methods. Figure 12a shows a synthetic image with three circular bumps and added white noise. The enhancement results shown in (b) and (c) demonstrate amplification of unwanted noise. Moreover, note that histogram equalization processing alters the object's boundary. However, the result shown in (d) accomplished by dyadic wavelet analysis provides a clearer image without orientation...

## Investigative Visualization

As the concepts in illustrative visualization became mature enough, they became widely used in various applications. The concept of investigative visualization slowly emerged as a form of visualization for addressing specific questions that required collective use of various graphics concepts described in the earlier section on illustrative visualization. This corresponds to fourth generation systems. The application of many 3D volume visualization techniques remained limited to specific...

## Determination of a Gold Standard

The typical scenario for evaluating diagnostic accuracy of computer processed medical images involves taking some database of original unprocessed images, applying some processing to them, and having the entire set of images judged in some specified fashion by radiologists. Whether the subsequent analyses will be done by ROC or some other means, it is necessary to determine a gold standard that can represent the diagnostic truth of each original image and can serve as a basis of comparison for...

## Morphometric Methods for Virtual Endoscopy

Summers 1 Overview of Virtual National institutes of Health 2 Current Problems in Virtual 3 Shape-Based Detection of Endoluminal Lesions Using Curvature Analysis 748 3.1 Clinical Application of Shape-Based Lesion Detection 4 Fractal Measures of 4.1 Clinical Application of Fractal Measures of Roughness Virtual endoscopy (VE) is a novel display method for three-dimensional medical imaging data. It produces endoscope-like displays of the interior of hollow anatomic structures such as...

## Comparison Between Artificial Neural Networks and Bayesian Belief Networks

ANN and BBN use different machine learning concepts for pattern recognition and have very different characteristics. Table 1 summarizes and compares the basic characteristics of these two networks. In medical image processing, usually a large number of features are extracted. In a complex and multidimensional TABLE 1 Characteristics of an ANN and a BBN Optimization method Simple heuristic approach Probabilistic approach Explainable learning process No Yes Flexibility in topology design No Yes...

## Multidimensional Spatial Frequencies and Filtering

At a conceptual level, there is a great deal of similarity between 1D signal processing and signal processing in higher dimensions. For example, the intuition and knowledge gained from working with the 1D Fourier transform extends fairly straightforwardly to higher dimensions. For overviews of signal processing techniques in 2D see Lim 3 , or Granlund and Knutsson for higher dimensional signal processing 4 . The only difference between the classical notions of time frequencies and spatial...

## Two Dimensional Shape and Texture Quantification

1.1 Compactness 1.2 Spatial Moments 1.3 Radial Distance Measures 1.4 Chain Codes 1.5 Fourier Descriptors 1.6 Thinning 2.1 Statistical Moments 2.2 Co-Occurrence Matrix Measures 2.3 Spectral Measures 2.4 Fractal Dimension 2.5 Run-length Statistics 228 Two of the most informative visual cues in medical image interpretation, shape, and texture can be quantified with numerous automated techniques that address different aspects of the data. This chapter describes relatively established techniques for...

## Cortical Pattern Matching

Cortical surfaces can be matched using a procedure that also matches large networks ofgyral and sulcal landmarks with their counterparts in the target brain 26,35,111,113,123 . Differences in the serial organization of cortical gyri prevent exact gyrus-by-gyrus matching of one cortex with another, but an important intermediate goal has been to match a comprehensive network of sulcal and gyral elements that are consistent in their incidence and topology across subjects. Elastic matching of...

## Surface Rendering

Surface rendering techniques characteristically require the extraction of contours (edges) that define the surface of the structure to be visualized, and representing that surface by a mosaic of connected polygons. A tiling algorithm is applied that places surface patches (or tiles) at each contour point, and with hidden surface removal and shading, the surface is rendered visible. The advantage of this technique lies in the relatively small amount of contour data, resulting in fast FIGURE 2...

## Methods of Correction

Most of the described distortions due to physical factors can to a great extent be corrected for by appropriate preprocessing of the raw data prior to image reconstruction or directly incorporated into the image reconstruction. For instance, the correction for the problem of nonuniform sampling depends on the image reconstruction method that is used. If a conventional filtered backprojection algorithm is used, each projection needs to be interpolated into equidistant sampling points prior to...

## Anatomical and Functional Variability

The traditional anatomical space'' taught in medical and graduate schools is feature based. The brain is named and divided in terms of visual landmarks (sulci and gyri, nuclei and tracts). The assumption is that these landmarks bear reliable relationships to underlying functional architecture. This assumption is tenuous, at best. The caudate and putamen are so similar in cell structure, connectivity, and function as to be considered a single functional entity 47 , yet they are divided by a...

## Warping

The fact that the Talairach brain fails to match individual scans stems partly from two facts. First, Talairach registration is only based on linear transformations (rotation, scaling, translation). Second, the origin of the coordinate system was selected to solve mapping and localization problems deep in the brain where individual variability is relatively low. Atlases can be greatly improved if they are elastically deformed to fit a new image set from an incoming subject. Local warping...

## Fifth Generation Systems II Virtual Reality

Virtual reality visualization represents the next milestone in biomedical visualization. While stereoscopic visualization provided the 3D perception, such a presentation also required intrinsically intuitive 3D interaction with the display. The traditional interaction paradigm using a tool or stylus such as a mouse or pointer that is away from the display lacks the intuitive control of hand-eye coordination. A more natural and intuitive interaction can be obtained by manipulating the image...

## Validation with Real Data

The experiment is performed using multiple 2D contiguous magnetic resonance images (MRI) that constitute a 3D FIGURE 12 (Left) Example of MS images. The same slice of one acquisition in echo-1(le t) and echo-2 (right). (Right) evolution of an image row going through a lesion across 24 time points over a year. Left without registration Right after registration and intensity correction. Original 3D images courtesy of Dr. Charles Guttmann and Prof. Ron Kikinis from the Brigham and Woman's Hospital...

## Wavelet Filter Selection

Where (x), (y), and (z) contain the low-pass filter h in the x, y, and z directions, respectively (see Eq. (5)). The seven wavelet functions have the form contain the high-pass filter g in the x, y and z directions, respectively. During each level of the transform, the scaling function and the seven wavelet functions are applied, respectively, to the smooth (or the original) image at that level, forming a total of eight images, one smooth and seven detailed images. The wavelet coefficients are...

## LV Anatomy and Motion

Tagged MR image analysis has focused almost exclusively on the myocardium of the left ventricle (LV), which will be the topic of this chapter as well. Many of the techniques we will discuss are readily extendible to the right ventricle and other moving bodies. The LV is the primary heart chamber responsible for pumping blood throughout the body, with thick, muscular walls the myocardium delivering the required pressure. These walls form a hollow, ellipsoidal body, with the aortic and mitral...

## Joint Contact Pressure and Ligament Tension Analysis

The joint contact force can be broken down further into the joint contact pressure distribution and the ligament tension using the graphical models (Fig. 4). The bones of the joint are treated as rigid bodies. The articular cartilage within the joint is treated as a matrix of linear compressive springs, and the ligaments are treated as linear tensile springs to quantify the joint contact pressure distribution and the ligament tension 3,20,35 . This analysis technique is known as discrete...

## Rapid Back Projection Reconstruction

Although volume visualization is an area of continuing progress, there is another need that is growing with new types of imaging techniques visualization of a 3D structure using a set of projection images, i.e., images acquired from different orientations. Concerns of exposure to radiation and the need for high speeds make projection images a preferred mode of acquisition for some applications. Such requirements may be difficult to meet while acquiring the images in 3D mode. In this case, if...

## Visualization in Medicine

Visualization is one of the rapidly developing areas of scientific computing. The cost of high performance computing has become increasingly more affordable in recent years. This has promoted the use of scientific visualization in many disciplines where the complex data sets are rich in quality and overwhelming in quantity. In medicine, more than cost, advancement of the physics of imaging has become a major influencing factor that has spurred the growth of image computing and visualization....

## Joint Histograms

A joint histogram is a useful tool for visualizing the relationship between the intensities of corresponding voxels in two or more images. Such histograms are widely used with multi-spectral data e.g., dual echo MR images as the basis for statistical classifiers for image segmentation, and are used as co-occurrence matrices for texture analysis. For two images A and B, the joint histogram is two-dimensional and is constructed by plotting the intensity a of each voxel in image A against the...

## Ratio Image Uniformity

A cost function that does allow for global differences in image intensity without the need for formal modeling of an intensity scaling parameter is the ratio uniformity cost function introduced in 1992 20 . If one image is divided by the other image on a voxel-by-voxel basis, the resulting ratio image should have a constant uniform value when the images are well registered. Any misregistration will induce nonuniformities. The ratio image cost function quantifies this lack of uniformity by...

## Id Zo Id Jo

FIGURE 10 Image segmentation using correlation mapping. A First image in a sequence of 60 temporal images with 3x3 pixel ROIs drawn in tumor and normal area B plot of the average intensity of the reference ROI tumor and the normal ROI for 60 images in a sequence C correlation map of the tumor See also Plate 5. segmentation and visualization tools for temporal sequences of images. They are particularly useful for evaluation of disease processes, drug treatments, or radiotheraphy results....

## Info

A 512x512 image was isosurface. larger numbers of processors gt 64 can be explained by load imbalances and the time required to synchronize processors at the required frame rate. The efficiencies would be higher for a larger image. Table 2 shows the improvements that were obtained through the data bricking and spatial hierarchy optimizations. In this last section, we give examples of the NOISE, view-dependent, and real-time ray tracing algorithms given in the three previous sections. The...

## Vf x ye sup fx1 yf x2 y27

Where the supremum is taken over all data pairs x1 y1 , FIGURE 2 Pig pulmonary embolus model. A Axial CT image shows pulmonary embolus arrow in right pulmonary artery. B Anteroposterior view of three-dimensional surface rendering of main pulmonary arteries. C Closeup view of right pulmonary artery showing indentation in surface reconstruction due to presence of embolus. D Virtual angioscopic view showing narrowing of vessel lumen by embolus. Red coloring indicates area detected by...

## Intermodality or Multimodality Coregistration

Combination of functional and structural imaging provides unique information not available from independent analysis of each modality. Coregistered high-resolution anatomy in MRI or CT images provides a much more precise anatomical basis for the interpretation of functional image data. This includes improved detection of focal functional disturbances of cerebral activity, better comprehension of pathophysiologic structural-functional relationships, and more accurate identification of specific...

## Permutation and Progressive Roundoff Approach

Once the topology of a network and the database are determined, the most reliable method for the optimization of feature selection is a complete permutation search. In this method, all possible combinations of features are tested in the network. A set of features that generate the best testing performance in the network is then defined as an optimal set of features. For example, in one study 31 , a complete permutation method was applied to search for an optimal feature set in a BBN used for...

## Image Standardization in PACS

Silesian University of 2 Background 784 Technology 2 i Collimator-Caused Background 2.2 Removal of Background Outside Patient Boundary 3.1 Window Level Correction 3.2 Histogram Modification 4.1 Detection of the Rotation Angle 4.2 Image Rotation 5 On the Accuracy of Quantitative Measurements in Image Intensifier Systems 793 5.1 Geometrical Description of Pincushion Distortion 5.2 Surface Area Correction 6 Implementation of Image Standardization Functions in HI-PACS 797 6.1 Industrial Standard...

## Image Registration for Treatment Planning

A critical step in the radiotherapy procedure is the delineation of the target volume. Since the introduction of CT, the use of this image modality has become standard practice in precision radiotherapy. The CT scan has a high geometric accuracy, and the pixel values in the CT data are used directly to compute transport of the beam through the patient. Using a computer system, an optimal beam arrangement is searched to obtain a high dose in the tumor, while sparing critical normal tissues as...

## Detection of the Rotation Angle

The orientation procedure is anatomy-dependent. The procedure uses some anatomical features in order to determine the current orientation and necessary rotation angle. Three procedures are described for three anatomical structures chest, pelvis, and hand wrist. In chest images the analysis is performed in three steps. First, the mediastinum is located and its orientation is found. This step excludes 90 rotations clockwise and counterclockwise in both groups of images nonflipped and flipped ....

## Compression and Communication

Dolecek 2 Compression and 761 Robert L. Holland 2.1 Joint Photographic Experts Group JPEG Compression 2.2 Moving Picture Experts Group Joan E Fetter MPEG Compression 2.3 Wavelet Compression 2.4 Fractal Compression fohns Hopkins University 3 766 3.1 Signal Hierarchy and Transfer Rates 3.2 Network Interoperability 3.3 Telemedicine Applications Compatibility 770 The principal objectives of this chapter are to introduce basic concepts and standards for data compression and communications...

## Data Sets

Parker 2 Accelerated 732 Christopher R. Johnson 2.1 The Span Space 2.2 The NOISE Algorithm 2.3 Optimization 2.4 Other Span Space 3 View Dependent 3.1 Visibility 3.2 Image Space Culling 3.3 Warped IsoSurface Extraction WISE 4 Real-Time Ray 4.1 Ray-Isosurface Intersection 4.2 Optimizations 4.3 Real-Time Ray Tracing Results 5 Example Isosurface extraction is a powerful tool for investigating volumetric scalar fields and has been used extensively in medical imaging ever since the seminal...

## Method for Combined Denoising and Enhancement

5.1 Incorporating Wavelet Shrinkage into Contrast Enhancement The method of denoising by wavelet shrinkage can be incorporated trivially into a nonlinear enhancement framework by simply adding an extra segment to the enhancement function E x , defined earlier in Eq. 13 x K l Te KTn, if x lt -Te K x Tn , if T lt x lt -Tn K x Tn , if Tn lt x lt Te x K l Te KTn, if x gt Te. However, there are two arguments that favor shrinking gradient coefficients instead of Laplacian coefficients. First,...

## Physical Distortions of PET

The physical distortions seen in PET images can be divided into two main groups. First, there are artifacts produced by the scanner geometry and the detection system itself, and second, distortions introduced by the various processing steps applied to the data before the final image is produced. The result of both types of distortions is images where the activity distribution is distorted, which in the end will affect how well the PET image volume can be coregistered to a second data set. Some...

## Genetic Algorithm Approach

The genetic algorithm GA is another popular machine learning method with some type of biological paradigm that emulates Darwinian evolution by following the only the strongest survive strategy. The fundamental principle of GA is based on natural selection. To solve an optimization task in feature selection, GA usually involves the following five steps 1 Initialization. The GA starts from a population of randomly selected chromosomes, which are represented by binary or gray-level digital...

## Electronic Portal Imaging Verification of Radiation Therapy

One of the first application of the chamfer matching algorithm in the medical profession was in the field of treatment verification for radiotherapy. The aim of external beam radiotherapy is to eradicate a tumor by irradiating it repeatedly by high-energy photons with multiple beams from multiple directions . Since the irradiation is typically repeated 20 or more times over a period of several weeks, the patient has to be repeatedly aligned on the treatment machine with high accuracy. To verify...

## Quantitative Analysis of Cardiac Function

Osman Ratib 1 Dynamic Image Acquisition 359 UCLA School of Medicine 2 Dynamic Analysis of Left Ventricular Function 360 2.1 Geometric Calculation of Changes in Cardiac Volumes 2.2 Densitometric Calculation of Volumes 2.3 Quantitative Evaluation of Regional Function 2.4 Temporal Evaluation of Ventricular Wall Motion 2.5 Dynamic Analysis of Myocardial Contraction 3 Quantitative Evaluation of Flow Motion 368 3.1 Two-Dimensional Color Doppler Ultrasound 3.2 Velocity Encoded Cine-MRI 371 371 In...

## Segmentation

5 Overview and Fundamentals of Medical Image Segmentation Jadwiga Rogowska. . . 69 6 Image Segmentation by Fuzzy Clustering Methods and Issues Melanie A. Sutton, James C. Bezdek, and Tobias C. 7 Segmentation with Neural Networks Axel Wismiller, Frank Vietze, and 8 Deformable Models Tim Mclnerney and Demetri Terzopoulos 127 9 Shape Constraints in Deformable Models Lawrence H. Staib, Xiaolan Zeng, James S. Duncan, Robert T. Schultz, and Amit Chakraborty 147 10 Gradient Vector Flow Deformable...

## Medical Applications of Chamfer Matching

Most applications of the chamfer matching algorithm have been in the field of radiotherapy, although a few authors have published applications outside this field 18 . In the next sections, first the use of 2D chamfer matching for treatment verification for radiotherapy is described, then the use of 3D TABLE 1 Simplified comparison of three classes of automatic image registration algorithms function complexity typical example for 3D images TABLE 1 Simplified comparison of three classes of...

## Contributors

School of Computing Science Simon Fraser University Burnaby, BC V5A 1S6, Canada Chapter 11 INRIA Sophia-Projet Epidaure 06902 Sophia Antipolis Cedex, France Chapter 31 Applied Physics Laboratory Johns Hopkins University Laurel, MD 20723 Chapters 14, 53 Computer Graphics Laboratory Department of Computer Science Division of Engineering and Applied Science California Institute of Technology Pasadena, CA 91125 Chapter 13 Computer Science Department University of West Florida Pensacola, FL 32514...

## Hanning Apodization

Apodization, being defined as the multiplication of a sinc function by some window, corresponds in the Fourier domain to a convolution-based construction. The Hanning window is one out of several attempts to design a window that has favorable properties in the Fourier domain. The result is sinc W x sinc W xM 2cos w r With L 0, the order of approximation of Hanning interpolation is no better than that of Dirichlet interpolation the constant Cv is significantly improved, though. Whereas it was C...

## Anatomical Distortions

Many anatomical and biological factors can affect the PET and SPECT images. Some affect the shape of the organ structural outline, some affect the relative distributions, and some affect both. These factors need to be taken into consideration when one tries to align two sets of images to examine the similarities differences changes. They impose very challenging problems for image coregistration and distinguish medical image coregistration from registrations in other imaging areas. In the...

## Osteoporotic Change in Trabecular Pattern of the Vertebral Body

Osteoporosis is characterized not only by a reduction in bone mass but also by alteration in the architecture of trabecular bone. Changes in BMD have long been considered the most important factor in the diagnosis of osteoporosis and in predicting the risk of fractures caused by osteoporosis. However, recent studies have demonstrated that similar BMD values have been associated with different osteoporosis-induced fracture outcomes. Changes in the trabecular architecture of the osteoporotic...

## Radial Distance Measures

The shape of a structure of interest can be determined by analyzing its boundary, the variations and curvature of which constitute the information to be quantified. This is achieved by transforming the boundary into a 1D signal and analyzing its structure. A common technique is based on the radial distance measured from a central point in the region to each pixel x n , y n on the boundary. Generally the centroid xc, yc is used as the central point and the radial distance sequence Typically...

## Quantifying Anatomy via Shape Transformations

This section presents a general mathematical framework for representing the shape characteristics of an individual's brain. Since this framework is based on a shape transformation, we first define exactly what we mean by this term. Consider a three-dimensional volumetric image, J, of an individual's brain. Let each point in this image be denoted by x x, y, z .A shape transformation, T , of J is a map that takes each point x e J and maps it to some point T x .In the context of our development, x...

## Tag Line Tracking

The most intuitively straightforward use of tagged MR images is to view the dark tag lines apparent in Fig. 2 as features to be tracked. For best results, SPAMM pulse sequences with 3 to 7 RF pulses and a total tip angle of 90 are applied. This results in a tag pattern with no net magnetization, f0 p 0, wherever gTp 2mn, m an integer. The set of material points satisfying this condition comprise parallel planes of tissue, called tag planes. In subsequent images, clearly defined lines of minimal...

## Thickness Correction

Figure 8b summarizes the essential information necessary for the thickness correction. As mentioned, the thickness is not explicitly determined rather, an estimate of the thickness is used in the correction. The gray level of the signal at each point FIGURE 8 a A smoothed representation of the image, s x, y , is obtained from a low-pass filtering operation. The low-pass filter shown schematically in 1 dimension is a first-order Butterworth filter with a cutoff frequency of 0.05 cycles mm. b...

## Introduction

Because of the critical nature of its function, distributing oxygenated blood from the heart to all the organs of the body, the arterial vascular system has been the object of extensive study in medicine. Since a significant portion of human morbidity and mortality is associated with vascular diseases, diagnostic imaging methods for blood vessels, especially arteries, have received a great deal of attention in the research arena. New imaging and image processing methods produced by the research...

## Bone Structure and Loading Relationship in the Proximal Tibia

It is well known that the density and trabecular orientation of cancellous bone adapts to its loading environment 13 . Distribution of the density in the subchondral bone trabecular bone underneath the joint surface reflects the loading history of the joint associated with physiological activity. Therefore, trabecular orientation adjacent to the joint surface may reveal the biomechanical function of the joint. This information would be especially beneficial for determining the physiological...

## Stepwise Feature Selection

The stepwise feature selection method is another well established statistical approach to search for the features that can enhance the performance of a classifier. Although the stepwise feature selection method was initially associated with linear Another common criterion is minimization of Wilks' lambda 22 . When using an ANN or a BBN in medical image processing, the statistical criterion can also be the Az value. The first step in the stepwise feature selection method is to define a small...

## Temporal Evaluation of Ventricular Wall Motion

The clinical usefulness of global evaluation of ventricular function through the measurement of ventricular volume and ejection fraction is well demonstrated and widely accepted. However, from a clinical point of view, a better evaluation of the ventricular function should allow the detection and the measurement of regional dysfunctions in ventricular wall motion 35 . A wide number of wall motion and regional ventricular function evaluation methods have been reported. Regional ejection fraction...

## Ligament Tension and Joint Contact Pressure in the Wrist

An image-based model of the wrist was developed for a biomechanical analysis of a limited intercarpal fusion for the treatment of Kienbock's disease 20 . The model was used to quantify the wrist joint contact pressure distribution and ligament tension for multiple intercarpal fusion procedures. The goal of the study was to determine how the procedures alter the force transmission through the wrist joint, in general, and to determine if any of the procedures reduce the load applied to the...

## N 1

l s l - gt m A s Am m l - 14 For completeness, we mention that the formula of Eq. 14 can be seen as a multiscale and nonlinear extension of the original unsharp masking operator defined by Eq. 9 . We argue that multiscale unsharp masking as defined by Eq. 14 makes a marked improvement over traditional techniques in two respects 1. The fast multiscale or multimask decomposition procedure efficiently identifies features existing within distinct levels of scale, eliminating the need for search....