## A

For linear enhancement, the selection of filters g m(ffl) (and thus k m(ffl)) makes little difference. However, this is not true for the nonlinear case. For the nonlinear approach described later, we show that a Laplacian filter should be favored. By selecting a Laplacian filter, we can be assured that positions of extrema will be unchanged and that no new extrema will be created within each channel. This is possible for the following reasons 1. Laplacian filters are zero-phase. No spatial...

## Local Operators

Local operators enhance the image by providing a new value for each pixel in a manner that depends only on that pixel and others in a neighborhood around it. Many local operators are linear spatial filters implemented with a kernel convolution, some are nonlinear operators, and others impart histogram equalization within a neighborhood. In this section we present a set of established standard filters commonly used for enhancement. These can be easily extended to obtain slightly modified results...

## Ee

That is, the raw (fc-space) data can be simply phase-shifted by an amount corresponding to the location shift of the image and result subjected to an inverse Fourier transform to get the translated image. This computation can be performed with the FFT algorithm by simply regarding Eq. (1) as the DFT of the quantity in square brackets. The implementation of a rotation is a little more subtle. If we let x (x, y) and k (kx, ky) and write ,F(I) I(k) I(x) exp i2n(xTk) ,F 1(i) I(x) Y I(k) exp...

## Concluding Remarks

This chapter has focused on fundamental enhancement techniques used on medical and dental images. These techniques have been effective in many applications and are commonly used in practice. Typically, the techniques presented in this chapter form a first line of algorithms in attempts to FIGURE 9 Filtering with the Butterworth filter. (a) Fourier transform of MRI image in (e) the five circles correspond to the 3 values 75, 90, 95, 99, and 99.5 . (b) Fourier transform of low-pass filter with 3...

## Info

FIGURE 6 Matrix logarithm and matrix exponential based decomposition of the rotational component of the numerical example illustrating three-dimensional rigid-body movements. See Fig.4 legend for additional details. In this case, rotation is applied around the fixed axis. Note that the positions of the two round dots do not change, and that the intervening positions constitute optimal intermediates without extraneous movement. The decomposition into three steps is arbitrary,the required 18.8571...

## Heterogeneous and Anisotropic Model

The density, anisotropy, and microstructure are evaluated in this model for which micro CT can be used 16 . In addition to the density and macroscopic anisotropy, the microstructure, such as thickness and connectivity of the trabeculae, can be evaluated. Because of ease of measurement, the bone density measurement has been widely used to predict material properties of the bone. Strong correlation between the material properties and bone density has been reported. However, the relationship...

## Iv

26 Physical Basis of Spatial Distortions in Magnetic Resonance Images 27 Physical and Biological Bases of Spatial Distortions in Positron Emission Tomography Images Magnus Dahlbom and Sung-Cheng (Henry Huang) 439 28 Biological Underpinnings of Anatomic Consistency and Variability in the Human Brain N Tzourio-Mazoyer, F. Crivello, M. Joliot, and B. Mazoyer 449 29 Spatial Transformation Models Roger P. Woods 465 30 Validation of Registration Accuracy Roger P. Woods 491 31 Landmark-Based...

## Mammographic Density

Figure 1 is a composite of six mammographic images of the breast. These images illustrate that the breast has a wide range of appearance on mammography, associated with differences in composition. Radiographically the breast consists mainly of two component tissues fibroglandular tissue and fat. Fibroglandular tissue is a mixture of fibrous connective tissue (the stroma) and the functional (or glandular) epithelial cells that line the ducts of the breast (the parenchyma). The remainder of the...

## Conclusion

Many quantitative analysis techniques have been developed for more accurate evaluation of cardiac wall motion and ventricular function from dynamic cardiac images. Most conventional techniques are usually based on global or regional evaluation of differences between end-diastolic and end-systolic frames. Such methods do not depict differences in timing of wall motion along different segments of the ventricle. Several studies have already demonstrated the importance of temporal evaluation of...

## Anisotropic Adaptive Filtering

5.1 Anisotropic Adaptive Filtering in Two Dimensions On the basis of the characteristics of the human visual system, Knutsson et al. 16 argued that local anisotropy is an important property in images and introduced an anisotropic component in Abramatic and Silverman's model (Eq. (36)) Ha i H +(1 - a)(y + (1 - y) cos2(< p - 6))(1 - H), (37) where the parameter y controls the level of anisotropy, defines the angular direction of the filter coordinates, and 6 is the orientation of the local...

## Contents

1 Fundamental Enhancement Techniques Raman B. 2 Adaptive Image Filtering Carl-Fredrik Westin, Hans Knutsson, and Ron 3 Enhancement by Multiscale Nonlinear Operators Andrew Laine and Walter 4 Medical Image Enhancement with Hybrid Filters Wei 5 Overview and Fundamentals of Medical Image Segmentation Jadwiga 6 Image Segmentation by Fuzzy Clustering Methods and Issues Melanie A. Sutton, James C. Bezdek, Tobias C. 7 Segmentation with Neural Networks Axel Wismiller, Frank Vietze, and Dominik R. 8...

## Other Special Constrained Affine Transformations

Erroneous calibration of equipment may occasionally warrant the use of other special spatial transformation models in which additional degrees of freedom are added to the rigid-body model to account for certain inaccuracies. For example, if the voxel sizes are uncertain along all three axes and subject to session-to-session variations, one dimension can be kept fixed and the other five dimensions (two from the same session and three from the other session) can be rescaled, producing an...

## Overview

VolVis was developed by The Center for Visual Computing at Stony Brook, under the direction of Dr. Arie Kaufman 1 . It is a comprehensive volume visualization software system that has served as the basis for many projects at Stony Brook and elsewhere. VolVis unites numerous visualization methods within one system, providing a flexible tool for the physician, scientist, and engineer as well as the visualization developer and researcher. The VolVis system has been designed to meet the following...

## Techniques

University of Regina 2 Preliminaries and 3 3.1 Compensation for Nonlinear Characteristics of Display or Print Media 3.2 Intensity Scaling 3.3 Histogram Equalization 4.1 Noise Suppression by Mean Filtering 4.2 Noise Suppression by Median Filtering 4.3 Edge Enhancement 4.4 Local-Area Histogram Equalization 5.1 Noise Suppression by Image Averaging 5.2 Change Enhancement by Image Subtraction 17

## Application to Medical Image Characterization

Two series ofexperiments with real images are presented. In the first series, the objective is to characterize the texture of some MR-t2 brain images for the purpose of finding features that characterize the presence of pathologies with nonlocal manifestation, i.e., pathologies that result in the change of the textural appearance of the brain rather than the development of a tumor. In the second series of experiments, the change in the anisotropy descriptor of the brain images of some patients...

## Linear

The linear interpolant enjoys a large popularity because the complexity of its implementation is very low, just above that of the nearest-neighbor moreover, some consider that it satisfies Occam's razor principle by being the simplest interpolant one can think of that builds a continuous function f out of a sequence of discrete samples fk . It is made of the (continuous-signal) convolution of a square pulse with itself, which yields a triangle, sometimes also named a hat or a tent function...

## Least Squares and Scaled Least Squares

Another index of image similarity is the squared difference in image intensities averaged across all voxels. This value should be minimal when the images are registered. If large differences in image intensity are present, a global scaling term can be added as an additional parameter to be optimized. Calculus-based minimization is especially robust for least squares problems, making this cost function especially attractive and easy to implement 1,8,10,11,12,21,22 . Even for highresolution MRI...

## N

Which is equal to the adaptive filter we wanted to construct (Eq. (39)). The under-braced terms sums to 1 because of the dual basis relation between the two bases Mk and Nk. 5.4 Estimation of Multidimensional Local Anisotropy Bias Knutsson 27 has described how to combine quadrature filter responses into a description of local image structure using tensors. His use of tensors was primarily driven by the urge to find a continuous representation of local orientation. The underlying issue here is...

## Introduction

In the past few years, it has become possible to obtain mammographic images in digital form, either by means of high-resolution film digitizers that are now widely available or with first-generation direct digital mammography systems, which are now undergoing clinical testing at several centers. In each case, a digital radiograph of the breast is available with spatial resolution from 10 to 25 samples mm and precision of 12-14 bits. These two developments have opened several opportunities for...

## Discussion and Conclusions

Arterial tree morphometry is an important application of image processing and analysis in clinical practice and the biomedical sciences. The severity of coronary artery disease is routinely assessed in the clinic with the aid of sophisticated image processing software to quantify stenoses. Presurgical planning for vascular abnormalities such as cerebral aneurysms is facilitated by segmentation and visualization of the intracerebral vasculature. Clinical studies provide information about...

## Ill

14 Two-Dimensional Shape and Texture Quantification Isaac N. Bankman, 15 Texture Analysis in Three Dimensions as a Cue to Medical Diagnosis 16 Computational Neuroanatomy Using Shape Transformations Christos Davatzikos 249 17 Arterial Tree Morphometry Roger Johnson 261 18 Image-Based Computational Biomechanics of the Musculoskeletal System Edmund Y. Chao, N. Inoue, J.J. Elias, and F.J. Frassica 285 19 Three-Dimensional Bone Angle Quantification Jens A. Richolt, Nobuhiko Hata, Ron Kikinis, Jens...

## Volumetric Segmentation

Pham 2 National Institutes of Health 3 Image Segmentation 3.1 Thresholding 3.2 Region Growing 3.3 fc-Nearest-Neighbor (fcNN) Classifier 3.4 Gaussian Classifier Clustering Methods 3.5 Parzen Window Classifier 3.6 Neural Networks 3.7 Adaptive Fuzzy c-Means Segmentation 3.8 Adaptive Bayesian Segmentation 4 Comparison and 5 Brain Image Segmentation via Normalization into Stereotaxic Space 191 6 Concluding

## Image Compression

Image compression seeks to reduce the number of bits involved in representing an image. Most compression algorithms in practice are digital, beginning with an information source that is discrete in time and amplitude. If an image is initially analog in space and amplitude, one must first render it discrete in both space and amplitude before compression. Discretization in space is generally called sampling this consists of examining the intensity of the analog image on a regular grid of points...

## General Affine Model

The general affine model has six independent parameters in two dimensions and 12 independent parameters in three dimensions. One of the geometric constraints of this model is that lines that are parallel before transformation remain parallel after transformation. Unlike all of the previous models, the general affine model does not require computation of sines and cosines to implement. Instead, the elements of the transformation matrix itself serve as the independent parameters. In two...

## Extremal Points Registration Using Alignment

With the development of completely automated methods to extract crest lines and the higher resolution of images, the number of crest lines drastically increased, leading to a much higher density of invariants in the hash table. This could lead to an important number of false positives that would overwhelm the correct matches. The maximum complexity would then be reached and the algorithm could even provide a wrong answer. To address this problem, Thirion reduced once again the image information...

## The Three Data Sets

In this chapter and the following two chapters, results are presented for three data sets computerized tomography (CT), magnetic resonance (MR), and mammographic images. As will be seen later, these three studies provide examples of the detection, localization, measurement, and management aspects of a radiologist's interpretative functions. The CT study involved two different sets of chest images. In one, the diagnostic task was the detection of abnormally enlarged lymph nodes, and in the...

## Thresholding

Threshold-based segmentation 25 seeks to determine an intensity value, or range of intensities, which isolates a target region of interest (ROI) from a scene. Thresholding works best when the objects of interest have nonoverlapping intensities or nearly so, making possible the removal of voxels above or below a certain intensity value, called the threshold. For instance, bone is easily separated from soft tissue in X-ray CT images by thresholding manipulation. On the other hand, cerebral GM and...

## Effect of Case Difficulty

Nishikawa et al. demonstrated that the accuracy of a computerassisted diagnosis scheme was inversely related to the percentage of difficult or subtle medical images in the database. In principle, when using a limited number of images to train an ANN or other classifiers used in medical image diagnosis, the classifiers can achieve any accuracy from 0 to 100 depending on the nature or difficulty of the database 20 . For example, with only 10 change in the composition of the database, the...

## Image Generation and Display

A variety of methods and systems have been developed for 3D display 19,56,63,65 . But as previously noted, display and visualization are not fully synonymous. Visualization of 3D biomedical volume images has traditionally been divided into two different techniques surface rendering 7,15,20,21, 34,54 and volume rendering 6,11,26,31,48,54,57 . Both techniques produce a visualization of selected structures in the 3D volume image, but the methods involved in these techniques are quite different,...

## Mathematical Foundations of Deformable Models

The mathematical foundations of deformable models represent the confluence of geometry, physics, and approximation theory. Geometry serves to represent object shape, physics imposes constraints on how the shape may vary over space and time, and optimal approximation theory provides the formal underpinnings of mechanisms for fitting the models to measured data. Deformable model geometry usually permits broad shape coverage by employing geometric representations that involve many degrees of...

## GVF Deformable Contours

Our overall approach is to use the dynamic force equation (8) as a starting point for designing a deformable contour. We now FIGURE 1 (a) The convergence of a deformable contour using (b) traditional potential forces, (c) shown close-up within the boundary concavity. Reprinted from C. Xu and J. L. Prince, Snakes, shapes, and gradient vector flow. IEEE Trans, on Image Processing, 7(3) 359-369, March, l998. l998 IEEE. FIGURE 1 (a) The convergence of a deformable contour using (b) traditional...

## Suq

FIGURE 16 Implementation of standardization functions in clinical PACS. case there is a failure of preprocessing functions. With standardization performed on acquisition gateway, if undesirable modification of the image occurs, the radiological procedure has to be repeated. A comparison of both installations is made in Table 1. The standardization function to be implemented depends on the modality as well as the anatomy shown in the image. Not all of the images have to be subjected to all...

## Image Segmentation Methods

In this section, we describe volumetric segmentation methods that will later be compared numerically. Some of these have been implemented in commercial packages such as Mayo Clinic's Analyze software l9 and MEDx image-processing software (Sensor Systems, Sterling, VA). Here our goal is to present a representative sample of available intensity-based segmentation methods for MR images. Greater detail is provided in describing the more recently developed techniques. For additional surveys on...

## Runlength Statistics

Consecutive pixels along a selected orientation tend to have the same intensity in a smooth region while their values change significantly in rough regions. A run is defined as a string of pixels with same value, aligned in a given orientation. The run length information is collected typically by using the orientations 0 0 , 45 , 90 , and 135 . For each orientation 0, the number of runs with a length of m pixels at gray scale k is computed to form the run-length histogram (m, k). A smooth...

## References

Dynamic Noncooperative Game Theory. Academic Press, 1982. 2. P. Baxandall and H. Liebeck. Vector Calculus. Oxford University Press, 1986. 3. S. M. Blinkov and 1.1. Glezer. The Human Brain in Figures and Tables A Quantitative Handbook. Plenum Press, New York, 1968. 4. M. Bomans, K. Hohne, U. Tiede, and M. Riemer. 3-D segmentation of MR images of the head for 3-D display. IEEE Trans. Med. Imaging, 9(2) 177-183, 1990. 5. M. E. Brummer, R. M. Mersereau, R. L. Eisner, and...

## Computing Voxel Histograms

Histograms can be calculated in constant-sized rectangular bins, sized such that the width of a bin is smaller than the standard deviation of the noise within the dataset. This ensures that significant features are not lost in the histogram. The bins are first initialized to zero. Each voxel is subdivided into subvoxels, usually four for 2D data or eight for 3D data, and p(x) and its derivative evaluated at the center of each subvoxel. p(x) is interpolated from the discrete data using a...

## Experiments

In this section, we first show several examples of GVF field computations on simple objects and demonstrate several key properties of GVF deformable contours. We then show the results of applying GVF deformable contours on both a noisy image and a real MR image. We used a 0.6 and ft 0.0 for all deformable contours and p 0.2 for GVF unless stated separately. The deformable contours were dynamically repar-ameterized to maintain contour point separation to within 0.5-1.5 pixels (cf. 13 ). All edge...

## Bayesian Belief Networks

A Bayesian belief network (BBN), which also may be called a Bayesian causal probabilistic network, is a graphical data structure that compactly represents the joint probability distribution of a problem domain by exploiting conditional dependencies. A BBN can capture knowledge of a given problem domain in a natural and efficient way 19 . A BBN builds an acyclic graph in which nodes represent feature variables, and connections between nodes represent direct probabilistic influences between the...

## Challenges in 3D Brain Imaging

The complexity of human brain structure mandates the use of engineering approaches drawn from computer vision, image analysis, computer graphics, and artificial intelligence research fields to manipulate, analyze, and communicate brain data. The rapid growth in brain imaging technologies has also been matched by an extraordinary increase in the number of investigations analyzing brain structure and function in clinical and research settings. Image registration is central to many of the...

## Anatomical Variability and Functional Areas

4.1 Relationships Between Macroscopic Anatomy and Cytoarchitectonic Microanatomy Prior to the advent of functional imaging, the microscopic anatomy, or cytoarchitecture, of a brain region was assumed to be a direct indication of the function of that region. This assumption holds true if one considers the brain region designated as Brodmann area 4, also known as the primary motor area, lesion of which produces motor deficits. But even for primary cortical regions (those regions that either...

## Applications of Mutual Information

The great attraction of mutual information (with or without normalization) as a voxel similarity measure for image registration is that it makes no assumption about the relationship between the intensity of a particular anatomical structure in the modalities being aligned. As a result, it can be used for both intramodality registration and intermodality registration and is far more generally applicable than any automatic medical image registration algorithm previously proposed. There is a con...

## Slipped Capital Femoral Epiphysis

One of the diseases carrying major 3D problems is slipped capital femoral epiphysis (SCFE), defined as the slippage of the femoral head relative to the femoral neck along the proximal femoral growth plate. This disease affects particularly the proximal femur of adolescents whose growth plate is not yet calcified and therefore is soft enough to give way for a slippage under certain circumstances. During a slippage the femoral head shifts and rotates along the proximal end of the femoral neck,...

## Planning of Correctional Osteotomies Based on 3D Computer Models

Conventional planning methods of osteotomies are traditionally focused on the amount of slippage of the femoral epiphysis to improve the alignment of the acetabulum and the proximal femur. The acetabular orientation and the geometry of the proximal femur are generally not taken into consideration for preoperative planning of correctional osteotomies. It is known, that the slippage of the femoral head and the deformation of the proximal femur cause an impingement between the acetabulum and the...

## Acknowledgments

This work was made possible with the help of EU INTAS-96-785 grant, which is gratefully acknowledged. Most of the material in this chapter is reproduced with kind permission from IEEE, as it was originally published in 19 . FIGURE 13 Monitoring change in various pathological cases, with the help of feature F3. Underneath each pair of bars, which represent F3 for the same patient but with time lapse between the two scans, we show two corresponding slices from the 3D scans. (a) MR-t2 images...

## Applications of Mammographic Density Measurements

In general, factors that allow the identification of women at increased risk have important applications in both clinical and research aspects of the disease. Because it is a strong risk factor that is present in a large proportion of breast cancer cases, this is particularly true of mammographic density. Additional applications arise from the potential to modify a factor that is so strongly associated with the disease. It is important to remember that risk factors are derived based on...

## Axial View Coronal View Sagittal View

FIGURE 5 (a) Axial and sagittal views of the bounding box after manual adjustment to match the bounding limits of the cerebrum. The anterior, posterior, left, right, superior, and inferior bounds are illustrated however, bounds do not generally fall within any one section view of the brain (e.g., posterior bound in axial view and inferior bound in sagittal view). (b) Axial, coronal, and sagittal views of the bounding box limits for the inferior margin of the temporal lobe. The cross-hairs for...

## Background

A traditional 2D parametric deformable model or deformable contour is a curve x(s) x(s), y(5) , 5e 0,1 , that moves through the spatial domain of an image to minimize the energy functional E jO1 H*'(5) 2 + x(5) 2) + Eext(x(5))d5 (1) where a and ft are weighting parameters that control the deformable contour's tension and rigidity, respectively, and x'(5) and x(5) denote the first and second derivatives of x(5) with respect to 5. The external potential function Eext is derived from the image so...

## Biomedicine

Meiyappan Solaiyappan 1 Visualization in Johns Hopkins University 1.1 The Genealogy of Visualization 1.2 Visualization Genotypes 2 Illustrative 2.1 First Generation Systems 2.2 Second Generation Systems 2.3 Third Generation Systems 3 Investigative 4 Imitative 4.1 Fifth Generation Systems I (Modeling and Simulation) 4.2 Fifth Generation Systems II (Virtual Reality) 4.3 Imitative Visualization by Sensory Feedback 5 Visualization in 6 Visualization in Spatial 7 Parametric 8.1 Speed Issues in...

## Cardiac and Coronary Artery Disease

There are significant evolving applications of 3D interactive visualization in the treatment of heart and coronary artery in the background. The accurate localization of the prostate tumor relative to critical anatomic structures, such as the urinary sphincter, seminal vesicles, and neurovascular bundles, improves physician navigation and performance in resection of pathology during the prostatectomy procedure. FIGURE 25 Dynamic volume models of beating heart and coronary arteries at...

## Computational Neuroanatomy Using Shape Transformations

Christos Davatzikos 1 Quantifying Anatomy via Shape fohns Hopkins University 2 The Shape 3 Measurements Based on the Shape 3.1 Measurements from Volumetric Images 3.2 Measurements on Surfaces 4 Spatial Normalization of Image 4.1 Structural Images 4.2 Functional Activation Images 4.3 Other Applications The explosive growth of modern tomographic imaging methods has provided clinicians and scientists with the unique opportunity to study the structural and functional organization of the human...

## Cubic Interpolation

Figure 19 proposes three synthesis functions of identical support which have essentially the same computational cost. On the left, despite the use of the optimal parameter a Keys offers the poorest visual performance since the central part of the figure is blurred. In addition, close inspection ( particularly on a monitor screen) discloses blocking artifacts that betray themselves as moire patterns. Those are absent with cubic spline and cubic o-Moms interpolation, although patterns unrelated...

## Data Acquisition for Vascular Morphometry

This section provides an overview of the most important methods that have been used to acquire data from which to extract or calculate arterial tree morphometry. Such methods fall into two major categories the older destructive techniques, including histology and vascular casting, and the increasingly useful nondestructive imaging methods that are the subject of this chapter. Historically, most anatomical data, particularly microana-tomical data on the remodeling of small arteries, was derived...

## Dynamic Brain Atlases

Atlasing of developmental brain data presents unique challenges. Imposition of standardized coordinate systems is difficult, and their relationship to anatomic nomenclature is hard to define, when potentially drastic morphological differences exist among data sets. In Yoon et al. 136 , a photographic atlas of the human embryo was created, based on detailed observations in utero from the 4th to the 7th week after ovulation (Carnegie Stages 10-18). In Chong et al. 13 , 26 normal formalin-fixed...

## Rxt

Reprinted from 59 with permission. features are obtained, classifiers can be designed for the classification of malignant and benign lesions. Several research groups have shown that the accuracy of computer classification can be comparable to or better than the performance of radiologists. These conclusions were reached after comparing computer classification with radiologists' diagnoses using ROC analysis. These encouraging results suggest that computer...

## Geometric Calculation of Changes in Cardiac Volumes

The most common volume measurement in the heart is the left ventricular volume because it is the most clinically relevant for evaluating cardiac performance. The method used to make this measurement depends on the type of images that are used. The imaging modality can be a digital contrast angiogram, a radionuclide angiogram, or a set of tomographic images. A geometric calculation of the ventricular volume relies on proper identification of the edges of the ventricular cavities on these images....

## In the Brain

Health Science Center at San Antonio 1 Spatial 2 General Spatial Normalization 3 Feature 5 Talairach 6 Manual SN 7 Accuracy of Spatial 8 Transformed Image 9 Anatomical and Functional 10 Uses in Functional and Anatomical To answer questions about where in the brain as opposed to where in this brain, images from many subjects are often combined to form consensus mappings of the brain. These composite images help to standardize teaching of brain anatomy and support powerful statistical analyses...

## Measurements from Volumetric Images

As we mentioned in Section 1, the transformation determined by elastically morphing a template to an individual brain carries all the morphological characteristics of the individual brain. From this transformation, various quantities, each reflecting different aspects of anatomy, can be calculated. In most of this section we focus on regional volumetric measurements, which have long been of interest in the brain imaging community. By regional volumetric measurements we mean local size...

## On the Accuracy of Quantitative Measurements in Image Intensifier Systems

The image intensifier (II) tube is an electrooptical device used to detect, intensify, and shutter optical images. It is a vacuum tube that contains four basic elements input phosphor screen and photocathode, electrostatic focusing lens, accelerating anode, and output phosphor. In diagnostic radiology, image intensifiers are applied in fluoroscopy and angiography where the viewing of images in real time is desired. This means that the X-radiation pattern emerging from the patient has to be...

## Phantoms and Cadavers

Unlike people, phantoms designed for medical imaging can remain perfectly still and can be displaced and sometimes even rotated with considerable accuracy. For imaging modalities with low resolution, such as PET, phantoms can produce images that are indistinguishable from real images by casual inspection 12 . Aside from biological factors (e.g., violations of rigid-body constraints or absence of realistic high-resolution partial volume effects), images of phantoms will reproduce many factors...

## Pixel Operations

In this section we present methods of image enhancement that depend only upon the pixel gray level and do not take into account the pixel neighborhood or whole-image characteristics. 3.1 Compensation for Nonlinear Characteristics of Display or Print Media Digital images are generally displayed on cathode ray tube (CRT) type display systems or printed using some type of photographic emulsion. Most display mechanisms have nonlinear intensity characteristics that result in a nonlinear intensity...

## Preprocessing

The concept of voxel-based multispectral image segmentation requires anatomically correct alignment of the data sets acquired within different image acquisition procedures. As pointed out in Section 5 for MRI data sets of the human brain, this may already be achieved during the acquisition procedure itself by stabilizing the subject's head position and applying a constant field of view in the different MRI sequences. In general, this will be sufficient in order to obtain an acceptable...

## Prostate Cancer

It is common practice to surgically remove many cancerous prostates, even though subsequent pathological examination of the excised tissues suggest that some surgeries could have been avoided 13,68 . Radical prostatectomy is a challenging procedure because of anatomical variability and the presence of adjacent vital structures, including the external urinary sphincter and neurovascular bundles. There is significant risk of serious morbidity in the form of urinary incontinence and impotence. The...

## Quality Evaluation for Compressed Medical Images Diagnostic Accuracy

UniversityeofCalifornia, 2 CT Study Example of Detection Accuracy 821 San Diego 2.1 Behrens-Fisher-Welch f-statistic Ro i rt Gra 3 MR Study Example of Measurement Accuracy 826 Ricnard Olsnen 3.1 Study Design and Statistical Analysis 3.2 Discussion Stanford Univarsity 4 Mammography Study Example of Management Accuracy 832 4.1 Statistical Analysis 4.2 Results and Discussion 838

## Quantitative Evaluation of Flow Motion

Analysis of cardiac function with dynamic imaging techniques is not limited to the evaluation of cardiac motion, and some dynamic imaging techniques provide means to measure and evaluate the kinetic patterns of blood flow through the ventricular cavities and the large vessels. The measurement of flow velocity and identification of abnormal flow patterns allow better evaluation of the severity of valvular diseases, the presence of abnormal shunts, the alterations and dissections of vascular...

## Region Growing

Region growing 26 is a segmentation method used to extract a connected region of acceptably similar voxels from a scene. The similarity criteria are, in general, determined by a range of intensity values or by well-defined edges in the image. A seeded region growing requires an initialization seed, usually provided by the operator, to be placed within the target ROI. The algorithm then examines neighboring voxels, one at a time, adding those that fall within the acceptance criteria. Since each...

## Results and Discussion

The clinical experiment took place at Stanford University Hospital during spring 1996. The gold standard was established by E. Sickles, M.D., Professor of Radiology, University of California at San Francisco, and Chief of Radiology, Mt. Zion Hospital, and D. Ikeda, Assistant Professor and Chief, Breast Imaging Section, Department of Radiology, Stanford University, an independent panel of expert radiologists, who evaluated the test cases and then collaborated to reach agreement. The majority of...

## Sensitivity to Starting Parameters and Statistical Modeling

For registration methods that must employ an iterative search algorithm to optimize some cost function, it is possible to evaluate how consistent registration results are as a function of the starting parameters used to initialize the search. This strategy gives an estimate of the accuracy with which the search optimizes the cost function. For registrations that involve least squares minimization, the accuracy with which the minimum has been identified can even be computed on the basis of a...

## Speed Issues in Visualization Systems

Speed issues often become the essential factors that determine the usefulness of a visualization system. Visualization involves two types of basic graphic operations One is related to the geometry, such as the transformation of the vertices of a polygon, and the other is associated with displaying pixels. In the graphics processing pipeline, the overhead can happen in either of these two operations and adversely affect the speed of the entire system. Thus, for instance, drawing a large number...

## Structural Images

One of the most common kinds of analysis of structural images has been volumetric analysis. More specifically, a brain image is partitioned into a number of structures that are of interest to the investigator, and the volume of each structure is then measured and compared across subjects. Spatial normalization offers a highly automated and powerful way of performing volumetric analysis. We will follow our previous work on a method for regional volumetric analysis, referred to as Regional...

## Validation by Visual Inspection

One of the quickest validation methods to implement is simple visual inspection of the results. Although this may seem like an informal and potentially unreliable approach, Fitzpatrick et al. 1 have shown that visual inspection can detect 2-millimeter misregistrations of brain MRI images to brain CT images quite reliably. Misregistration can be accurately identified even when one of the images is a low-resolution PET image. Wong et al. 10 found that translations of 2 millimeters along the x-...

## Vector Quantization

After performing the preprocessing steps explained in the previous section, we obtain multispectral data G e IR(mx,my,l,n) consisting of n correctly aligned, normalized data sets, where extracerebral voxels are excluded by a presegmentation mask. This can be interpreted as follows. Each voxel of the multispectral 3D data set represents an n-dimensional feature vector x that is determined by the tissue class for this voxel FIGURE 7 Segmentation. (a) T1 weighted image of a 3D data set. (b)...

## Volume Rendering Techniques

Representing a surface contained within a volumetric data set using geometric primitives can be useful in many applications however, there are several main drawbacks to this approach. First, geometric primitives can only approximate surfaces contained within the original data. Adequate approximations may require an excessive amount of geometric primitives. Therefore, a trade-off must be made between accuracy and space requirements. Second, since only a surface representation is used, much of...

## Sylv

CALCa SV eformation - Y (mm> CALL etal. 76 extract a 3D skeletonized representation of deep sulci and parse it into an attributed relational graph of connected surface elements. They then define a syntactic energy on the space of associations between the surface elements and anatomic labels, from which estimates of correct labelings (and therefore correct matches across subjects) can be derived. Ultimately, accurate warping of brain data requires the following. (1) Matching entire systems of...

## Imaging

To describe a tagged MR image, we designate each position within the image by its 2D image coordinate vector y y1 y2 T and the image brightness at each position by I(y, t). The image is obliquely oriented in 3D space and each image coordinate y can be related to its 3D position x by the function x(y) y1 h1 + y2h2 + x0 where h1 and h2 are two 3D, orthogonal, unit vectors describing the image orientation and FIGURE 2 Tagged MR images immediately after tag application at end-diastole (a) and 260...

## Figure

An X-ray projection of an MRI scan of a brain. See also FIGURE 6 A composited projection of an MRI scan of a brain. See also Plate 130. color and opacity at each grid location, can be generated using preprocessing techniques. The interpolation functions f(x, y, z), fc(x, y, z), and fa(x, y, z), which specify the sample value, color, and opacity at any location in R3, are then defined. f. and fX are often referred to as transfer functions. Generating the array Sc of color values involves...

## Criticisms of Mutual Information

Mutual information and its normalized variants have been criticized for failing to take account of the spatial coherence of information in images. By analogy with communication theory, all the voxel values are sent down a communication channel one after another, with all spatial information about their relative positions being lost. This can be nicely illustrated 3An affine transformation maps parallel lines to parallel lines. It includes skew and scaling as well as the rigid body degrees of...

## Frequency Domain Techniques

Linear filters used for enhancement can also be implemented in the frequency domain by modifying the Fourier transform of the original image and taking the inverse Fourier transform. When an image g(m, n) is obtained by convolving an original image (m, n) with a kernel w(m, n), the convolution theorem states that G(m, v), the Fourier transform of g(m, n), is given by where W(m, v) and F(m, v) are the Fourier transforms of the kernel and the image, respectively. Therefore, enhancement can be...

## Velocity Encoded CineMRI

More recently several authors have demonstrated that dynamic MR imaging can be envisioned as an attractive alternative to echocardiography 58,59 . In addition to being a noninvasive technique, MR imaging has several advantages, such as providing three-dimensional anatomical and functional data, dynamic evaluation of flow and velocity measurements, and potentially more accurate measurements of ventricular function than echocardiography 60 . The clinical use of velocity-encoded MR (VEC-MR)...

## Flow Vector Visualization

In volume visualization, generally the data at each point in the volume lattice is a scalar quantity. Recently, new MR imaging techniques that provide diffusion images of water molecules produce information that is a vector in each data point, and new types of visualization techniques for such vector field data become necessary. For instance, one approach would try to produce continuous flow-field-lines through the volume that follow the vectors in the 3D space. Such visualization techniques...

## K

F (7j k, n) E nkfk (yj , ), ( ) k l where yj is the intensity of voxel j, and fk is the Gaussian distribution parameterized by a mean and variance o . The variables nk are mixing coefficients that weight the contribution of each density function. Gaussian classifiers require training data similar to the kNN classifier implementation 20 . Using the training data, the parameters o, and n are estimated for each class. Gaussian clustering is an unsupervised technique in which no interactive...

## Schaums Functions

Like the o-Moms, the pseudo-Lagrangian kernels proposed by Schaum in 28 can also be represented as a weighted sum of B-splines and their even-order derivatives. They have same order and same support as B-splines and o-Moms. Their main FIGURE 12 o-Moms of third degree (central part). Function shape. (Right) Equivalent interpolant. Function shape. (Right) Equivalent interpolant. interest is that they are interpolants. Their main drawback with respect to both o-Moms and B-splines is a worse...

## Prediction of Material Properties of Trabecular Bone Based on Image Data

Quantification of the material properties of bone, such as strength and elastic modulus, using noninvasively measured parameters is important to predict fracture risk and evaluate effects of treatment for osteoporotic patients. Osteoporotic change is initiated from trabecular bone within both ends of long bones, vertebral bodies of the spine, flat bones such as the pelvis, and carpal and tarsal bones. Therefore, fractures related to osteoporosis occur in the trabecular-bone-rich regions. The...

## Industrial Standard for Image Format and Communication

Although since 1992 DICOM 3.0 has become accepted worldwide, in clinical procedures, equipment as well as databases typically still comply with the ACR-NEMA 2.0 standard. Thus, in most cases an ACR-NEMA 2.0 to DICOM 3.0 conversion is required. The DICOM 3.0 standard provides several major enhancements to the earlier ACR-NEMA version. Two fundamental components of DICOM, described in detail in Chapter 47, are information object class and service class. The information objects define the contents...

## 1

Reparameterized at times 0 < tm < tm+1 < 1. The M warps mapping the full surface system and surrounding volume from one time point to the next are concatenated to produce the final transformation. This incremental evolution of the transformation is visualized in a published video 115 . Extensions of the core algorithm to include continuum-mechanical, and other filter-based models of deformation (cf. 26,46,65,96 ) have yielded similar encouraging results. Experiments illustrating the...

## Sph

The assumption of a linear relationship between voxel values is also, in general, untrue for images of different modalities, as is 1This strict requirement is seldom true in intramodality registration, either, as noise in medical images such as modulus MRI scans is frequently not Gaussian, and also because there is likely to have been a change in the object being imaged between acquisitions. Here, (a) and aB(a) are the mean and standard deviations of the values of voxels in image B that...

## Brain Segmentation Method

Segmentation is achieved in three stages as shown in Fig. 2 removal of the background using intensity histograms, generation of an initial mask that determines the intracranial boundary with a nonlinear anisotropic diffusion filter, and final segmentation with an active contour model 22 . The use of a visual programming environment such as WiT 3 makes prototype development more convenient by allowing some exploration 5 . Preferably the T2-weighted image is used otherwise the PD-weighted or...

## Visualization in Biology

Although visualization in biology is a less pervasive technology today than it is in medicine, there is an increasing trend toward using powerful visualization tools in biology. It is important to note that many of the investigative research techniques in biology and medicine are pursuing similar paths. Imaging methods in medicine are increasingly becoming microscopic in scale, while imaging in biology requires addressing the functional properties of microscopic structures (Figs 17-20). These...

## A3 Recursive Filtering

The following routine performs the in-place determination of a 1D sequence of interpolation coefficients cn from a sequence of data samples fk . The returned coefficients cn satisfy where the synthesis function is represented by its poles. The values of these poles for B-splines of degree n e 2, 3,4, 5 and for cubic o-Moms are available in Table 3. (The B-spline poles of any degree n> 1 can be shown to be real and lead to a stable implementation.) This routine implicitly assumes that the...

## Benefits of Vector Valued Data

As with many other techniques, what is described here works on vector-valued volume data, in which each material has a characteristic vector value rather than a characteristic scalar value. Vector-valued datasets have a number of advantages and generally give better classification results. Such datasets have improved SNR and frequently distinguish similar materials more effectively (see Fig. 13).

## Comparison of 2D Wavelets 3D Wavelets and JPEG

This section presents some compression results using two 3D image data sets. The first is a 3D MR brain data set obtained with a GE 5x Sigma Scanner with 26 images and a slice distance of 6 mm. Each image is 256 x 256 x 12 bits. The second set is a 3D CT spine from a GE CT scanner with 69 images and a slice distance of 3 mm. Each image is 512 x 512 x 12 bits. The 3D wavelet, 2D wavelet, and JPEG compression were applied to FIGURE 8 Compression ratio versus RMSE for three different filter banks...

## Course Materials Conference Proceedings

13. 3D Visualization in Medicine ACM SIGGRAPH 98. Course Organizer Terry S. Yoo. Lecturers Henry Fuchs, Ron Kikinis, Bill Lorensen, Andrei State, Michael Vannier. 14. Data Visualization '99 (E. Groller, H. Loffelmann, W. Ribarsky, Eds.), Proceedings of the Joint Eurographics and IEEE TCVG Symposium on Visualization, Vienna, Austria. Springer, Wien. 15. Visualization in Scientific Computing '95, Proceedings of the Eurographics Workshop in Chia, Italy, May 3-5, 1995 (R. Scateni, J. van Wijk, and...

## Across Modality Registration Using Intensity Based Cost Functions

Hawkes 2 Background to the Use of Voxel Similarity Measures 538 King's College London 3 joint 539 4.1 Measuring Information 4.2 joint Entropy 4.3 Mutual Information 4.4 Normalized Mutual Information 543 5.1 Discrete and Continuous Formulations of Mutual Information 5.2 Image Resampling 5.3 Capture Range 5.4 Search Strategy 6.1 Mutual Information for Registration Involving Affine Transformations 6.2 Mutual Information for 2D 3D Registration 6.3 Mutual Information for Nonrigid...

## Medicine

Kaufman 1 State University of New York at 2 Volumetric Data 713 Stony Brook 3 Surface Rendering 4 Volume Rendering 4.1 Object-Order Techniques 4.2 Image-Order Techniques 4.3 Domain Volume Rendering 5 Volume Rendering 6 Volumetric Global 6.1 Volumetric Ray Tracing 6.2 Volumetric Radiosity 7 Special-Purpose Volume Rendering

## Global Shape Constraints

We apply our integrated boundary finding and region-based segmentation to the problem of locating structure from images where there is prior knowledge ofshape that can be represented in a global shape model. We want to determine the surface (or curve, in 2D) parameters that correspond to the structure that matches both the boundary strength in the image and the region homogeneity properties. Integration can be achieved in a sequential manner, where the region-based segmentation is determined...

## Perspective Transformations

The most general linear transformation is the perspective transformation. Lines that were parallel before perspective transformation can intersect after transformation. This transformation is not generally useful for tomographic imaging data, but is relevant for radiologic images where radiation from a point source interacts with an object to produce a projected image on a plane. Likewise, it is relevant for photographs where the light collected has all passed through the focal point of the...

## Partition of Unity

How can we assess the inherent quality of a given synthesis function We answer this question gradually, developing it more in the next section, and we proceed at first more by intuition than by a rigorous analysis. Let us consider that the discrete sequence of data we want to interpolate is made of samples that all take exactly the same value fk f0 for any k e Zq. In this particular case, we intuitively expect that the interpolated continuous function f (x) should also take a constant value...

## Mammography

Mammography is a radiographic examination of the breast. An X-ray beam from a metallic target is directed toward the breast and the transmitted X-rays are detected by an image receptor. Most commonly, the image receptor is a fluorescent screen, held in intimate contact with a sheet of single-emulsion photographic film in a light-tight cassette. In mammography, the X-ray spectrum is most frequently emitted by a molybdenum target, although rhodium or tungsten may be used for imaging large or...

## Features Extraction Extremal Points and Lines

To extract reliable curves on a surface, most approaches try to generalize the notion of edges to smooth surfaces to find the most salient features on the surface ridges. Prior to the late 1980s and early 1990s, the interest in ridges was mostly theoretical, in areas of mathematics related to catastrophe theory 1,20,24,32,33 Crest lines were then defined as the cuspidal edges of a caustic surface, and the link between caustics and curvatures on a surface was established. Practical applications...

## Cost Function and Distance Transform

Mathematically, the cost functions for chamfer matching and gray value registration are related. Let us consider the classical image correlation function, C, between two images, which is defined as a volume integral or sum, C(T) J F(T.r) G(r)dr, (1) where r is a three-dimensional integration variable, F and G are the images to be correlated, and T is a geometrical transformation. For practical image registration applications, the correlation function must be suitably normalized and the maximum...

## Biological Underpinnings of Anatomic Consistency and Variability in the Human Brain

Crivello 2 Cerebral Anatomy at the Macroscopic Level 450 M. Joliot 2.1 Brain Size and Gross Morphology 2.2 Sulcal and Gyral Anatomy B. Mazoyer 3 Cerebral Anatomical 454 Universit de Caen 3.1 Sulcal Variability in Stereotactic Space 3.2 Brain Asymmetries 4 Anatomical Variability and Functional Areas 459 4.1 Relationships Between Macroscopic Anatomy and Cytoarchitectonic Microanatomy 4.2 Relationships Between Macroscopic Anatomical Variability and Functional Areas 461 462