## J7Vud

Where Vm is the magnitude of the gradient, with some constraints was proposed for the restoration of images. Their optimization was based on the simulated annealing approach to find the global minimum. Here, the anisotropic diffusion problem is posed as a cost-functional minimization problem. Therefore, if we know the shape of the surface defined by the energy functional, we can understand the behavior of the diffusion whether the diffusion process is well-posed or ill-posed. The boundary, or...

## Magnetic Resonance Imaging

Magnetic resonance imaging (MRI or MR) can be simply defined as imaging the macrolevel behavior of atomic nuclei that possess magnetic property, under a strong magnetic field. The term magnetic property will be explained later in the section. For clarification purposes we should mention that hydrogen (H) is the most commonly used atom in MRI. Before moving forward, it is worthwhile to mention several unique advantages of MRI over other imaging modalities. Unlike computer tomography (CT), single...

## Intensity Based Image Segmentation

6.2 Between-Class 6.2.1 Criterion Functions Equivalent to 6.2.2 BCV as an Image Bimodality 6.2.2.1 Bimodality Threshold for Uniform 6.2.2.2 Bimodality Threshold for Normal Distribution 232 6.2.3 An Iterative Implementation of BCV for Trimodal 6.3 Minimum Error 6.4 Extention to 6.5 Entropy-Based 6.5.1 One-Dimensional Entropy-Based 6.5.2 Two-Dimensional Entropy-Based 6.6 Image Segmentation by K-Means 6.7 Image Segmentation by Fuzzy C-Means 6.8 Mixture-Modeling-Based Image segmentation using...

## A27 Calculation of Modulation Transfer Function MTF from a Line Source and a Point Source Image

Optical transfer function (OTF) of a medical imaging system can be defined as the Fourier transform of its point spread function. The modulation transfer function (MTF) is the magnitude of the OTF. In practice, to calculate the OTF, the image of a point source is acquired by the imaging system and its Fourier transform is computed. It is also common to acquire the image of a line source oriented along the x and y directions to calculate the MTF along the y and x directions, respectively. In...

## A31 Introduction

As islet transplantation and immunosuppressive regimens become increasingly successful, islet transplantation is likely to find widespread clinical application for curing patients with insulin-dependent diabetes mellitus. An important determinant of successful transplantation is the quantity of islets engrafted, with many advocating at least 5000 equivalents per kilogram to be transplanted. The measurement of islet equivalents has been traditionally a manual process. Automated color image...

## Introduction

In this chapter, we discuss the major medical imaging modalities used in diagnostic imaging. These modalities generate an image of the body either through the detection of photons or the use of electromagnetic waves. Let us recall the dual nature of light. The duality theory asserts that light has the properties of both waves and particles. This duality is also applicable to the photons that are involved in our imaging modalities. Figure 1.1 shows the positions of these imaging modalities in...

## O

Left panel A synthetic edgemap containing a circular ring. Right panel The circle detected (gray) using our Hough transform functions routines is overlaid on the original synthetic edgemap. thres .5*max(h( )) subplot(1,2,2) mipextractcircles(I,h,rl,thres), axis on title('Detected circle') To further investigate how the Hough transform of our synthetic image looks, we can generate a 3-D view of our accumulator array using the following MATLAB commands. The resultant graph is shown in Figure...

## Signal Detection Relaxation

After a magnetized spin system is perturbed from its equilibrium condition by an RF pulse, it will return to the equilibrium state after a sufficient time once the perturbation is removed. This process is known as free induction decay or relaxation, which was first discovered by Bloch in his seminal work 5 . The recovery of the longitudinal component Mz is called longitudinal or Ti relaxation, whereas the decay of the transverse magnetization Mxy is called transverse or T2 relaxation. The...

## H

Hammersley-Clifford theorem, 287 Harris corner detector, 106 Head image, CT slice, 235 Hessian matrix, 102,103 Hexagon image MATLAB code, 292 segmented, 294 vectorized version, 295 Histogram cDNA microarray image, 239 cell image, 245, 251 equalization, fundus camera, 216 gray-level, 242,246 human head CT image, 235 image, 67-71 joint histogram computing, 70-71 2-D histogram, 68-70 modes, 262 MRI brain image, 305,306 normally distributed regions, 225 synthetic hexagon image, 240 two-dimensional,...