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Chapter 11

3D Medical Imaging

Philip G. Batchelor, P.J. “Eddie” Edwards, and Andrew P. King

Abstract This chapter overviews three-dimensional (3D) medical imaging and the associated analysis techniques. The methods described here aim to reconstruct the inside of the human body in three dimensions. This is in contrast to optical methods that try to reconstruct the surface of viewed objects, although there are similarities in some of the geometries and techniques used. Due to the wide scope of medical imaging it is unrealistic to attempt an exhaustive or detailed description of techniques. Rather, the aim is to provide some illustrations and directions for further study for the interested reader. The first section gives an overview of the physics of data acquisition, where images come from and why they look the way they do. The next section illustrates how this raw data is processed into surface and volume data for viewing and analysis. This is followed by a description of how to put images in a common coordinate frame and a more specific case study illustrating higher dimensional data manipulation. Finally, we describe some clinical applications to show how these methods can be used to provide effective treatment of patients.

11.1 Introduction

Medical imaging dates back to the discovery of X-rays by Wilhelm Röntgen in November 1895. His discovery was published in early 1896 and rapidly led to the proliferation of 2D X-Ray imaging equipment. The clinical implications of the fact that X-rays pass through the soft tissue and can image bone was quickly realized

and X-rays were used to image fractures and diagnose the presence and location of foreign bodies such as gunshot wounds.

Much of the 3D imaging described in the earlier chapters of this book is based on one or more optical cameras imaging a visible surface. In contrast, the aim of 3D medical imaging is to model structures beneath the surface of the skin. The techniques of stereo and multi-view reconstruction, such as those described in Chap. 2, can also be applied to X-rays, which have the same projective geometry as camera images. For example, the 3D shape of vessels can be reconstructed from biplanar 2D X-rays [32]. However, such applications have been largely part of research and, for over 70 years since its inception, the field of medical imaging remained largely 2D.

In the 1970s, however, research began on imaging modalities that produce a fully 3D representation of the patient. The first of these was computed tomography (CT), a 3D reconstruction using X-rays. The second was magnetic resonance imaging (MRI) which utilizes the nuclear magnetic resonance effect. These developments were in part only possible due to the increasing power of computing occurring at the same time. Both of these modalities produce volumetric images. These can be considered as a series of aligned slices but really form a continuous 3D block of data. The individual elements are generally referred to as voxels rather than pixels. In a sense, the surface data described in much of this book is not truly 3D, since it represents a 2D surface, albeit a surface embedded in 3D space. In this chapter, we will concentrate on fully volumetric 3D medical imaging modalities, but also look at how surfaces can be extracted from or registered to such images.

Despite being three dimensional imaging modalities, the most common way for a radiologist to view these images is as a series of 2D slices. Until remarkably recently, these would actually be viewed as printed films on a light box. However, with the widespread adoption of standardized networking and reviewing of images via picture archiving and communication systems (PACS), viewing on a computer screen is now the norm. Viewing as 2D slices does enable the full image data to be explored, but viewing in 3D can provide improved perception and the majority of radiologists are now used to navigating and viewing datasets in 3D.

Chapter Outline In Sect. 11.2, we will summarize the principles behind the leading 3D anatomical medical imaging modalities, namely CT and MRI, as well as briefly touching on positron emission tomography (PET). CT and MRI are sometimes described as anatomical modalities, whereas PET is considered functional, in the sense that it shows where metabolism is occurring. There are also functional forms of MRI, however, but discussion of this is beyond the scope of this chapter. In Sect. 11.3, we present methods for surface extraction and volumetric visualization. The following section deals with volumetric image registration, while Sect. 11.5 presents segmentation methods. Section 11.6 considers higher dimensional imaging with the example of diffusion tensor MRI and the final main section describes some clinical applications of 3D imaging; in particular, surgical guidance.

There are, of course, many other medical imaging modalities. Ultrasound is a real-time and largely 2D modality, but can be made 3D by the addition of tracking or 2D phased array probes. There is nuclear medicine, SPECT, thermography, electrical impedance tomography, elastography, optical coherence tomography, confocal microscopy, magnetoencephalography, fluorescence lifetime imaging, near infrared optical tomography and spectroscopy and the list goes on. It is not possible to cover the huge field of medical imaging in one chapter. Rather, we provide an introduction to the subject that summarizes the basics of 3D medical imaging. For more details, we refer the reader to some excellent textbooks [4, 16, 39], as well as online references; for example, the online Encyclopedia of Medical Physics (EMITEL) [77].

11.2 Volumetric Data Acquisition

Before discussing how we can process and analyze 3D medical imaging data, it is important to examine the issues relating to data acquisition. The human body is largely opaque to optical imaging, so medical images must use other physical processes to image tissue properties. The techniques used will have significant influence on the types of tissue that can be imaged and the quality of the 3D data obtained in terms of contrast, noise characteristics and artifacts.

In this section, we will summarize the methods behind volumetric data acquisition. For 3D imaging of human anatomy, two modalities dominate, CT and MRI. We describe briefly the physics and the computational methods used to reconstruct these modalities, as well as considering the functional modality, PET. We consider the characteristics of the reconstructed data from the point-of-view of 3D and describe some of the artifacts that can occur.

11.2.1 Computed Tomography

Computed tomography (CT) is essentially a 3D version of classical X-Rays. The overall idea is fairly simple. An X-Ray is a projection through the object, in the sense that the pixel intensities can be interpreted as related to an integral along projected rays through the object. If we take multiple X-Rays at different angles, we might be able to solve for the 3D voxel intensities. In fact, the process really reconstructs a single 2D slice and the patient is moved through the scanning plane to collect multiple slices and create a 3D volume.

So, how is such a 2D slice reconstructed? The object (slice through the patient) can be considered as a 2D array of X-ray attenuation coefficients μ(x, y). The aim of CT imaging is then to reconstruct the function μ(x, y). If the incident intensity from the X-ray source is I0, the transmitted intensity I having passed along a single ray through the patient will be: