The primary objective of this thesis is to show how stereology can be effectively implemented on digital images. This goal is achieved through the development of EASY MEASURE - an interactive software package that enables the convenient application of stereological methods for estimating volume, surface area and length. The thesis is predominantly concerned with images of in-vivo human anatomy that are obtained by MRI. However, digital images of mathematical objects are used for validation purposes.

## 2.1 Materials

At the heart of this thesis is EASY MEASURE - an interactive computer program for performing stereology on digital images. The software operates under Microsoft (Redmond, Washington, USA) Windows 95/98/2000 or NT4.0 and is written in Microsoft Visual C++ 6.0. The recommended requirements for running EASY MEASURE are a personal computer (PC) with at least an Intel Pentium P133 (or equivalent) CPU. As a rule of thumb, 32 megabytes plus "twice the size of image under investigation" megabytes of RAM should be installed on the PC. A fast graphics card is also recommended that should ideally support resolutions of 1024 by 768 pixels, 24-bit colour and a refresh rate of 75Hz.

EASY MEASURE is used to perform stereological investigation of various digital images in Chapters 7, 8 and 9. These images can be divided into two groups. The first group is made up of well-defined mathematical objects (see Chapter 7). These images were generated using EASY MEASURE. The second group comprises images acquired by MRI. The MR scanner in operation at MARIARC is a 1.5 Tesla SIGNA whole body MR imaging system (General Electric, Milwaukee, USA). Unless otherwise stated, this scanner was used to acquire the images described below:

- In Section 8.1, T1-weighted images of the vertebral columns of four female volunteers (average age 20) with negligible scoliosis are investigated. Sagittal-oblique images were produced in which the spinous processes of the vertebral bodies had maximal cross-section.
- Under investigation in Section 8.2 are 3D SPGR images of five pears.
- Section 8.3.1 is concerned with 3D SPGR images of six post mortem, formalin fixed brains that were bequeathed by three males and three females with no history of any neurodegenerative disorder.
- Finally, in Section 8.3.2 a paradigm brain dataset provided by Holmes et al. (1998) is investigated. The dataset was constructed from a series of 27 3D T1-weighted MR scans obtained from a single 30 year old male using a 1.5 Tesla GYROSCAN MR scanner (Philips Medical Systems, The Netherlands).

MR images that required some pre-processing procedures not supported by EASY MEASURE were transferred to Ultra 1 workstations (Sun Microsystems, California, USA) where data manipulation was carried out using the ANALYZE software package (Mayo Clinic, Minnesota, USA).

Other materials used were stereological test systems, which were photocopied onto acetates, and two high precision cutting tools (both similar to the cutting tool described by Kroustrup and Gundersen, 1983). These additional materials were required for the experiments described in Sections 8.2 and 8.3.1.

## 2.2 Objectives

The primary objective is to show how stereology can be effectively implemented on digital images. This is realised through the development (described in this thesis) of an interactive and convenient to use computer package called EASY MEASURE. At the outset of this project, the following key objectives were decided upon:

- EASY MEASURE should have the ability to sample appropriately acquired digital images with a wide range of test systems (see Chapter 4), including test systems of
- Points (Sections 4.3, 5.5.1 and 5.5.2).
- Orthogonal or parallel lines (Sections 4.5, 4.8.1, 5.1 and 5.5.1).
- Horizontal rolling circles (Sections 4.5, 4.8.1, 5.2 and 5.5.2).
- Horizontal rolling cycloids (Sections 4.8.2, 4.8.3, 4.8.4, 5.3 and 5.5.2).
- Vertical rolling cycloids (Sections 4.9, 5.3 and 5.5.2).

- EASY MEASURE should be able to generate appropriate digital images (through digital sectioning) onto which test systems described in objective 1 can be overlain (Section 5.7).
- Validate methods that underpin EASY MEASURE through the investigation of well-defined objects such as circles, ellipses and squares. In Chapter 7, the validation process is accompanied by a discussion concerning precision. In Section 4.10.2, a specific theoretical result for the circle under a square grid of lines is presented which is corroborated empirically using EASY MEASURE.
- Illustrate the application of EASY MEASURE.
- In Section 8.1, the lengths of four vertebral columns are estimated from sagittal-oblique MR images using test systems of parallel and orthogonal lines as well as horizontal rolling circles.
- Section 8.2 describes two approaches for estimating pear surface area and volume from exhaustive vertical sections (see Sections 4.8.3 and 4.3). The first approach employs EASY MEASURE to interrogate reformatted MR images of the pears with appropriate test systems. The second approach involves physically sectioning the pears so that acetates containing appropriate test systems can be overlain.
- The thickness of the cerebral cortex is estimated in Section 8.3, by dividing the volume of the cerebral cortex by the mean of its inner (grey/white matter) and outer (pial) surface areas. Volumes are estimated using the Cavalieri method (Section 4.3), while surface areas are estimated using the exhaustive vertical sections method (Section 4.8.3). Six formalin-fixed brains are investigated in Section 8.3.1, while the paradigm brain dataset (described in point 4 of Section 2.1) is investigated in Section 8.3.2.

- Automate the stereological processes of point and intersection counting for binary images. This objective is achieved using the transition counting rule described in Section 5.6 and Appendix A.