Accuracy

Surgical image-guidance systems consist of several interacting parts, each having its own intrinsic level of accuracy. The objective of this thesis is to quantitatively characterize the error introduced by some of these elements, namely the registration algorithms, the localizing device and the MR geometrical distortions.

The accuracy in can be conceived as follows. The registration procedure is used to find a 3-D transformation between the patient and the image. Because of the imperfection of the input data (image and digitized points on the patient's head), the transformation found will not perfectly relate the patient to its image. This suggests that the analysis of the accuracy of can be performed in two steps.

1. Analyze the behavior of registration algorithms under non-ideal input data, i.e., study the effect of perturbations in the input data on the registration error. This is discussed in Chapter 3.
2. Quantify the possible error on the input data. This is the objective of chapters 4 and 5.

Chapter 2 describes the constituents of and their mutual interaction in a more detailed manner. Presented in this chapter is a model of in which the role of imaging, patient's surface digitization, anatomical changes and registration is discussed. This chapter clarifies the manner in which the different elements of interact to produce the overall result.

The topic of registration is treated in Chapter 3, starting with the definition of the registration error and an analysis of its statistical behavior under conditions of noisy data. Clinical comparison measurements between two registration techniques are also reported.

An experiment, whose goal is to compare the accuracy of a mechanical and an optical digitizing devices against an external reference is discussed in Chapter 4.

Finally, the issue of MR images geometrical distortion is addressed in Chapter 5, in which an analysis of 3-D MR data of the stereotactic frame is performed. Additionally, an evaluation of the use of the three-point-Dixon MR acquisition technique as a method of measuring the magnetic field inhomogeneity is made.

The original contributions of this work are:

• the use of a graphical means of describing the difference between two registrations in 3-D space that has the advantage of clearly showing the three-dimensional spatial dependence of the registration error,
• to show that there exists a simple relationship between the RMS rotational and translational errors and the RMS registration error associated with a registration method and
• to show that relevant statistical information on the translational and rotational error associated with a registration technique can be deduced from the comparison of a large number of registrations and
• to compare homologous point matching with surface matching registration technique applied in the context of .