VERIFICACIÓN DE LA IMPLEMENTACIÓN

Different scans o f brain contain complementary information which may be useful when correlated and displayed simultaneously. Correlation of structural and functional images is essential in quantitative image analysis and understanding o f the origin o f some abnormalities. Using structural information provided by morphological images is important in data analysis of functional images. Many brain functions are related to structures o f very small size, for which

data correlation is required in assessment o f the physiological information o f these regions.

The research presented in this thesis is an investigation into the problems o f the registration and display of brain images obtained by different imaging modalities. Following the introduction o f the research objectives, the research topics and organization o f this thesis were presented in chapter 1. Some clinical useful application o f the registration and superimposition were also defined. This chapter also demonstrated the imaging and computer systems and facilities employed for developing the work presented in this thesis.

The various widely used registration algorithms were introduced in chapter 2. The applicability o f these methods to medical images was also described in this chapter. The advantages and disadvantages o f each algorithm were described. A registration process based on the reliability criteria was selected and introduced in this chapter. In this approach, the edge- based algorithms, which are based on a least-square-distance matching, were suggested for registering of brain images. These algorithm minimise the sum o f square-distances between the two surfaces. The minimization is applied over a set of six geometrical transformation parameters (3 shifts and 3 rotations) which indicate how one surface should be transformed in order to match with the other surface.

The general technique o f the surface fitting, as defined by the other workers, was described in chapter 3. A number o f improvements to the general surface fitting algorithm were also suggested in this chapter. One o f the suggested key improvements was the use o f a global minimization algorithm which increases the accuracy o f the registration. This algorithm has led to two novel approaches: sequential and multi-grid registrations, as discussed in two separate chapters (6 and 7).

In chapter 3, the imaging parameters and data types used through this project were also introduced. Most o f the data introduced in this chapter was used as well-defined image models for verifying the applicability o f the different aspects o f the registration process. Based on this data the proposed technique was verified and its results were presented in a separate section. In general, a number o f local minima were shown to exist in the distance function between the two surfaces. The sampling strategy (e.g. position and number o f sample points) was also shown to

depends on the resolution of the data set and thus varies with the type of imaging study. The accuracy was shown to be of the order of half the pixel size o f the original grey-scale image.

A survey of surface reconstruction methods, as an essential element o f the surface fitting, was presented in chapter 4. In this respect, surface representation, segmentation (2-D edge detection), and surface formation were studied. Potential techniques were selected following the introduction of suitability criteria. The representation capabilities of most o f the representation techniques were defined to be poor in satisfying all of these criteria. However a voxel-based approach was implemented using a 3-D binary array which can maintain the level of details comparable to that o f original 2-D slices. Due to the nature o f original grey-scale data in most medical applications, a slice-level boundary detection mainly based on a gradient operator was suggested. For the surface formation process, various interpolation methods were outlined; among them the shape based methods were found to be superior and therefore used extensively throughout this project.

Chapter 4 also outlined the new approaches for handling the abnormal regions and deformities occurring in some nuclear medicine brain images. A verification known as the circularity check, for the shape of the detected head contours was defined, based on the curvature measurement. Any unacceptable deformity or hole in the brain surface can be detected by the

circularity check and then reformed by a type of interpolation process. Two techniques were suggested, based on median filtering and contour reflection, to correct for Çreform') these abnormal regions.

Chapter 5 described various methods for solving the minimization problems. The iterative approaches were indicated as an essential process for surface fitting algorithms. Gradient methods were used to generate a sequence of linear searches along successive directions o f a multi-dimensional function. Golden section search and quadratic interpolation methods were addressed in a linear search strategy as two powerful methods for quadratic functions. The

Powell method, the Fletcher-Reeves method and Newton type methods were also described as the most efficient multi-dimensional minimization techniques available at the present time. In this chapter the properties of a suitable minimization algorithm were also outlined, and the Powell method was selected as the best algorithm satisfying most of these characteristics.

In chapter 6, the application of the sequential process for 3-D surface registration was described, in a new approach. A reduction in computational cost with respect to the global grid search was obtained while the quality o f the result was not degraded. The cumulative error was suggested for use instead of the mean distance error for evaluating the mismatch between two surfaces. The different sources o f errors contributing to the cumulative distance error were outlined. Using this type o f error analysis, the application o f a variable threshold was implemented. It produced a very efficient method for termination o f mismatch locations. An expression for the calculation o f the threshold sequence was also developed.

In chapter 6, the computational implementation o f the sequential process was presented as well as the cost prediction. Various factors influencing the computational cost were also studied. The expected time required for the algorithm to decide that there is not a match at a given location was shown to depend on the threshold, sampling strategy, and ordering o f the sample points.

In chapter 7, a novel approach for a modified fast registration algorithm was presented. The approach, known as multi-resolution, employs a variable grid search on two low resolution (small image size) binary surfaces. It applies only the most promising transformations on a corresponding bigger (high resolution) image. In this approach, results computed on the basis of some few voxels matched in a coarse resolution image are used for the next resolution level, and in due course for the original high resolution image.

A degradation technique was introduced and the error incorporated in the surfaces created by this technique was studied. In addition to that, other sources o f error were also studied. In chapter 7, an expression for the definition o f the threshold sequence used in multi-resolution sequential methods was also derived. Various parameters influencing this variable threshold were discussed. The expected computational cost and the factors influencing this cost were also explored. The analysis shown in this chapter confirmed a potential reduction o f the computational cost by using a multi-resolution sequential method at a grid-based search strategy instead o f a pure sequential method.

8. A number of well defined clinical image data sets, selected and modified to assess the above mentioned algorithms, were described in chapter 8. The technical aspects of the routine imaging systems producing these clinical data were also addressed. The advantage of a sequential process and the superiority of the variable as opposed to the constant threshold level, was also demonstrated in the experiments set forth in this chapter.

The probability analysis presented in chapter 8 investigated the importance of the effects of different threshold levels and various number of sample points used at each resolution levels. The results of this probabilistic analysis confirmed that a threshold level (g) of 2 to 3 (S.Ds of the individual distance error measures at match location) is required for detecting the true match location while keeping the FAP {false alarm probability) sufficiently low. It was also shown that using a higher number of points (e.g. 200 in the original finest resolution level; i.e. image size of 256^) provides a better matching performance than a smaller number of points. The number of points required at any resolution level was shown to correspond to nearly half of that required in the next higher resolution level. The number and fraction o f sample points which are matched in a mismatch location, and on the other hand, the number o f points mismatched in a match location, are two important factors indicating the reliability o f the matching process.

Following the specification of the problems associated with the registration algorithm, a set of experiments was designed to determine the matching accuracy. An expected accuracy of about 1, 1.5 and 2 voxels (whose size is in the order o f 1mm) for MR, PET, and SPECT

registration was achieved, using the arbitrary misregistered data sets. Using some selected reference points (e.g. external markers or internal landmarks) to verify the proposed algorithm, the accuracy of 1.44^0.42 mm, 1.82^0.65, 2.38^0.88 and 3.17? 1.12 was obtained for MR-MR, MR-CT, MR-PET and MR-SPECT registration, respectively. The computational cost was also determined with respect to certain search windows, template sizes (number o f sample points) and other parameters as required for the process. The cost of the multi-resolution process was shown to be about 200 seconds (on the VAX II) for the actual search process. The results obtained by the conventional MR and SPECT images show that the algorithm can be used for the routine imaging studies.

In chapter 9, the problem of superimposition o f resulting images was defined, as overlaying and combining the correlated images and displaying them to an observer. Some of

displaying clinical images were discussed. The display technique employed in the current work was a type o f surface rendering technique based on voxels in a 3-D space. The surface normals

used in shading method were defined in an image-based approach. The volume rendering

process was also used for displaying the skin surface and the surface o f some internal structures o f the head in order to improve visualization.

Four types o f combining and displaying the correlated (registered) images were employed, as described in chapter 9. The correlated 2-D slices were displayed side-by-side illustrating the corresponding clinical information between the two studies. The contours o f regions o f interest (e.g. ventricles or tumours) were superimposed on the 2-D grey-scale images o f the other study. A linked cursor was used, moved manually by a digitizer on the screen and showed the corresponding structures between the two images, A colour-coded display in which different colour ranges are assigned to the structures o f each image was also suggested. Due to the difference in grey level ranges o f the registered images, different interactive image processing tasks were applied during display process.

The images o f thirty patients were studied using the proposed registration processes. The fidelity of the registration process and data alignment was judged by the clinicians and radiologists in the department where the work was carried out. The potential work o f the research outlined in this thesis provides a suitable algorithm for registering medical images, integrating the correlated images, and displaying them.