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Parallel and Related Work

Rueckert et al. [] describe statistical deformation models (SDM's) which are in essence surprisingly similar to appearance model. As it turns out, they are explicitly set to construct an appearance model using statistical analysis as described in Chapter . They do this analysis in a strategically different and indirect way though. To transform images, B-Splines are used which are quite powerful, well-understood and commonly used, e.g. in computer graphics rendering and curve fitting. However, they suffer from one main drawback which is deficiency of diffeomorphism. What this practically means is that parts of the data can be torn or folded, i.e. structures can disappear. This cannot happen if the CPS-based warps are used, but a valid comparison is needed to discover if this attribute really is all about gains.

Similar concepts have been applied to segmentation in []. Much work has concentrated on using the knowledge and techniques from each one of these two to establish a more powerful framework of full appearance statistical models. The work is described in Chapter cha:Project-Goals with reference to research that is associated with the GC (some of the cross-over papers are relevant in this context). An exclusive introduction to Rueckert's work will attempt to elucidate the current registration concepts which future research relies upon.

Non-rigid registration methods have been applied in several medical domains of expertise. Amongst these is the renowned brain analysis task, contrast-enhanced MR mammography and segmentation and tracking of the heart. The procedures currently employed are inclined to follow higher-order entropy measures that will not be delved any further. Rueckert's homepage [WWW-2] which is listed at the end gives the full details and references. Chapter on information theory explained in brevity some of the basic ideas behind these so-called entropy measures.

The success of temporal non-rigid image registration method is dependent upon two factors:

1. Search algorithm: As earlier illustrated in the context of active appearance mode, good warps need to be searched to achieve good similarity.
2. Similarity: The performance relies on a suitable choice of similarity measures which guide the search until a sufficiently good fit is declared.

Learning the properties of similarity measures, the way they affects the search duration and the effect warps have on similarity are all important aspects of registration method development. This is reminiscent of the process in which correlation between parameter changes and intensity changes are learned in appearance models.

Statistical parametric mapping (SPM) are being used in University College London [WWW-16] in order to register bio-medical data. The term SPM refers to construction and assessment of spatially extended statistical process that can be used to test hypotheses about given medical data, especially in the domain of neurology. SPM spatially normalises images into a standard regular space and then applies some smoothing. Statistics which are then extracted from the registration of the data are addressed by theory of continuous random fields. None of this is arcane, though the concepts are rather unique to UCL.

Also in UCL, registration is performed which is based on fluid models. The rigid movement of objects does not usually impose problems as those introduced by soft tissue. Fluid registration is a matching technique which models these awkward morphological changes as compressible viscous fluid. The idea is presently applied in brain imaging where greater interest has existed for some time.

Change in organs due to resection (craniotomy being a banally-encountered scenario), expansion, movement etc. is often modelled using thin-plate splines [] and the motion of organs can be handled using free-form deformation (FFD) which are based on B-splines. Prior to this embedment of high-order functions, the effects of rigid-body motion is annulled by Euclidean transformation. Similarity measures guide this process of rigid registration just as well. It is the technical description of the algorithms used that proves why these methods, which are used in Guy's Hospital, are extremely effective. As earlier mention, current work is done using the bi-harmonic [] clamped-plate splines and possible investigation is considered for a model-based objective function that uses other morphometrical methods.