Non-rigid image registration using bone growth model

Non-rigid registration has traditionally used physical models like elasticity and uids. These models are very seldom valid models of the di erence between the registered images. This paper presents a non-rigid registration algorithm, which uses a model of bone growth as a model of the change between time sequence images of the human mandible. By being able to register the images, this paper at the same time contributes to the validation of the growth model, which is based on the currently available medical theories and knowledge. This paper studies the process of bone growth in the human mandible. Based on the available medical knowledge, a bone growth model is established, and experiments are carried out to determine the validity of the model. These experiments uses a unique data set containing three voxel images of the mandible of a child, taken at di erent times. Being able to model the growth of the facial bones is both interesting for understanding the development of the cranio-facial complex, and for understanding the e ects of cranio-facial surgery on children. After children with growth defects have undergone surgery to restore normal function and appearance, the bones continue to grow. This growth often introduces new deformations and new surgery has to be performed. It is, therefore, important to understand the growth of the bones. It would be useful for the surgeon to be able, not only to predict the instantaneous result of the surgery, but also to predict the evolution of the face after surgery. Using such knowledge, the surgeon could possibly anticipate this development and correct for it in advance. The process of modeling the growth can be seen as a registration problem, and the discussion follows the notation and semantics of the general registration methodology. 1 Non-rigid registration as a physical problem Non-rigid registration is used to register images that are di erent. As 'non-rigid' indicates, more than just a simple superposition of the images is required to get a complete correspondence, and some sort of deformation must be included in the transformation, to map dissimilar images onto each other. Optimally, the non-rigidness of the transformation allows a full correspondence to be determined, and at the same time limit excessive deformations by including some sort of regularization e ect. Most non-rigid registration methods are directly or indirectly based on elastic (eg. [1, 12] or viscousuid models (eg. [9, 8]). Although many methods do not use the terminology of these continuum models, they follow the same ideas algorithmicly. The use of elastic and viscous uid models for registration of images has often been criticized, because they represent the application of a physical model, which does not re ect the actual physical development between the images. A correct physical model, for registration of images of the brain of two individuals, would re ect the actual biologic and genetic development of these brains. Since a common genetic basis exists for these brains, it should, conceptually, be possible to create a development model for the two brains down through history to a common ancestor. Using this development model a correspondence could be created. Image 2 Non-rigid registration using arbitrary physical model registration Rigid Unknown physical model Elastic or fluid model Known physical model Simulation Non-rigid registration using valid physical model