Developing A Learning-Based Deformable Registration Framework For Volumetric Brain Images

The essential of image registration is to establish the accurate correspondence between two images, i.e., solve the deformation of each point. Because of its importance to the following clinical applications, deformable registration of MR brain images is widely investigated in the area of medical image processing. Therefore, various methods have been proposed in decades.First, the type of image features is not always effective in distinguishing different parts of images, which is not reliable to establish the correspondences between the template and subject image. In another hand, the size of neighborhood used to extract the features is fixed and ad hoc in previous methods, regardless of the spatial variation in local image regions. Second, equally treating each point during the registration procedure might eventually undermine the registration performance. Actually, some brain regions are more reliable to be distinguished, compared to other regions. Third, simple constraints on the smoothness of voxel-wise deformation fields might not be effective, which neglecting the local image information and the population information inherited in the deformation fields.In order to overcome the limitation of the previous registration methods, a learning-based registration framework for MR brain images is proposed in this paper. There are several novelties in our registration framework, which will be detailed next. 1. Learning best neighborhood size on each point. First, two criteria are created for learning best neighborhood size, i.e., the image feature on each point extracted with best neighbor size should be maximumly different against its nearby points and similar with its corresponding subject points across individual brains, which are called saliency criterion and consistency criterion respectively. Then the entropy is used to formulate these two criteria and Markov random field is used to make the best neighborhood size spatially smooth. Finally, the energy function is developed and solved by the gradient-based optimization method. As the result, each point has its best neighbor size to establish the reliable correspondence.2. Learning best feature on each point. First, the feature pool is constructed from several typical local image descriptors, which are calculated with different neighborhood size. Then the entire brain is partitioned into a number of similar regions and adaboost algorithm is employed to select the best features for each image region. In order to improve the performance of our leaning method, the step of adaptively partition the image and the step of learning best feature on regions should be completed simultaneously. It is because the partition of brain depends on the best features selected for each region and learning best feature depends on the available reasonable partitioned regions. In particular, we iteratively perform these two stages until the algorithm converges. The selected best features are evaluated by several experiment and verified that our learning method is reasonable.3. Learning active point. The importance of different points in registration is different even the points have the same best features. In order to avoid being trapped in local minima, the overall measurement is created to hierarchically select the most important points, called active point, and let these points steer the deformation. This measurement requires the best feature on particular point salient in its nearby points and consistent with its corresponding individual subject points. The active point selected by our method usually located at the corner of ventricle, the crown of gyrus and the roots of sulci, which can identify themselves reliably.4. Learning deformation statistics. First, the multi-level B-Splines is utilized to represent the whole deformation field from coarse to fine level. Because of the limited number of training samples and huge dimension of the statistical model, the control points are adaptively placed in the image level by level according the approximating degree and the overall measurement of point importance. Second, Principle Component Analysis (PCA) is applied on the parameters of control point in each level to capture the statistics of deformation in each level.5. Presenting the learning-based intelligent deformable registration framework. The proposed leaning-based registration framework can be divided into two stages, i.e. learning stage and registration stage. At the learning stage, the best feature is learned by adaboost, the active point is hierarchically selected by the overall measurement, and the deformation statistic is captured by multi-level B-Splines and PCA. At the registration stage, the active points are first selected to find their corresponding points in subject image by the learnt best features. The rest of points just follow the deformation of those active points. At the end of each iteration, the statistical model on deformation field is used to reasonable regularize the deformation field.In conclusion, a leaning-based registration framework is proposed in this paper, which focused on learning best feature, active point and deformation statistics. This framework has several applications, including improve the performance of HAMMER algorithm and extent HAMMER method from pre-segmented image to intensity image domain, which greatly overcome it limitation. In the first application, after the fixed scale used in HAMMER algorithm to extract GMI feature is replaced with the learnt best scale and active point is learnt according to the saliency and consistency measurement, more accurate registration results have been obtained in both real data and simulated data. In the second application, the best features are learnt from different local image descriptors computed with different neighborhood size in the intensity image domain. Moreover, provided 100 deformation field, the statistical model on control point parameters in each level is developed and used to regularize the deformation field in registration. Finally, not only the accuracy but also the consistency of the registration results has been greatly improved by our registration method. It is worth noting that the averaged deformation error has been decreased from 0.95mm by HAMMER to 0.66mm by our method, which has obtained nearly 30% error reduction.