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Magnetic resonance imaging (MRI) is the dominant modality for neuroimaging in clinical and research domains. The tremendous versatility of MRI as a modality can lead to large variability in terms of image contrast, resolution, noise, and artifacts. Variability can also manifest itself as missing or corrupt imaging data. Image synthesis has been recently proposed to homogenize and/or enhance the quality of existing imaging data in order to make them more suitable as consistent inputs for processing. We frame the image synthesis problem as an inference problem on a 3-D continuous-valued conditional random field (CRF). We model the conditional distribution as a Gaussian by defining quadratic association and interaction potentials encoded in leaves of a regression tree. The parameters of these quadratic potentials are learned by maximizing the pseudo-likelihood of the training data. Final synthesis is done by inference on this model. We applied this method to synthesize T2-weighted images from T1-weighted images, showing improved synthesis quality as compared to current image synthesis approaches. We also synthesized Fluid Attenuated Inversion Recovery (FLAIR) images, showing similar segmentations to those obtained from real FLAIRs. Additionally, we generated super-resolution FLAIRs showing improved segmentation.

Segmentation of brain images often requires a statistical atlas for providing prior information about the spatial position of different structures. A major limitation of atlas-based segmentation algorithms is their deficiency in analyzing brains that have a large deviation from the population used in the construction of the atlas. We present an expectation-maximization framework based on a Dirichlet distribution to adapt a statistical atlas to the underlying subject. Our model combines anatomical priors with the subject's own anatomy, resulting in a subject specific atlas which we call an "adaptive atlas". The generation of this adaptive atlas does not require the subject to have an anatomy similar to that of the atlas population, nor does it rely on the availability of an ensemble of similar images. The proposed method shows a significant improvement over current segmentation approaches when applied to subjects with severe ventriculomegaly, where the anatomy deviates significantly from the atlas population. Furthermore, high levels of accuracy are maintained when the method is applied to subjects with healthy anatomy.

A common goal in deformable registration applications is to produce a spatial transformation that is diffeomorphic, thereby preserving the topology of structures being transformed. Because this constraint is typically enforced only on the continuum, however, topological changes can still occur within discretely sampled images. This work discusses the notion of homeomorphisms in digital images, and how it differs from the diffeomorphic/homeomorphic concepts in continuous spaces commonly used in medical imaging. We review the differences and problems brought by considering functions defined on a discrete grid, and propose a practical criterion for enforcing digital homeomorphisms in the context of atlas-based segmentation.

This paper presents a novel approach for object segmentation in medical images that respects the topological relationships of multiple structures as given by a template. The algorithm combines advantages of tissue classification, digital topology, and level-set evolution into a topology-invariant multiple-object fast marching method. The technique can handle any given topology and enforces object-level relationships with little constraint over the geometry. Applied to brain segmentation, it sucessfully extracts gray matter and white matter structures with the correct spherical topology without topology correction or editing of the subcortical structures.