A probabilistic framework is presented that enables image registration, tissue classification, and bias correction to be combined within the same generative model. A derivation of a log-likelihood objective function for the unified model is provided. The model is based on a mixture of Gaussians and is extended to incorporate a smooth intensity variation and nonlinear registration with tissue probability maps. A strategy for optimising the model parameters is described, along with the requisite partial derivatives of the objective function.

The notion of using context information for solving high-level vision and medical image segmentation problems has been increasingly realized in the field. However, how to learn an effective and efficient context model, together with an image appearance model, remains mostly unknown. The current literature using Markov Random Fields (MRFs) and Conditional Random Fields (CRFs) often involves specific algorithm design, in which the modeling and computing stages are studied in isolation. In this paper, we propose the auto-context algorithm. Given a set of training images and their corresponding label maps, we first learn a classifier on local image patches. The discriminative probability (or classification confidence) maps created by the learned classifier are then used as context information, in addition to the original image patches, to train a new classifier. The algorithm then iterates until convergence. Auto-context integrates low-level and context information by fusing a large number of low-level appearance features with context and implicit shape information. The resulting discriminative algorithm is general and easy to implement. Under nearly the same parameter settings in training, we apply the algorithm to three challenging vision applications: foreground/background segregation, human body configuration estimation, and scene region labeling. Moreover, context also plays a very important role in medical/brain images where the anatomical structures are mostly constrained to relatively fixed positions. With only some slight changes resulting from using 3D instead of 2D features, the auto-context algorithm applied to brain MRI image segmentation is shown to outperform state-of-the-art algorithms specifically designed for this domain. Furthermore, the scope of the proposed algorithm goes beyond image analysis and it has the potential to be used for a wide variety of problems in multi-variate labeling.

A statistical model is presented that combines the registration of an atlas with the segmentation of magnetic resonance images. We use an Expectation Maximization-based algorithm to find a solution within the model, which simultaneously estimates image artifacts, anatomical labelmaps, and a structure-dependent hierarchical mapping from the atlas to the image space. The algorithm produces segmentations for brain tissues as well as their substructures. We demonstrate the approach on a set of 22 magnetic resonance images. On this set of images, the new approach performs significantly better than similar methods which sequentially apply registration and segmentation.

Computational anatomy (CA) is the mathematical study of anatomy I a I = I a BG, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g a G of anatomical exemplars Iaa I. The observable images are the output of medical imaging devices. There are three components that CA examines: (i) constructions of the anatomical submanifolds, (ii) comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g a G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P(d) on the images I for inference and disease testing within anatomical models. This paper reviews recent advances in these three areas applied to shape, growth, and atrophy.

Abstract. Modeling and understanding the variability of brain structures is a fundamental problem in the neurosciences. Improved mathematical representations of structural brain variation are needed to help detect and understand genetic or disease related sources of abnormality, as well as to improve statistical power when integrating functional brain mapping data across subjects. In this paper, we develop a new mathematical model of normal brain variation based on a large set of cortical sulcal landmarks (72 per brain) delineated in each of 98 healthy human subjects scanned with 3D MRI (age: 51.8 +/- 6.2 years). We propose an original method to compute an average representation of the sulcal curves, which constitutes the mean anatomy. After a ne alignment of the individual data across subjects, the second order moment distribution of the sulcal position is modeled as a sparse eld of covariance tensors (symmetric, positive de nite matrices). To extrapolate this information to the full brain, one has to overcome the limitations of the standard Euclidean matrix calculus. We propose an a ne-invariant Riemannian framework to perform computations with tensors. In particular, we generalize radial basis function (RBF) interpolation and harmonic di usion partial di erential equations (PDEs) to tensor elds. As a result, we obtain a dense 3D variability map which agrees well with prior results on smaller subject samples. Moreover, "leave

High quality segmentation of brain MR images is a challenging task. To deal with this problem many automatic segmentation methods rely on atlas information of anatomical structures. We further investigate this line of research by introducing hierarchical representations of anatomical structures in an Expectation-Maximization framework. This new approach enables us to divide a complex segmentation scenario into less difficult sub-problems reducing the scenario’s statistical complexity. We demonstrate the method’s strength by segmenting a set of brain MR images into 31 different anatomical structures as well as comparing it to other methods.

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Abstract. The paper introduces an algorithm which allows the automatic segmentation of multi channel magnetic resonance images. We extended the Expectation Maximization-Mean Field Approximation Segmenter, to include Local Prior Probability Maps. Thereby our algorithm estimates the bias field in the image while simultaneously assigning voxels to different tissue classes under prior probability maps. The probability maps were aligned to the subject using nonrigid registration. This allowed the parcellation of cortical sub-structures including the superior temporal gyrus. To our knowledge this is the first description of an algorithm capable of automatic cortical parcellation incorporating strong noise reduction and image intensity correction. 1

Abstract — In this paper, a hybrid discriminative/generative model for brain anatomical structure segmentation is proposed. The learning aspect of the approach is emphasized. In the discriminative appearance models, various cues such as intensity and curvatures are combined to locally capture the complex appearances of different anatomical structures. A probabilistic boosting tree (PBT) framework is adopted to learn multi-class discriminative models that combine hundreds of features across different scales. On the generative model side, both global and local shape models are used to capture the shape information about each anatomical structure. The parameters to combine the discriminative appearance and generative shape models are also automatically learned. Thus low-level and high-level information is learned and integrated in a hybrid model. Segmentations are obtained by minimizing an energy function associated with the proposed hybrid model. Finally, a grid-face structure is designed to explicitly represent the 3D region topology. This representation handles an arbitrary number of regions and facilitates fast surface evolution. Our system was trained and tested on a set of 3D MRI volumes and the results obtained are encouraging. Index Terms — Brain anatomical structures, segmentation, probabilistic boosting tree, discriminative models, generative models I.

Due to the finite spatial resolution of imaging devices, a single voxel in a medical image may be composed of mixture of tissue types, an effect known as partial volume effect (PVE). Partial volume estimation, that is, the estimation of the amount of each tissue type within each voxel, has received considerable interest in recent years. Much of this work has been focused on the mixel model, a statistical model of PVE. We propose a novel trimmed minimum covariance determinant (TMCD) method for the estimation of the parameters of the mixel PVE model. In this method, each voxel is first labeled according to the most dominant tissue type. Voxels that are prone to PVE are removed from this labeled set, following which robust location estimators with high breakdown points are used to estimate the mean and the covariance of each tissue class. Comparisons between different methods for parameter estimation based on classified images as well as expectation–maximization-like (EM-like) procedure for simultaneous parameter and