Modeling the structure of multivariate manifolds: Shape maps

We propose a shape population metric that reflects the interdependencies between points observed in a set of examples. It provides a notion of topology for shape and appearance models that represents the behavior of individual observations in a metric space, in which distances between points correspond to their joint modeling properties. A Markov chain is learnt using the description lengths of models that describe sub sets of the entire data. The according diffusion map or shape map provides for the metric that reflects the behavior of the training population. With this metric functional clustering, deformation- or motion segmentation, sparse sampling and the treatment of outliers can be dealt with in a unified and transparent manner. We report experimental results on synthetic and real world data and compare the framework with existing specialized approaches. 1

Keypoint Transfer for Fast Whole-Body Segmentation

We introduce an approach for image segmentation based on sparse correspondences between keypoints in testing and training images. Keypoints represent automatically identified distinctive image locations, where each keypoint correspondence suggests a transformation between images. We use these correspondences to transfer label maps of entire organs from the training images to the test image. The keypoint transfer algorithm includes three steps: (i) keypoint matching, (ii) voting-based keypoint labeling, and (iii) keypoint-based probabilistic transfer of organ segmentations. We report segmentation results for abdominal organs in whole-body CT and MRI, as well as in contrast-enhanced CT and MRI. Our method offers a speed-up of about three orders of magnitude in comparison to common multi-atlas segmentation, while achieving an accuracy that compares favorably. Moreover, keypoint transfer does not require the registration to an atlas or a training phase. Finally, the method allows for the segmentation of scans with highly variable field-of-view.Comment: Accepted for publication at IEEE Transactions on Medical Imagin

Classification of Tensors and Fiber Tracts Using Mercer-Kernels Encoding Soft Probabilistic Spatial and Diffusion Information

In this paper, we present a kernel-based approach to the clustering of diffusion tensors and fiber tracts. We propose to use a Mercer kernel over the tensor space where both spatial and diffusion information are taken into account. This kernel highlights implicitly the connectivity along fiber tracts. Tensor segmentation is performed using kernel-PCA compounded with a landmark-Isomap embedding and k-means clustering. Based on a soft fiber representation, we extend the tensor kernel to deal with fiber tracts using the multi-instance kernel that reflects not only interactions between points along fiber tracts, but also the interactions between diffusion tensors. This unsupervised method is further extended by way of an atlas-based registration of diffusion-free images, followed by a classification of fibers based on nonlinear kernel Support Vector Machines (SVMs). Promising experimental results of tensor and fiber classification of the human skeletal muscle over a significant set of healthy and diseased subjects demonstrate the potential of our approach

Situating the default-mode network along a principal gradient of macroscale cortical organization

Understanding how the structure of cognition arises from the topographical organization of the cortex is a primary goal in neuroscience. Previous work has described local functional gradients extending from perceptual and motor regions to cortical areas representing more abstract functions, but an overarching framework for the association between structure and function is still lacking. Here, we show that the principal gradient revealed by the decomposition of connectivity data in humans and the macaque monkey is anchored by, at one end, regions serving primary sensory/motor functions and at the other end, transmodal regions that, in humans, are known as the default-mode network (DMN). These DMN regions exhibit the greatest geodesic distance along the cortical surface-and are precisely equidistant-from primary sensory/motor morphological landmarks. The principal gradient also provides an organizing spatial framework for multiple large-scale networks and characterizes a spectrum from unimodal to heteromodal activity in a functional metaanalysis. Together, these observations provide a characterization of the topographical organization of cortex and indicate that the role of the DMN in cognition might arise from its position at one extreme of a hierarchy, allowing it to process transmodal information that is unrelated to immediate sensory input

Functional geometry alignment and localization of brain areas

Matching functional brain regions across individuals is a challenging task, largely due to the variability in their location and extent. It is particularly difficult, but highly relevant, for patients with pathologies such as brain tumors, which can cause substantial reorganization of functional systems. In such cases spatial registration based on anatomical data is only of limited value if the goal is to establish correspondences of functional areas among different individuals, or to localize potentially displaced active regions. Rather than rely on spatial alignment, we propose to perform registration in an alternative space whose geometry is governed by the functional interaction patterns in the brain. We first embed each brain into a functional map that reflects connectivity patterns during a fMRI experiment. The resulting functional maps are then registered, and the obtained correspondences are propagated back to the two brains. In application to a language fMRI experiment, our preliminary results suggest that the proposed method yields improved functional correspondences across subjects. This advantage is pronounced for subjects with tumors that affect the language areas and thus cause spatial reorganization of the functional regions.National Institutes of Health (U.S.) (P01 CA067165)National Institutes of Health (U.S.) (U41RR019703)National Institutes of Health (U.S.) (NIBIB NAMIC U54- EB005149)National Institutes of Health (U.S.) (NCRR NAC P41-RR13218)National Science Foundation (U.S.) (CAREER Grant 0642971)National Science Foundation (U.S.) (Grant IIS/CRCNS 0904625