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.

In this paper, we describe an algorithm called Fast Marching Watersheds that segments a triangle mesh into visual parts. This computer vision algorithm leverages a human vision theory known as the minima rule. Our implementation computes the principal curvatures and principal directions at each vertex of a mesh, and then our hillclimbing watershed algorithm identifies regions bounded by contours of negative curvature minima. These regions fit the definition of visual parts according to the minima rule. We present evaluation analysis and experimental results for the proposed algorithm. 1.

In this paper, we propose a generic automatic approach for the parcellation of the cortical surface into labeled gyri. These gyri are defined from a set of pairs of sulci selected by the user. The selected sulci are first automatically identified in the data, then projected onto the cortical surface. The parcellation stems from two nested Vorono diagrams computed geodesically to the cortical surface. The first diagram provides the zones of influence of the sulci. The boundary between the two zones of influence of each selected pair of sulci stands for a gyrus seed. A second diagram yields the gyrus parcellation. The distance underlying the Vorono diagram allows the method to interpolate the gyrus boundaries where the limiting sulci are interrupted. The method is illustrated with twelve different hemispheres.

In this paper, we propose a new representation of the cortical surface that may be used to study the cortex folding process and to recover some putative stable anatomical landmarks called sulcal roots usually burried in the depth of adult brains. This representation is a primal sketch derived from a scale space computed for the mean curvature of the cortical surface. This scale-space stems from a diffusion equation geodesic to the cortical surface. The primal sketch is made up of objects defined from mean curvature minima and saddle points. The resulting sketch aims first at highlighting significant elementary cortical folds, second at representing the fold merging process during brain growth. The relevance of the framework is illustrated by the study of central sulcus sulcal roots from antenatal to adult age. Some results are proposed for ten different brains. Some preliminary results are also provided for superior temporal sulcus.

Abstract—In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified

The current threats to U.S. security both military and civilian have led to an increased interest in the development of technologies to safeguard national facilities such as military bases, federal buildings, nuclear power plants, and national laboratories. As a result, the Imaging, Robotics, and Intelligent Systems (IRIS) Laboratory at The University of Tennessee (UT) has established a research consortium, known as SAFER (Security Automation and Future Electromotive Robotics), to develop, test, and deploy sensing and imaging systems for unmanned ground vehicles (UGV). The targeted missions for these UGV systems include—but are not limited to—under vehicle threat assessment, stand-off check-point inspections, scout surveillance, intruder detection, obstaclebreach situations, and render-safe scenarios. This paper presents a general overview of the SAFER project. Beyond this general overview, we further focus on a specific problem where we collect 3D range scans of under vehicle carriages. These scans require appropriate segmentation and representation algorithms to facilitate the vehicle inspection process. We discuss the theory for these algorithms and present results from applying them to actual vehicle scans.

Segmentation and representation of the human cerebral cortex from magnetic resonance (MR) images play an important role in neuroscience and medicine. A successful segmentation method must be robust to various imaging artifacts and produce anatomically meaningful and consistent cortical representations. A method for the automatic reconstruction of the inner, central, and outer surfaces of the cerebral cortex from T1-weighted MR brain images is presented. The method combines a fuzzy tissue classification method, an efficient topology correction algorithm, and a topology-preserving geometric deformable surface model (TGDM). The algorithm is fast and numerically stable, and yields accurate brain surface reconstructions that are guaranteed to be topologically correct and free from selfintersections. Validation results on real MR data are presented to demonstrate the performance of the method.

We present a matching criterion for curves and integrate it into the large deformation diffeomorphic metric mapping (LDDMM) scheme for computing an optimal transformation between two curves embedded in Euclidean space R d. Curves are first represented as vector-valued measures, which incorporate both location and the first order geometric structure of the curves. Then, a Hilbert space structure is imposed on the measures to build the norm for quantifying the closeness between two curves. We describe a discretized version of this, in which discrete sequences of points along the curve are represented by vector-valued functionals. This gives a convenient and practical way to define a matching functional for curves. We derive and implement the curve matching in the large deformation framework and demonstrate mapping results of curves in R 2 and R 3. Behaviors of the curve mapping are discussed using 2D curves. The applications to shape classification is shown and

Most of the approaches dedicated to automatic morphometry rely on a point-by-point strategy based on warping each brain towards a reference coordinate system. In this paper, we describe an alternative object-based strategy dedicated to the cortex. This strategy relies on an artificial neuroanatomist performing automatic recognition of the main cortical sulci and parcellation of the cortical surface into gyral patches. A set of shape descriptors, which can be compared across subjects, is then attached to the sulcus and gyrus related objects segmented by this process. The framework is used to perform a study of 142 brains of the International Consortium for Brain Mapping (ICBM) database. This study reveals some correlates of handedness on the size of the sulci located in motor areas, which was not detected previously using standard voxel based morphometry.

Sulcal fundi are 3D curves that lie in the depths of the cerebral cortex and are often used as landmarks for downstream computations in brain imaging. We present a sequence of geometric algorithms which automatically extract the sulcal fundi from magnetic resonance images and represent them as smooth polylines lying on the cortical surface. First we compute a geometric depth measure for each point on the cortical surface, and based on this information we extract sulcal regions by checking the connectivity above a depth threshold. We then extract the endpoints of each fundus and delineate the fundus by thinning each connected region keeping the endpoints fixed. The curves thus defined are smoothed using weighted splines on the gray-matter surface to yield highquality representations of the sulcal fundi 1.