This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. This technical subproject deals with the problem of processing and analyzing scientific and medical data. The state of the art for data processing varies, depending on the type of data and goals of the application. For instance, the field of signal processing, which we use here to refer to the analysis of one-dimensional functions or waveforms, is somewhat mature. Important research topics remain in signal processing, but there are a variety of well-known, effective, general algorithms for filtering and classifying signals. Specific applications abound, from speech recognition to cardiac monitoring. Images are multidimensional signals, that is, functions defined on two-dimensional, three-dimensional, or higher- dimensional domains. The field of image processing is younger and proven to be challenging. The important aspects of images are encoded not only in their grey-scale (or spectral) values, but also in the shapes that they describe. For instance, when considering MRI data, the cortex is defined not simply by its intensities but also by its shape and its spatial relationships to other anatomy. Researchers are developing effective technologies for image analysis, but the techniques are far from mature and are not yet widely adopted within the community of biomedical scientists. Geometry refers to collections of points that are organized in space to form manifolds. Unlike signals and images, geometric objects (or manifolds) are not necessarily functions. The space in which these manifolds live could be two-dimensional, three-dimensional, or n-dimensional (where n > 3). Furthermore these points can be organized in different ways to form curves, surfaces, hypersurfaces, or more complex objects that consist of combinations of these other objects. Geometry processing for digital surfaces is relatively young field, and a great many theoretical and practical questions remain. For instance, the problem of representing digital surfaces is itself quite complex, and researchers are still investigating a variety of possibilities including point sets, meshes, polynomial patches, and implicit surfaces. Geometry processing, includes both the analysis of geometric objects and the generation of geometric models from scientific data. This project addresses the processing of images and geometry for biomedical applications. We will consider signal processing as a somewhat mature technology, and we will include it in our applications by integrating with other toolkits and relying on the work of our collaborators. Our research and development aims in image and geometry processing will reflect the relative maturity of each of these technologies, their current availability to biomedical researchers, the expertise of the Scientific Computing and Imaging Institute and our collaborators, and the specific needs of driving applications. The fields of image and geometry processing are vast, and the data processing needs of various biological researchers are extensive. The Center's resource associated with this technical domain are relatively smallif we compare them to either the field as a whole or even to other ongoing projects and centers that focus more exclusively on image analysis (for instance). With this in mind, we have adopted, for this core, a strategy of leveraging ongoing research in image and geometry processing, at Utah and elsewhere, and extending this work to address the specific roadblocks that prevent our collaborators from taking full advantage of state-of-the-art technologies. In light of this, we have focused the aims to address primarily issues of usability and scalability. Addressing these issues will entail some fundamental research, but it will also entail a tight integration with other technical cores in this proposal and significant collaborations with other teams working in biological areas. The specific aims of this project are divided into two groups: research goals and development goals. The research goals are those for which we expect there will be some fundamental work or extensive engineering at the algorithm level. It also implies some development of methods that have not been tested for the associated applicationsimplying some risk or some potential reworking of algorithms. The development goals refer to the development of new implementations of known algorithms and the integration of algorithms into new systems. However, it also includes the development of faster implementations on specialized computing architectures and includes, in some cases, the investigation of parallel algorithms for which there is a high likelihood of success. Research Goals for Image Processing: (1) Robust Filtering Methods: The development of new, more general methods for image filtering that can be more easily applied across a wide range of applications with less tuning of free parameters. (2) Segmentation of Incomplete and Noisy Image Datasets: Methods for automatic and semiautomatic segmentation of image datasets. (3) User-Interactive Segmentation: The refinement of segmentation algorithms to interact effectively with two-dimensional and three-dimensional visualization capabilities. Research Goals for Geometry Processing: (1) Statistical Shape Characterization: Formulations for the statistical characterization of shape deformations with applicability to large, articulated anatomical models. (2)Stochastic Model Generation: The data-driven generation of mesoscale models for simulation of aggregate effects of microscopic (e.g., cellular) structures. Development Goals for Image Processing: (1) Parallel Implementations: Parallel (distributed and shared memory) implementations of iterative algorithms for filtering and registration. (2) Atlas-Based Head Segmentation: Integrate atlas-based head segmentation into model generation and EEG source localization pipeline. (3) Active Shape Models (ASMs): Extend the ITK implementation of adaptive shape models to include: support for three-dimensional models, integration with semi-automated segmentation methods (e.g., watersheds and level-set models), and hierarchical articulated models. Development Goals for Geometry Processing: (1) Mesh Generation: Two-dimensional and three-dimensional mesh generation, including tetrahedral and hexahedral meshes that incorporate application-specific geometric constraints. (2) Manual Mesh Editing: User-guided manipulation of mesh geometries and topologies. (3) Point-Based Registration: Integration of point/curve/surface-based registration algorithms into the inverse-problems workflow.