The main focus of the CCB is on the brain, and specifically on neuroimaging. This area has a long tradition of employing sophisticated mathematical and computational techniques. Nevertheless, new developments in related areas of mathematics and computational science such as Computer Graphics, Computer Vision, and Image Processing, as well as from Computational Mathematics and the Computational Sciences, have emerged in recent years . We are confident that many of these ideas can be applied beneficially to neuroimaging.
CCB investigators publish extensively and continuously the Center’s mathematical models, computational tools and neuroscientific findings. To explore or search the CCB publications click here. You can also find all CCB publications on PubMed and GoogleScholar.
CCB Research Areas
The mathematical research is focused on addressing fundamental problems in the computational modeling of biological structures. The solutions and techniques that we are proposing build on our recent advances in image analysis, differential equations, numerical analysis, and differential geometry, as well as our many years’ work in mathematics and neuroscience. More
We have organized the modeling research to look at two areas of modeling techniques. The first area investigates surface modeling and conformal mapping, and the second area is focused on the invesitgation of image segmentation using level sets and geometrical PDEs. More
We are developing methods for interacting with data and algorithms. Included in these methods is the development of interactive visual environments for data processing. More
Our research in data analysis emphasizes the importance of combining the mathematics we have developed with biomedical research applications, and delivering these tools and techniques to the research community. More
The CCB neurobiological research is divided into a number of different individual research studies. These studies include the following: More
- Identifying Age Related Atrophy Using Levelset Registration of Embedded Maps
- Developmental origin of phenotypic variation in Drosophila melanogaster
- Mapping Brain Changes in HIV/AIDS
- Vervet Genetics and Brain Morphology
Shape Modeling and Analysis
A complete description of a biological object (e.g., organ) is complemented by both shape features and shape attributes. A shape feature is any characterization of shape based on both local and global geometry as well as the object’s topology. On the other hand, a shape attribute is any local or global information important to visualize the nature of the object and to model the study or processing step required by the study. Examples of shape attributes we study include textures, colors, displacement vectors and other characteristics related to the biological object bound by the shape (e.g., functional data from fMRI, PET, MRI/DTI, cross-sectional and longitudinal data, lobular or sulcal/gyral labels).