This subproject is one of many research subprojects utilizing theresources provided by a Center grant funded by NIH/NCRR. The subproject andinvestigator (PI) may have received primary funding from another NIH source,and thus could be represented in other CRISP entries. The institution listed isfor the Center, which is not necessarily the institution for the investigator.The development of diffusion tensor magnetic resonance imaging (DTI) has catalyzed research at the intersection of medical imaging and mathematical image processing. DTI is uniquely able to probe the directional microstructure of tissue, and empirical evidence supports multiple connections between clinically important tissue properties and parameters of the tensor model. We propose that effective DTI processing algorithms can be designed around the connections between tissue properties and tensor parameters, by wielding the tensor parameters to organize and quantify the mathematical elements of the algorithm.We describe a framework that uses tensor shape and orientation parameters to develop novel measures of tensor field gradients and covariance. Tensor shape and orientation each have three degrees of freedom, which are spanned by invariant gradients and rotation tangents, respectively.
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