DIFFUSION TENSOR ANALYSIS WITH INVARIANT GRADIENTS AND ROTATION TANGENTS

这个子项目是许多利用 由NIH/NCRR资助的中心赠款提供的资源。子项目和 研究者（PI）可能从另一个NIH来源获得了主要资金， 因此可在其他CRISP条目中表示。所列机构为 研究中心，而研究中心不一定是研究者所在的机构。 扩散张量磁共振成像（DTI）的发展促进了医学成像和数学图像处理交叉点的研究。DTI是唯一能够探测组织的方向性微观结构，经验证据支持临床上重要的组织特性和张量模型参数之间的多种联系。我们提出，有效的DTI处理算法可以设计周围的组织属性和张量参数之间的连接，通过挥舞张量参数来组织和量化的算法的数学元素，我们描述了一个框架，使用张量形状和方向参数来开发新的措施张量场梯度和协方差。张量形状和方向各有三个自由度，分别由不变梯度和旋转切线跨越。

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. 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.