Application of 3D Geometric Tensors for Segmenting Cylindrical Tree Structures from Volumetric Datasets

摘要

Many diagnostic problems involve the assessment of vascular structures or bronchial trees depicted in volumetric datasets, but previous algorithms for segmenting cylindrical structures are not sufficiently robust for them to be widely applied clinically. Local geometric information that is of importance in segmentation consists of voxel values and their first and second derivatives. First derivatives can be generalized to the gradient and more generally the structure tensor, while the second derivatives can be represented by Hessian matrices. It is desirable to exploit both kinds of information, at the same time, in any voxel classification process, but few segmentation algorithms have attempted to do this. This project compares segmentation based on the structure tensor to that based on the Hessian matrix, and attempts to determine whether some combination of the two can demonstrate better performance than either individually. To compare performance in a situation where a gold standard exists, the methods were tested on simulated tree structures. We generated 3D tree structures with varying amounts of added noise, and processed them with algorithms based on the structure tensor, the Hessian matrix, and a combination of the two. We applied an orientation-sensitive filter to smooth the tensor fields. The results suggest that the structure tensor by itself is more effective in detecting cylindrical structures than the Hessian tensor, and the combined tensor is better than either of the other tensors.