3D Tortuosity computation as a shape descriptor and its application to brain structure analysis

In this study, we propose a novel method for quantifying tortuosity in 3D voxelized objects. As a shape characteristic, tortuosity has been widely recognized as a valuable feature in image analysis, particularly in the field of medical imaging. Our proposed method extends the two-dimensional approach of the Slope Chain Code (SCC) which creates a one-dimensional representation of curves. The utility of 3D tortuosity ( \(\tau _{3D}\) ${\tau }_{3D}$ ) as a shape descriptor was investigated by characterizing brain structures. The results of the \(\tau _{3D}\) ${\tau }_{3D}$ computation on the central sulcus and the main lobes revealed significant differences between Alzheimer’s disease (AD) patients and control subjects, suggesting its potential as a biomarker for AD. We found a \(p<0.05\) $p<0.05$ for the left central sulcus and the four brain lobes.