Evaluation Algorithm of Root Canal Shape Based on Steklov Spectrum Analysis

In recent years, we have seen more and more interest in the field of medical images and shape comparison motivated by the latest advances in microcomputed tomography (μCT) acquisition, modelling, and visualization technologies. Usually, biologists need to evaluate the effect of different root canal preparation systems. Current root canal preparation evaluation methods are based on the volume difference, area difference, and transportation of two root canals before and after treatment. The purpose of root canal preparation is to minimize the volume difference and ensure the complete removal of the smear layer. Previous methods can reflect some general geometric differences, but they are not enough to evaluate the quality of root canal shape. To solve this problem, we proposed a novel root canal evaluation method based on spectrum and eigenfunctions of Steklov operators, which can be served as a better alternative to current methods in root canal preparation evaluation. Firstly, the ideal root canal model was simulated according to the root canal model before and after preparation. Secondly, the Steklov spectrum of the two models was calculated. Thirdly, based on the spectrum and the histogram of the Gaussian curvature on the surface, the weight of each eigenvalue was computed. Therefore, the Steklov spectrum distance (SSD), which measures shape difference between the root canals, was defined. Finally, the calculation method that quantifies the root canal preparation effect of root canals was obtained. Through experiments, our method manifested high robustness and accuracy compared with existing state-of-the-art approaches. It also demonstrates the significance of our algorithm's advantages on a variety of challenging root canals through result comparison with counterpart methods.