Prediction of the Facial Growth Direction: Regression Perspective

Abstract

First attempts to predict the direction of facial growth (FG) direction were made half a century ago. Despite numerous attempts and elapsed time, a satisfactory method has not been established yet, and the problem still poses a challenge for medical experts. In our recent papers, we presented the results of applying various machine learning algorithms to the prediction of the FG direction formulated as a classification task, along with a preliminary discussion on its inherent complexity. In this paper, we summarize the previous findings and then delve into explaining the reasons for the FG estimation difficulty. To this end, we approach the task from a regression perspective. We employ Gaussian process regression (GPR) to investigate the predictive power of cephalogram-derived features in the estimation of the FG direction and to obtain a principled estimation of the regression uncertainty. Conducted data analysis reveals the inherent complexity of the problem and explains the reasons for the difficulty in solving the FG task based on 2D X-ray images. Specifically, to improve the regression performance, one needs to fit non-smooth regression functions, as smooth regression generally performs worse in this task. Even then, the estimated uncertainty remains large across all data points. These findings suggest a negative impact of noise in the available cephalogram-based features. We also uncover a clustering structure in the dataset that, to some extent, correlates with the source of annotations. The repeated landmarking process confirmed that the location of some landmarks is ambiguous and revealed that the consequent inaccuracies are significant in comparison to actual changes in growth periods. Overall, this translates to the weak explanatory power of the available cephalogram-based features in FG direction estimation.