Implicit Is Not Enough: Explicitly Enforcing Anatomical Priors inside Landmark Localization Models

The task of localizing distinct anatomical structures in medical image data is an essential prerequisite for several medical applications, such as treatment planning in orthodontics, bone-age estimation, or initialization of segmentation methods in automated image analysis tools. Currently, Anatomical Landmark Localization (ALL) is mainly solved by deep-learning methods, which cannot guarantee robust ALL predictions; there may always be outlier predictions that are far from their ground truth locations due to out-of-distribution inputs. However, these localization outliers are detrimental to the performance of subsequent medical applications that rely on ALL results. The current ALL literature relies heavily on implicit anatomical constraints built into the loss function and network architecture to reduce the risk of anatomically infeasible predictions. However, we argue that in medical imaging, where images are generally acquired in a controlled environment, we should use stronger explicit anatomical constraints to reduce the number of outliers as much as possible. Therefore, we propose the end-to-end trainable Global Anatomical Feasibility Filter and Analysis (GAFFA) method, which uses prior anatomical knowledge estimated from data to explicitly enforce anatomical constraints. GAFFA refines the initial localization results of a U-Net by approximately solving a Markov Random Field (MRF) with a single iteration of the sum-product algorithm in a differentiable manner. Our experiments demonstrate that GAFFA outperforms all other landmark refinement methods investigated in our framework. Moreover, we show that GAFFA is more robust to large outliers than state-of-the-art methods on the studied X-ray hand dataset. We further motivate this claim by visualizing the anatomical constraints used in GAFFA as spatial energy heatmaps, which allowed us to find an annotation error in the hand dataset not previously discussed in the literature.