Graph convolutional network with probabilistic spatial regression: application to craniofacial landmark detection from 3D photogrammetry.

Quantitative evaluation of pediatric craniofacial anomalies relies on the accurate identification of anatomical landmarks and structures. While segmentation and landmark detection methods in standard clinical images are available in the literature, image-based methods are not directly applicable to 3D photogrammetry because of its unstructured nature consisting in variable numbers of vertices and polygons. In this work, we propose a graph-based convolutional neural network based on Chebyshev polynomials that exploits vertex coordinates, polygonal connectivity, and surface normal vectors to extract multi-resolution spatial features from the 3D photographs. We then aggregate them using a novel weighting scheme that accounts for local spatial resolution variability in the data. We also propose a new trainable regression scheme based on the probabilistic distances between each original vertex and the anatomical landmarks to calculate coordinates from the aggregated spatial features. This approach allows calculating accurate landmark coordinates without assuming correspondences with specific vertices in the original mesh. Our method achieved state-of-the-art landmark detection errors.