3D Weighted Geometric Graph Neural Networks for Sheep Facial Pain Assessment

Deep learning systems perform mainly within the 2D for a single image domain and take the face as a single-dimension representation, losing sight of the 3D anatomy of sheep and cross-landmark spatial relationships that are intrinsic to the clinically proven Sheep Pain Facial Expression Scale (SPFES). This paper presents the \textbf{3D Sheep Pain Facial Expression System (3D-SPFES)}, a novel, monocular depth-aware geometric graph neural network system that integrates each SPFES facial landmark, such as the ears, eyes, and nose, into 3D Euclidean space estimated from a single RGB camera by using VideoDepthAnything, thus preventing the need for specialized depth hardware. Each landmark node includes a feature vector containing its 3D spatial coordinates, estimated surface normal, and facial attribute class embedding. Edges linked to nodes are assigned weights based on an aggregate metric that combines both Euclidean distance and surface co-planarity in a 3D space. A Weighted Geometric Graph Neural Network (WG-GNN) studies this graph using $\mathcal{K} = 3$ geometry-aware message-passing layers enhanced by a scaled dot-product attention method that selectively enhances anatomically relevant inter-landmark messages. The resultant node embeddings are combined into $\mathcal{O} = 3$ pain-level clusters and integrated into a Normalized Pain Score (NPS) within the range of $[0, 100%]$ a confidence-weighted, SPFES-derived scoring method.