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Despite the recent efforts in accurate 3D annotations in hand and objectdatasets, there still exist gaps in 3D hand and object reconstructions.Existing works leverage contact maps to refine inaccurate hand-object poseestimations and generate grasps given object models. However, they requireexplicit 3D supervision which is seldom available and therefore, are limited toconstrained settings, e.g., where thermal cameras observe residual heat left onmanipulated objects. In this paper, we propose a novel semi-supervisedframework that allows us to learn contact from monocular images. Specifically,we leverage visual and geometric consistency constraints in large-scaledatasets for generating pseudo-labels in semi-supervised learning and proposean efficient graph-based network to infer contact. Our semi-supervised learningframework achieves a favourable improvement over the existing supervisedlearning methods trained on data with `limited' annotations. Notably, ourproposed model is able to achieve superior results with less than half thenetwork parameters and memory access cost when compared with the commonly-usedPointNet-based approach. We show benefits from using a contact map that ruleshand-object interactions to produce more accurate reconstructions. We furtherdemonstrate that training with pseudo-labels can extend contact map estimationsto out-of-domain objects and generalise better across multiple datasets.

S$^2$Contact: Graph-based Network for 3D Hand-Object Contact Estimation with Semi-Supervised Learning