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We present a family of methods for 2D–3D registration spanning both deterministic and non-deterministic branch-and-bound approaches. Critically, the methods exhibit invariance to the underlying scene primitives, enabling e.g. points and lines to be treated on an equivalent basis, potentially enabling a broader range of problems to be tackled while maximising available scene information, all scene primitives being simultaneously considered. Being a branch-and-bound based approach, the method furthermore enjoys intrinsic guarantees of global optimality; while branch-and-bound approaches have been employed in a number of computer vision contexts, the proposed method represents the first time that this strategy has been applied to the 2D–3D correspondence-free registration problem from points and lines. Within the proposed procedure, deterministic and probabilistic procedures serve to speed up the …