A Differentiable Optimization Framework for Registering Sequential Bounding Boxes with Point Cloud Stream

Refining a sequence of coarse 3D bounding boxes against a LiDAR point-cloud stream demands tracks that are geometrically accurate (high IoU) and temporally coherent (low roughness), preferably without training data. The usual recipe keeps the two concerns apart: register each frame independently, then smooth the trajectory afterwards with a Kalman~RTS or Savitzky--Golay filter. Smoothing displaces boxes from a geometric optimum and never re-optimises, so it trades accuracy for smoothness. We instead fold the temporal smoothness constraint into a training-free registration objective and solve for all poses jointly with L-BFGS. The payoff depends on how well the object is seen. On well-observed tracks it is large: within the low-roughness budget, the joint objective beats both post-hoc smoothers on paired multi-seed statistics and cuts roughness several-fold relative to frame-wise registration at matched accuracy. Treating visibility as an experimental variable exposes the limit. The advantage decays monotonically as views become one-sided, until it is indistinguishable from zero for near-edge-on objects and slightly negative under a ray-cast simulator with range-dependent density and ego motion, where the decoupled pipeline is in fact ahead at tight roughness budgets. We locate that boundary and trace it to one term: orientation alignment ties yaw to the estimated velocity and fails once that estimate is noisy. A ground-truth-free rule can choose the temporal scale and keep every track inside the roughness budget.