Uncertainty estimates for polyhedral object recognition

The author present a detailed analysis of uncertainty propagation in model-based object recognition, for both two-dimensional and three-dimensional objects that have linear boundaries. It is shown by direct geometric construction that previous uncertainty bounds on the location of polygonal or polyhedral objects can be tightened considerably. The improvement of the bounds is a result of considering the cross-coupling between rotational and translational uncertainties in the interpretation of the sensor data. The author states several general principles regarding geometric uncertainty in model-based recognition, readily deduced by examining the uncertainty equations presented: rotational uncertainty is independent of the scale of the models; translational uncertainty is highly dependent on the relative angles of the model components that are sensed; translational uncertainty is intimately related to rotational uncertainty, although the relationship is nontrivial; pose uncertainty varies roughly linearly with sensor error; and the poorer a valid match set is within the error bounds, the less uncertainty there is in deducting the pose parameters