Uncertainty Propagation in Model-Based Recognition

Robust recognition systems require a careful understanding of the effects of error in sensed features. In model-based recognition, matches between model features and sensed image features typically are used to compute a model pose and then project the unmatched model features into the image. The error in the image features results in uncertainty in the projected model features. We first show how error propagates when poses are based on three pairs of 3D model and 2D image points. In particular, we show how to simply and efficiently compute the distributed region in the image where an unmatched model point might appear, for both Gaussian and bounded error in the detection of image points, and for both scaled-orthographic and perspective projection models. Next, we provide geometric and experimental analyses to indicate when this linear approximation will succeed and when it will fail. Then, based on the linear approximation, we show how we can utilize Linear Programming to compute bounded propagated error regions for any number of initial matches. Finally, we use these results to extend, from two-dimensional to three-dimensional objects, robust implementations of alignment, interpretation-tree search, and transformation clustering.