Model-based Recognition

Building robust recognition systems requires a careful understanding of the eeects 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 rst show how error propagates when poses are based on three pairs of model and image points. In particular, we show how to simply and eeciently compute the 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. This result applies to objects that are fully three-dimensional, where past results considered only two-dimensional objects. The result is based on an approximation that accurately linearizes the relationship between matched image points and unmatched, projected model points. Secondly, based on the linear approximation, we show how we can utilize linear programming to compute the propagated error region 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.