A method and apparatus are provided for rapidly refining a given approximate location of a pattern to produce a more accurate location. The invention employs a multi-dimensional space that includes translation, orientation, and scale. The invention can serve as a replacement for the fine resolution phase of any coarse-fine system for pattern location. Patterns and images are represented by a feature-based description that can be translated, rotated, and scaled to arbitrary precision much faster than digital image re-sampling, and without pixel grid quantization errors. Thus, accuracy is not limited by the ability of a grid to represent small changes in position, orientation, or size (or other degrees of freedom). The invention determines an accurate object pose from an approximate starting pose in a small, fixed number of increments that is independent of the number of dimensions of the space, and independent of the distance between the starting and final poses, provided that the starting pose is within the “capture range” of the true pose. Thus, accuracy need not be sacrificed to keep execution time acceptable for practical applications. Specifying locations in four or more dimensions will often result in better matches between the pattern and image than two-dimensional location systems, thereby improving accuracy. Accuracy is not degraded if some portion of the object is missing or occluded, or if unexpected extra features are present.