Approximate point set match is the task to align a search pattern represented by a set of 2D or 3D points in a, usually large, search space consisting of 2D or 3D points as well. The challenge is not to find only perfect matches, but allowing certain types of flexibility of the search pattern when embedded in the search space. The match itself might be only approximative, in other words, some deviation between the pattern and its counterpart in the search space is allowed. The measurement of the deviation can be based on the root mean square (RMSD) distance, but other distance functions (like average distance or maximum distance) might be of interest as well.
One example application is the search for known substructures of protein molecules in a database of proteins. However, approximate point set match has many other possible applications.