This paper proposed the $N recognizer, as the name indicates, this is an extension of 1$ recognizer, but with many improvements, such as recognizing gestures comprising
multiple strokes, automatically generalizing from one multistroke template to all possible multistrokes with alternative stroke orderings and directions, recognizing 1D gestures such as lines, and providing bounded rotation invariance.
As an extension, $N recognizer is built on top of 1$ recognizer, the major difference is it has some more preprocessings to change a multi-stroke in to a unistroke, then compare with the template, for this part, 1$ and N$ are almost the same (well, the rotation part is a little different).
Dealing with Multistroke: The user needs to define all the permutation of a multi-stroke, that is the user needs to define one multistroke, and ensure that different stroke orders and/or directions will be properly recognized. At runtime, the multistroke will first be converted to a unistroke, and then follow 1$'s algorithm.
Dealing with Rotation: Here is a little bit similar to Protractor -- if the full rotation failed to capture some information, then perform a bounded rotation (within a range), as the author indicated, 45 degree is a good range.
Dealing with 1D gesture: A MINSIDE-to-MAXSIDE threshold is set to decide if the stroke is too "thin", if it is too "thin", then it's 1D, otherwise, it's 2D.
Discussion:
The main contribution of this paper is the part of how to deal with multi-stroke, the method of doing it here is pretty simple (take two direction for each stroke, and connect all the end points), however, I am wondering if it is really accurate. And, the speed is also questionable, defining each component stroke as a dichotomous [0,1] variable, which indicates a exponential complexity, 2^N for N strokes. But the author indicated the speed is fast and also said " most multistroke gestures have only a few strokes because more elaborate gestures are harder for users to remember and use". Well, this is also another quotation from some other paper. But if it comes with very few strokes, I won't be too surprised to see a high accuracy.
Tell me if I am wrong.......