Identifying Features via Homotopy on Handwritten Mathematical Symbols

In handwritten mathematics, it is common to have characters in various sizes and for writing not to follow simple baselines. For example, subscripts and superscripts appear relatively smaller than normal text and are written slightly below or above it. Rather than use the location, features and size to identify the character, it may be more effective to do the reverse --- to use knowledge about specific characters to determine baseline, size, etc. In this approach, it is necessary to find the location of certain expected features that are determined by particular points. In earlier work, we have presented a method to derive the determining points for a new instance of a symbol from those on an average model for each symbol type. For those characters that are significantly different from the average instance, one can use a numerical homotopy between the average instance and the target character, and apply the determining point algorithm at each step. The present article studies the factors to be taken into account in performing such homotopies. We examine two strategies for possible starting points for the homotopy, and we examine the relation between the distance and the number of steps required. The first starting point strategy performs a homotopy from the average of samples of the same type. The second strategy uses a homotopy from the nearest neighbour with known determining points. Our experimental results show a useful relation between the homotopy distance and the number of steps usually required and improved strategies to find determining points for poorly written characters.