Recovering Drawing Trajectory

Graph theory has many applications in solving real-life problems. However, the application of Eulerian graphs and Eulerian tours/trails seems to be comparatively limited. In this chapter, an application of graph theory in handwriting recognition is presented. There are a lot of studies regarding handwriting recognition. Most of these methods deal with either offline or online handwriting recognition. However, the discussed approaches in this chapter are distinct in the manner that they aim to extract the trajectory of writing so as to equip the offline handwritten image with temporal information. When the trajectory of writing is known, it can be possible to utilize online recognition methods which are more reliable. These trajectory extracting methods are based on Eulerian trails in semi-Eulerian graphs. Semi-Eulerian graphs are graphs with at most two odd vertices. Eulerian trail is a trail in which every edge is traversed exactly once. The methods can be helpful in recognition of single-stroke handwritten images. Relying on the minimum energy law, the methods try to find the smoothest trajectory of writing which contribute to the recognition process.