Prototype Pruning by Feature Extraction for Handwritten Mathematical Symbol Recognition

Author: Stephen M Watt, Xiaofang Xie

Summary:
Recognizer for large symbol sets - pruning prototypes to restrict search into small group of the sample. Preclassifying of the stroke based on certain features in done in this approach.
Preprocessing - chopping head and tail of the strokes(removing hooks), resampling , (average/gaussian) smoothing and size normalization.

Geometric features- number of loops, intersection and cusps.
* Loops - found using Minimum distance pair. Thresholds are fixed for time separation, distance between the pair, area of the loop.
* Intersections-modified Bently ottman sweepline algorithm - no detail
* Cusps - sharp turning point. Cusps are detected in this paper by finding 3 points which makes small angle. This algorithm also checks if the previous 2 points of the cusp lie on a straight line and also for next 2 points.

Ink Related Features: Number of Strokes, Point Density( dividing bounding box into 3 regions upper, middle and lower).

Directional features - Initial direction,End Direction and Initial End Direction.

Global Features - Initial and end position, Weight to Height Ratio

Discussion:
The author's thesis suggested some interesting stroke preprocessing - removing hooks(head/tail) from the start and end of the strokes based on sharp edges and Gaussian smoothing.
The calculation of point density is interesting. The bounding box is divided into 3 regions upper(40%),middle(20%) and bottom(40%).
I like the concept of finding out cusp and loops.In her thesis, she has discussed scenarios to where cusps can become loops while drawing and vice versa.
I am not able to understand how the author calculates the number of loops.