Symbol Recognition A nave approach Objective good enough

Symbol Recognition: A naïve approach • Objective: good enough for Math • Why not use commercial OCR programs? – Not modular – Proprietary – Tuned for wrong domain (business letters)

Requirements • Flexible and extensible wrt fonts (arbitrary characters) • Interactive/Learning – Monotonic • • Accurate Reasonably fast Scale independent Arbitrary character positions

Assumptions • All connected components are single characters (clearly false sometimes) – no joined characters – no split characters (patch up i j = etc) • Characters of modest complexity and low noise (clearly false sometimes) – x y z not x yz

Intuitions • A human can discern a character expressed as a grid (5 x 5) of gray scale blocks • (some examples) • If we wish to identify / distinguish letters, numbers and other symbols, 25 numbers (gray scale: 0 -255) plus height/width ratio plus height in pixels (28 numbers) may be sufficient.

We ignore • • • Concavity, angles, enclosures length of border, complexity of the border moments about the center, centroid, etc skeleton relation to baseline or other characters – , vs ’ , - vs _ , etc. – context (within numbers/letters/italics)

We could additional features and more grid sections 4 2 4 1 2 2 4 Different weighting schemes at edges: ignore, blur. overla

Clustering • Euclidean distance in 27 -d space – weighted? – Categorical (e. g. by h/w, then …) • Computing clusters, centers • Breaking/ merging clusters?

Neural network learning • Time consuming for many instances of glyphs • Choice of properties are critical • NN successful overall – touted in OCR as a winner – experimental results are curious sometimes