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On-Line Handwriting Recognition. Transducer device (digitizer) Input: sequence of point coordinates with pen-down/up signals from the digitizer Stroke: sequence of points from pen-down to pen-up signals Word: sequence of one or more strokes. System Overview. Pre-processing

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slide1

On-Line Handwriting Recognition

  • Transducer device (digitizer)
  • Input: sequence of point coordinates with pen-down/up signals from the digitizer
  • Stroke: sequence of points from pen-down to pen-up signals
  • Word: sequence of one or more strokes.

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide2

System Overview

Pre-processing

(high curvature points)

Input

Dictionary

Segmentation

Character Recognizer

Recognition Engine

Context Models

Word Candidates

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide3

Segmentation Hypotheses

  • High-curvature points and segmentation points:

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide4

Character Recognition I

  • Fisher Discriminant Analysis (FDA): improves over PCA (Principal Component Analysis).

p=WTx

Linear

projec-

tion

Original space

Projection space

  • Training set: 1040 lowercase letters, Test set: 520 lowercase letters
  • Test results: 91.5% correct

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide5

Fisher Discriminant Analysis

  • Between-class scatter matrix
    • C: number of classes
    • Ni: number of data vectors in class i
    • i: mean vector of class i and: mean vector
  • Within-class scatter matrix
    • vji: j-th data vector of class i.

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide6

Given a projection matrix W (of size n by m) and its linear transformation , the between-class scatter in the projection space is

Similarly

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide7

Fisher Discriminant Analysis (cont.)

  • Optimization formulation of the fisher projection solution: (YB, YW are scatter matrices in projection space)

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide8

FDA (continued)

  • Construction of the Fisher projection matrix:
    • Compute the n eigenvalues and eigenvectors of the generalized eigenvalue problem:
    • Retain the m eigenvectors having the largest eigenvalues. They form the columns of the target projection matrix.

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide9

Character Recognition Results

  • Training set: 1040 lowercase letters
  • Test set: 520 lowercase letters
  • Test results:

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide10

Challenge I

  • The problem of the previous approach is: non-characters are classified as characters. When applied to cursive words it creates several/too many non-sense word hypothesis by extracting characters where they don’t seem to exist.
  • More generally, one wants to be able to generate shapes and their deformations.

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide11

Challenge II

  • How to extract reliable local geometric features of images (corners, contour tangents, contour curvature, …) ?
  • How to group them ?
  • Large size data base to match one input, how to do it fast ?
  • Hierarchical clustering of the database, possibly over a tree structure or some general graph. How to do it ? Which criteria to cluster ? Which methods to use it ?

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide12

Recognition Engine

  • Integrates all available information, generates and grows the word-level hypotheses.
  • Most general form: graph and its search.
  • Hypothesis Propagation Network

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide13

H (t, m)

Class m's legal predecessors

List length

T

t

Look-back window range

3

2

1

Time

"a"

"b”

m

"y"

"z"

Hypothesis Propagation Network

Recognition of 85% on 100 words (not good)

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide14

Challenge III

  • How to search more efficiently in this network and more generally on Bayesian networks ?

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide15

“go”

Relative height ratio and positioning

“90”

Character heights

Visual Bigram Models (VBM)

  • Some characters can be very ambiguous when isolated: “9” and “g”; “e” and “l”; “o” and “0”; etc, but more obvious when put in a context.

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide16

VBM: Parameters

  • Height Diff. Ratio:
  • HDR = (h1- h2) / h
  • Top Diff. Ratio:
  • TDR = (top1- top2) / h
  • Bottom Diff. Ratio:
  • BDR = (bot1- bot2) / h

top1

top2

h1

h

h2

bot1

bot2

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide17

VBM: Ascendancy Categories

  • Total 9 visual bigram categories (instead of 26x26=676).

Work with student Jong Oh Davi Geiger, Courant Institute, NYU

slide18

VBM: Test Results

Work with student Jong Oh Davi Geiger, Courant Institute, NYU