# Adaptive Elastic Models for Hand-Printed
Character Recognition

Geoffrey Hinton, Christopher Williams

and Michael Revow

Department of Computer Science

University of Toronto

**Abstract**

Hand-printed digits can be modeled as splines that are governed by
about 8 control points. For each known digit, the control points have preferred
'home' locations, and deformations of the digit are generated by moving the control points
away from their home locations. Images of digits can be produced by placing Gaussian
ink generators uniformly along the spline. Real images can be recognized by finding
the digit model most likely to have generated the data. For each digit model we use
an elastic matching algorithm to minimize an energy function that includes both the
deformation energy of the digit model and the log probability that the model would
generate the inked pixels in the image. The model with the lowest total energy wins.
If a uniform noise process is included in the model of image generation, some of
the inked pixels can be rejected as noise as a digit model is fitting a poorly segmented
image. The digit models learn by modifying the home locations of the control points.

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*Advances in Neural Information Processing Systems 4. MIT Press,
Cambridge MA. *

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