# Using mixtures of deformable models to capture variations in
hand printed digits

Michael Revow, Christopher K. I. Williams

and Geoffrey E. Hinton

Department of Computer Science

University of Toronto

**Abstract**

Deformable models are an attractive way for characterizing
handwritten digits since they have relatively few parameters, are able to capture many
topological variations, and incorporate much prior knowledge. We have described a system
that uses learned digit models consisting of splines whose shape is governed by a small
number of control points. Images can be classified by separately fitting each digit model
to the image, and using a simple neural network to decide which model fits best. 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 use of multiple models for each digit can
characterize the population of handwritten digits better. We show how multiple models may
be used without increasing the time required for elastic matching.

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