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Email: fwilliam,dyyeung,[email protected] Abstract ... Template matching has long been used for printed character recognition. ... characters which have a great variety of handwriting styles, either a tremendous number of templates.

Recognition of Handwritten Digits Using Deformable Models Kwok-Wai Cheung, Dit-Yan Yeung and Roland T. Chin Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Email: fwilliam,dyyeung,[email protected]

Abstract Deformable models are used to recognize handwritten characters which have a great variety of handwriting styles. The overall character shape is modeled by a B-spline and individual pixels are modeled by Gaussian functions. Model parameters associated with the spline and the Gaussian functions, together with their relative strength, are estimated using Bayesian inference. Under such a Bayesian framework, classi cation becomes a process of model selection. This approach has been tested using data in a NIST database and the substitution rate (error rate) is about 4%.

1 Introduction Template matching has long been used for printed character recognition. To recognize handwritten characters which have a great variety of handwriting styles, either a tremendous number of templates is required to represent all the possible deformations or we need models that can deform. The latter alternative is more parsimonious and hence more manageable. Using deformable models, highly accurate recognition has been demonstrated using a small subset of a NIST database (about 1,000 digits) [1]. In this paper, we further test our approach using a much larger test set (about 10,000 digits). We demonstrate that such an approach, together with a rejection rule based on class posterior probabilities, can reduce the substitution rate to 4.05% with 9.88% rejection rate. The deformable model approach is especially attractive as it makes integrated segmentation and recognition possible. However, the application of deformable models to recognition is still limited, due mainly to the high computational complexity and scale-up ability. Some possible solutions have been proposed in [2]. Modeling of handwritten digits, which is adopted from [3], is described in Section 2. The algorithms for extraction and classi cation are summarized in Section 3. Some results and discussions can be found in Section 4 and Section 5 concludes the paper.

2 Modeling Deformable models are formulated by a model deformation energy function and a data-mis t energy function. Using the Gibbs distributions, they can equivalently be represented by probability distributions. Under a Bayesian framework, the model deformation energy is regarded as the prior distribution for the model parameters and the data-mis t energy is regarded as the likelihood function. Optimal feature extraction then becomes parameter estimation, which, in our case, is done by iteratively deforming the digit model to t the input imagery data, while classi cation becomes a model selection problem [4].

2.1 Deformation Model (Prior Distribution)

Handwritten characters are modeled as splines, which are parameterized by a small set of k control points. The degree of deformation, referred to as deformation energy, Ew (w), is measured by the Mahalanobis distance of the control point vector, w 2

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