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In this paper, we propose nonlinear shape normalization methods for gray-scale handwritten characters in order to minimize the loss of information caused by binarization and compensate for the shape distortions of characters. Two-dimensional linear interpolation technique has been extended to nonlinear space and the extended interpolation technique has been adopted in the proposed methods to enhance the quality of normalized images.In order to verify the efficiency of the proposed methods, the recognition rate, the processing time and the computational complexity of the proposed algorithms have been considered. The experimental results indicate that the proposed methods are efficient not only to compensate for the shape distortions of handwritten characters but also to maintain the information of gray-scale input characters.