Characterisation of the Discriminative Properties of the Radial Tchebichef Moments for Hand-written Digits

Feature extraction using simple formulations such as moments have found different applications in the field of image processing and computer vision. In the last few years, new moments based on orthogonal functions have been proposed. More specifically, the Radial Tchebichef Moments yield features that are numerically stable, and allow for a relatively accurate reconstruction of the image, even when using a limited number of moments. Although the reconstruction of images using Tchebichef moments, as well as their computational complexity and robustness against noise have been well studied, their discriminative characteristics have not been fully explored. This paper explores this gap, comparing the performance of classifiers trained with Tchebichef moments against other features, namely Haar-like features and raw pixels (the pixels themselves being used as features). To isolate the discriminative characteristics, we used two datasets of hand-written digits, the MNIST and the ICDAR 2013, and trained classifiers with AdaBoost.MH. Classifiers using Tchebichef moments as features achieved a significantly lower accuracy rate after 100000 rounds of boosting. However, with a more practical number of boosting iterations of 1000, the results showed that in some cases the Tchebichef moments can outperform raw pixels. Classifiers trained with Haar-like features always outperformed classifiers with Tchebichef moments.