KEYWORDS: Wavelets, Image filtering, Image denoising, Denoising, Linear filtering, Optical filters, Principal component analysis, Wavelet transforms, Optical engineering, Signal to noise ratio
In this paper, we propose an image denoising method based on nonseparable wavelet filter banks and two-dimensional principal component analysis (2D-PCA). Conventional wavelet domain processing techniques are based on modifying the coefficients of separable wavelet transform of an image. In general, separable wavelet filters have limited capability of capturing the directional information. In contrast, nonseparable wavelet filters contain the basis elements oriented at a variety of directions and different filter banks capture the different directional features of an image. Furthermore, we identify the patterns from the noisy image by using the 2D-PCA. In comparison to the prevalent denoising algorithms, our proposed algorithm features no complex preprocessing. Furthermore, we can adjust the wavelet coefficients by a threshold according to the denoising results. We apply our proposed technique to some benchmark images with white noise. Experimental results show that our new technique achieves both good visual quality and a high peak signal-to-noise ratio for the denoised images.
It is often difficult to obtain sufficient signature samples to train up a signature verification system. With insufficient training samples, the estimation of the statistical parameters such as the mean feature vector and covariance matrix becomes unreliable and system performance would be degraded. In this paper, a two-dimensional elastic matching method to generate additional samples is proposed to expand the limited training set so that a better estimate of the statistical variations can be obtained. The method differs from existing ones in that it is more suitable for the generation of signature samples. Besides this, a set of peripheral features, which is useful in describing both the internal and external structures of signatures, is employed to represent the signatures in the verification process. Results showed that verification system with the additional samples could reduce the error rate from 15.6% to 11.4%. It also outperformed another existing method which estimates the class covariance matrix through optimization techniques. Results also demonstrated that the peripheral features are useful for signature verification.
As the interest in fractal geometry rises, the applications are getting more and more numerous in many domains. This paper deals with the problem of recognizing and classification to optical character recognition. For this purpose, we present a new method of feature extraction based on the principles of fractal geometry and wavelet. This allows us to establish a classification of Chinese character in order to apply to each of the isolated categories the most adapt recognition methods. In particular, the proposed method reduces the dimensionality of a two-dimensional pattern by way of a central projection approach, and thereafter, performs Daubechies' wavelet transformation on the derived one-dimensional pattern to generate a set of wavelet transformation sub-patterns, namely, curves that are non-self-intersecting. Further from the resulting non-self-intersecting curves, the divider dimensions are computed with modified box-counting approach. These divider dimensions constitute a new feature vector for the original two-dimensional pattern, defined over the curve's fractal dimensions. We have conducted several experiments in which a set of printed alphanumeric symbols and Chinese characters of varying fonts and orientation were classified, based on the formulation of our new feature vector. The results obtained from these experiments have consistently shown the character recognition method with the proposed feature vector can yield an excellent classification rate 100%.
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