P. Raveendran

A comparative analysis of algorithms for fast computation of Zernike moments

Abstract This paper details a comparative analysis on time taken by the present and proposed methods to compute the Zernike moments, Z pq . The present method comprises of Direct, Belkasims, Pratas, Kintners and Coefficient methods. We propose a new technique, denoted as q -recursive method, specifically for fast computation of Zernike moments. It uses radial polynomials of fixed order p with a varying index q to compute Zernike moments. Fast computation is achieved because it uses polynomials of higher index q to derive the polynomials of lower index q and it does not use any factorial terms. Individual order of moments can be calculated independently without employing lower- or higher-order moments. This is especially useful in cases where only selected orders of Zernike moments are needed as pattern features. The performance of the present and proposed methods are experimentally analyzed by calculating Zernike moments of orders 0 to p and specific order p using binary and grayscale images. In both the cases, the q -recursive method takes the shortest time to compute Zernike moments.

Translation Invariants of Zernike Moments

Moment functions defined using a polar coordinate representation of the image space, such as radial moments and Zernike moments, are used in several recognition tasks requiring rotation invariance. However, this coordinate representation does not easily yield translation invariant functions, which are also widely sought after in pattern recognition applications. This paper presents a mathematical framework for the derivation of translation invariants of radial moments defined in polar form. Using a direct application of this framework, translation invariant functions of Zernike moments are derived algebraically from the corresponding central moments. Both derived functions are developed for non-symmetrical as well as symmetrical images. They mitigate the zero-value obtained for odd-order moments of the symmetrical images. Vision applications generally resort to image normalization to achieve translation invariance. The proposed method eliminates this requirement by providing a translation invariance property in a Zernike feature set. The performance of the derived invariant sets is experimentally confirmed using a set of binary Latin and English characters.

Translation and scale invariants of Legendre moments

Abstract By convention, the translation and scale invariant functions of Legendre moments are achieved by using a combination of the corresponding invariants of geometric moments. They can also be accomplished by normalizing the translated and/or scaled images using complex or geometric moments. However, the derivation of these functions is not based on Legendre polynomials. This is mainly due to the fact that it is difficult to extract a common displacement or scale factor from Legendre polynomials. In this paper, we introduce a new set of translation and scale invariants of Legendre moments based on Legendre polynomials. The descriptors remain unchanged for translated, elongated, contracted and reflected non-symmetrical as well as symmetrical images. The problems associated with the vanishing of odd-order Legendre moments of symmetrical images are resolved. The performance of the proposed descriptors is experimentally confirmed using a set of binary English, Chinese and Latin characters. In addition to this, a comparison of computational speed between the proposed descriptors and the aforesaid geometric moments-based method is also presented.

An Efficient Algorithm for Fast Computation of Pseudo-Zernike Moments

Pseudo-Zernike moments have better feature representation capability, and are more robust to image noise than those of the conventional Zernike moments. However, due to the computation complexity of pseudo-Zernike polynomials, pseudo-Zernike moments are yet to be extensively used as feature descriptors as compared to Zernike moments. In this paper, we propose two new algorithms, namely coefficient method and p-recursive method, to accelerate the computation of pseudo-Zernike moments. Coefficient method calculates polynomial coefficients recursively. It eliminates the need of using factorial functions. Individual order or index of pseudo-Zernike moments can be derived independently, which is useful if selected orders or indices of moments are needed as pattern features. p-recursive method uses a combination of lower order polynomials to derive higher order polynomials with the same index q. Fast computation is achieved because it eliminates the requirements of calculating polynomial coefficients, Bpqk, and power of radius, rk, in each polynomial. The performance of the proposed algorithms on moment computation and image reconstruction, as compared to those of the present methods, are experimentally verified using a set of binary and grayscale images.

The scale invariants of pseudo-Zernike moments

The definition of pseudo-Zernike moments has a form of projection of the image intensity function onto the pseudo-Zernike polynomials, and they are defined using a polar coordinate representation of the image space. Hence, they are commonly used in recognition tasks requiring rotation invariance. However, this coordinate representation does not easily yield a scale invariant function because it is difficult to extract a common scale factor from the radial polynomials. As a result, vision applications generally resort to image normalisation method or using a combination of scale invariants of geometric orradial moments to achieve the corresponding invariants of pseudo-Zernike moments. In this paper, we present a mathematical framework to derive a new set of scale invariants of pseudo-Zernike moments based on pseudo-Zernike polynomials. They are algebraically obtained by eliminating the scale factor contained in the scaled pseudo-Zernike moments. They remain unchanged under equal-shape expansion, contraction and reflection of theoriginal image. They can be directly computed from any scaled image without prior knowledge of the normalisation parameters, or assistance of geometric or radial moments. Their performance is experimentally verified using a set of Chinese and Latin characters. In addition, a comparison of computational speed between the proposed descriptors and the present methods is also presented.

VEP optimal channel selection using genetic algorithm for neural network classification of alcoholics

In this letter, neural networks (NNs) classify alcoholics and nonalcoholics using features extracted from visual evoked potential (VEP). A genetic algorithm (GA) is used to select the minimum number of channels that maximize classification performance. GA population fitness is evaluated using fuzzy ARTMAP (FA) NN, instead of the widely used multilayer perceptron (MLP). MLP, despite its effective classification, requires long training time (on the order of 10(3) times compared to FA). This causes it to be unsuitable to be used with GA, especially for on-line training. It is shown empirically that the optimal channel configuration selected by the proposed method is unbiased, i.e., it is optimal not only for FA but also for MLP classification. Therefore, it is proposed that for future experiments, these optimal channels could be considered for applications that involve classification of alcoholics.

A survey of image quality measures

Image quality assessment is one of the challenging field of digital image processing system. It can be done subjectively or objectively. PSNR is the most popular and widely used objective image quality metric but it is not correlate well with the subjective assessment. Thus, there are a lot of objective image quality metrics (IQM) developed in the past few decades to replace PSNR. This paper provides a literature review of the current subjective and objective image quality measures. The purpose of this paper is to collect reported quality metrics and group them according to their strategies and techniques.

New Invariant Moments for Non-Uniformly Scaled Images

Abstract:The usual regular moment functions are only invariant to image translation, rotation and uniform scaling. These moment invariants are not invariant when an image is scaled non-uniformly in the x- and y-axes directions. This paper addresses this problem by presenting a new technique to obtain moments that are invariant to non-uniform scaling. However, this technique produces a set of features that are only invariant to translation and uniform/non-uniform scaling. To obtain invariance to rotation, moments are calculated with respect to the x-y-axis of the image. To perform this, a neural network is used to estimate the angle of rotation from the x-y-axis and the image is unrotated to the x-y-axis. Consequently, we are able to obtain features that are invariant to translation, rotation and uniform/non-uniform scaling. The mathematical background behind the development and invariance of the new moments are presented. The results of experimental studies using English alphabets and Arabic numerals scaled uniformly/non-uniformly, rotated and translated are discussed to further verify the validity of the new moments.

EEG Peak Alpha Frequency as an Indicator for Physical Fatigue

The peak alpha frequency (PAF) has been associated with mental abilities. In this study, we use the EEG to investigate the relationship between PAF and physical fatigue. Eight right handed male subjects (age from 23 to 29) volunteered for the experiment. They have to perform a hand grip task for 30 seconds with each hand for 30 times or until they could not continue anymore. Electrodes are placed at 55 locations all over the scalp to detect EEG. Three electrodes are placed around the eyes region to detect EOG. The EEG signals of six subjects clearly indicated a reduction in the PAF around the motor cortex region after the physical exertion. Thus, this study shows that the reduction of PAF can be an indicator of physical fatigue.

Krawtchouk moments as a new set of discrete orthogonal moments for image reconstruction

Krawtchouk polynomials can be used to form the basis of a set of discrete orthogonal moments. In this paper, Krawtchouk moments are used to analytically reconstruct binary images. Their performance is compared to that of Zernike, Legendre (continuous) and Chebyshev (discrete) moments.