A high-precision and fast algorithm for computation of Jacobi-Fourier moments (JFMs) is presented. A fast recursive method is developed for the radial polynomials that occur in the kernel function of the JFMs. The proposed method is numerically stable and very fast in comparison with the conventional direct method. Moreover, the algorithm is suitable for computation of the JFMs of the highest orders. The JFMs are generic expressions to generate orthogonal moments changing the parameters α and β of Jacobi polynomials. The quality of the description of the proposed method with α and β parameters known is studied. Also, a search is performed of the best parameters, α and β, which significantly improves the quality of the reconstructed image and recognition. Experiments are performed on standard test images with various sets of JFMs to prove the superiority of the proposed method in comparison with the direct method. Furthermore, the proposed method is compared with other existing methods in terms of speed and accuracy.

Abstract. A detailed analysis of the quaternion generic Jacobi-Fourier moments (QGJFMs) for color image description is presented. In order to reach numerical stability, a recursive approach is used during the computation of the generic Jacobi radial polynomials. Moreover, a search criterion is performed to establish the best values for the parameters α and β of the radial Jacobi polynomial families. Additionally, a polar pixel approach is taken into account to increase the numerical accuracy in the calculation of the QGJFMs. To prove the mathematical theory, some color images from optical microscopy and human retina are used. Experiments and results about color image reconstruction are presented.

We present a novel method for gait phase detection based on Krawtchouk moments, which can be used in gait analysis. The low computational cost and high capacity of description of the Krauchouk moments makes it easy detect the parameters of the gait cycle, such as the swing phase, stance phase and double support. In addition, we present the results of the gait phases detection with the proposed method of 10 test subjects and compared with standard values.

We present a new approach for angle estimation in binary images from Hahn moments, which provide an approximate estimate with short computational times. The method proposed retrieving the angle formed from a reference point to another, through a multiple linear regression and a set of Hahn moments obtained in a training database. Finally, we discuss the performance analysis of our approach under noise conditions and scale change.

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