Color Image Analysis by Quaternion-Type Moments

International audienceIn this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. appears to be an optimal choice

Filter-generating system of Zernike polynomials

This work proposes a new approach to find the generating function (GF) of the Zernike polynomials in two dimensional form. Combining the methods of GFs and discrete-time systems, we can develop two dimensional digital systems for systematic generation of entire orders of Zernike polynomials. We establish two different formulas for the GF of the radial Zernike polynomials based on both the degree and the azimuthal order of the radial polynomials. In this paper, we use four terms recurrence relation instead of the ordinary three terms recursion to calculate the radial Zernike polynomials and their GFs using unilateral 2D Z-transform. A spatio-temporal implementation scheme is developed for generation of the radial Zernike polynomials. The case study shows a reliable way to evaluate Zernike polynomials with arbitrary degrees and azimuthal orders

Fast generic polar harmonic transforms

International audienceGeneric polar harmonic transforms have recently been proposed to extract rotation-invariant features from images and their usefulness has been demonstrated in a number of pattern recognition problems. However, direct computation of these transforms from their definition is inefficient and is usually slower than some efficient computation strategies that have been proposed for other methods. This paper presents a number of novel computation strategies to compute these transforms rapidly. The proposed methods are based on the inherent recurrence relations among complex exponential and trigonometric functions used in the definition of the radial and angular kernels of these transforms. The employment of these relations leads to recursive and addition chain-based strategies for fast computation of harmonic function-based kernels. Experimental results show that the proposed method is about 10× faster than direct computation and 5× faster than fast computation of Zernike moments using the q-recursive strategy. Thus, among all existing rotation-invariant feature extraction methods, polar harmonic transforms are the fastest

An Efficient Approach to Compute Zernike Moments with GPU-Accelerated Algorithm

The utilization of Zernike moments has been extensive in various fields, including image processing and pattern recognition, owing to their desirable characteristics. However, the application of Zernike moments is hindered by two significant obstacles: computational efficiency and accuracy. These issues become particularly noticeable when computing high-order moments. This study presents a novel GPU-based method for efficiently computing Zernike moments by leveraging the computational power of the Single Instruction Multiple Data(SIMD) architecture. The experimental results demonstrate that the proposed method can compute Zernike moments up to order 500 within 0.5 seconds for an image of size 512 * 512. To achieve greater accuracy in Zernike moments computation, a k * k sub-region scheme was incorporated into the approach. The results show that the PSNR value of the Lena image reconstructed from 500-order Zernike moments computed using the 9 * 9 scheme can reach 39.20 dB. Furthermore, a method for leaf recognition that leverages Zernike moments as image features, with the k-Nearest Neighbors (k-NN) algorithm serving as the classifier is proposed. The proposed method is evaluated on the Flavia leaf dataset, and the results affirm the effectiveness of the approach.Master of Science in Applied Computer Scienc

Accelerating Computation of Zernike and Pseudo-Zernike Moments with a GPU Algorithm

Although Zernike and pseudo-Zernike moments have some advanced properties, the computation process is generally very time-consuming, which has limited their practical applications. To improve the computational efficiency of Zernike and pseudo-Zernike moments, in this research, we have explored the use of GPU to accelerate moments computation, and proposed a GPUaccelerated algorithm. The newly developed algorithm is implemented in Python and CUDA C++ with optimizations based on symmetric properties and k × k sub-region scheme. The experimental results are encouraging and have shown that our GPU-accelerated algorithm is able to compute Zernike moments up to order 700 for an image sized at 512 × 512 in 1.7 seconds and compute pseudo-Zernike moments in 3.1 seconds. We have also verified the accuracy of our GPU algorithm by performing image reconstructions from the higher orders of Zernike and pseudo-Zernike moments. For an image sized at 512 × 512, with the maximum order of 700 and k = 11, the PSNR (Peak Signal to Noise Ratio) values of its reconstructed versions from Zernike and pseudo-Zernike moments are 44.52 and 46.29 separately. We have performed image reconstructions from partial sets of Zernike and pseudo-Zernike moments with various order n and different repetition m. Experimental results of both Zernike and pseudo-Zernike moments show that the images reconstructed from the moments of lower and higher orders preserve the principle contents and details of the original image respectively, while moments of positive and negative m result in identical images. Lastly, we have proposed a set of feature vectors based on pseudo-Zernike moments for Chinese character recognition. Three different feature vectors are composed of different parts of four selected lower pseudo-Zernike moments. Experiments on a set of 6,762 Chinese characters show that this method performs well to recognize similar-shaped Chinese characters.Master of Science in Applied Computer Scienc

Smooth functions and their use in optical modeling and design

Analytical description of unknown smooth optical functions such as optical surface and wavefront phases will have profound importance in optical modeling and design. Polynomial models have been extensively used to describe smooth function. Various forms of polynomials for describing the smooth functions may be considered both in optical modeling and design. In optics, the Zernike polynomials are potential candidates to describe optical surface and wavefront phases. However, they are restrained to specific geometry and suffer from numerical instability, especially for describing complex functions. More recently, spline model functions were also investigated for describing the optical surface shape and wavefront phase

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide