Efficient Legendre moment computation for grey level images

Feature descriptors for 3-D images have recently gained considerable attention in application for games, virtual reality environment and solid modeling. Numerous research had been introduced for 3-D invariants of geometric moments, complex moments and Zernike moments. In this paper, we present a theoretical framework to derive translation and scale invariants for 3-D Legendre moments, by using indirect and direct methods. Indirect method generates 3-D Legendre invariants from the existing 3-D geometric moment invariants. Direct method, on the other hand, eliminates the displacement and scale factors from Legendre polynomials to generate translation and scale invariants. Experiment using 3-D binary images are carried out to verify the proposed feature descriptors.

We propose a fast calculation to characterise images by Legendre moments. We first propose the recursive calculation of 1D Legendre moments. The fast algorithm is then generalized to 2D cases. With our algorithm, the computational complexity to calculate the Legendre moments is much reduced, and it is independent of the window size.

An Efficient Method for Computation of Legendre Moments

How to calculate Legendre moments of images by less computation is a very important problem for the application of orthogonal moments in pattern recognition and image processing. in the present paper we propose the fast calculation to characterise 1-D signals and 2-D images by Legendre moments. We present at first the projections of 1-D signals onto Legendre polynomials and deduce their recursive calculation. We then introduce the scaled Legendre polynomials, the Legendre moments of 1-D signals with arbitrary window size and theirfast calulation. The implementation in discrete cases is presented and its computational complexity is analysed as well. To apply our method to 2-D image processing and recognition, the recursive algorithm is generalized to 2-D cases. With the approach presented, the computational complexity to characterise images by Legendre moments is greatly reduced and the implementation is simple. As the moments are widely used in image filtering, image segmentation, texture analysis and pattern recognition, the use of the algorithm proposed could greatly reduce the computational complexity of such tasks.

Simple and fast computation of moments

Surveillance and security cameras help security forces in public places such as airports, railway stations, universities and office buildings to perform high-level surveillance tasks such as detecting suspicious activity or anticipating undesirable events. Re-Identification (Re-ID) is defined as the process of communicating between images of the person in different cameras in a surveillance environment. Changing the field of view of any camera presents challenges such as changing body posture, changing brightness, noise and blockage. This article focuses on extracting the most distinctive features to overcome these challenges. The features of Hu moment, Zernike moment in 9th order and Legendre moment in 9th order for each image are extracted and merged into a single feature vector to form a single feature vector for each image. Principal Component Analysis (PCA) was used to reduce the vector dimensionality and finally the Mahalanobis distance criterion was used for identification. The proposed method in the VIPeR database has achieved a re-ID rate of 96.5. Although the presented method is simple, the outcome has been superior compared to many of the state-of-the-art methods.

A comprehensive treaty on the theory and applications of moment functions in image analysis. Moment functions are widely-used in various realms of computer vision and image processing. Numerous algorithms and techniques have been developed using image moments, in the areas of pattern recognition, object identification, three-dimensional object pose estimation, robot sensing, image coding and reconstruction. This is a compilation of the theoretical aspects related to different types of moment functions, and their applications in the above areas. The book is organized in two parts. The first part discusses the fundamental concepts behind important moments such as geometric moments, complex moments, Legendre moments, Zernike moments, and moment tensors. Most of the commonly-used properties of moment functions and the mathematical framework for the derivation of basic theorems and results are discussed. This includes the derivation of moment invariants, implementation aspects of moments, transport properties, and fast methods for computing the moment functions for both binary and gray-level images. The second part presents the key application areas of moments, such as pattern recognition, object identification, image-based pose estimation, edge detection, clustering, segmentation, coding and reconstruction. Important algorithms in each of these areas are discussed. A list of bibliographic references on image moments is also included.

Visual odometry can be divided into direct and indirect methods. Indirect methods which have more computation complexities are more robust, while direct methods are faster but less robust. To achieve the goal in terms of efficiency and robustness, we propose a novel semi-direct visual odometry approach with depth prior, which can be applied to most monocular direct odometry approaches. The proposed method is implemented based Direct Sparse Odometry. Experimental results on TUM datasets show that the proposed approach, which combines the advantages of both the direct and indirect methods, are more efficient and robust than the state-of-the-art method.

In this paper, we propose a novel method for reconstruction of the multi-gray level images using the exact computation of Legendre moments. The purpose of this method is to ensure high accuracy and low computation time, by dividing the image into a set of blocks instead of treating the whole image. For mitigating the blocking artifact involved in the reconstruction process, we propose a new approach based on block Reconstruction using a Global Overlapping Block and Exact Legendre Moments computation (GOBRELM). A typical comparison of the proposed method with the conventional ones concludes to very impressive and promising results concerning image quality and time consuming. The main motivation of the proposed approach is to allow fast and efficient reconstruction algorithm, with improvement of the reconstructed image quality and time consumption. This makes our method attractive for real time applications.

This work presents a new approach and an algorithm for binary image representation, which is applied for the fast and efficient computation of moments on binary images. This binary image representation scheme is called image block representation, since it represents the image as a set of nonoverlapping rectangular areas. The main purpose of the image block representation process is to provide an efficient binary image representation rather than the compression of the image. The block represented binary image is well suited for fast implementation of various processing and analysis algorithms in a digital computing machine. The two-dimensional (2-D) statistical moments of the image may be used for image processing and analysis applications. A number of powerful shape analysis methods based on statistical moments have been presented, but they suffer from the drawback of high computational cost. The real-time computation of moments in block represented images is achieved by exploiting the rectangular structure of the blocks.

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.

Integration of wavelet transform, Local Binary Patterns and moments for content-based image retrieval

The aim of this study is to hide two binary BMP images in a single BMP grayscale image. The widespread technique in image steganography is to hide one image (stego image) into another (cover image). The proposed novel method is to hide two binary images into one grayscale bitmap cover image. First of all, the proposed technique starts with transforming all grayscale cover image pixels into multiples of five using Five Modulus Method (FMM). Clearly, any modulus of five is either 0, 1, 2, 3, or 4. The transformed FMM cover image could be treated as a good host for carrying data. Obviously, it is known that the pixel value for the binary image is either 0 or 1. Therefore, by concatenating the two binary images, the composite results are 00, 01, 10 and 11. In fact, these concatenated values could be mapped using simple mapping that assigns a positive integer value such as 1 for 00, 2 for 01, 3 for 10 and 4 for 11. Consequently, a new matrix will be constructed that contains a number varying from 1 to 4 only. Fortunately, the four integer values are the same as the previously mentioned reminders of division by 5, hence, adding these four integers to the transformed FMM cover image. On the recipient side, a reverse process will be implemented to extract the two binary images. In terms of PSNR values, the cover image and the two extracted stego images have acceptable PSNR values, which yields that the proposed method is very efficient in information hiding.

This paper presents a low-complexity, cost-effective digital beamformer architecture for a high-frequency ultrasound imaging system. The proposed beamformer uses a lookup table and linear interpolation methods for computing the dynamic receive focusing delays and a postfiltering technique to minimize hardware complexity. In the postfiltering technique, channel radio-frequency data having the same fractional delay (i.e., 16f0 resolution) are aggregated prior to interpolation. Thus, only four polyphase structure filters are required in the developed beamformer. In addition, a quadrature bandpass filter that generates an analytic signal is utilized as an interpolation filter; this allows decimation during beam formation and a reduction in computational complexity. The proposed method was evaluated through a 20- [Formula: see text] wire phantom experiment, and the -6-dB lateral and axial resolutions obtained therein were measured and compared with those obtained using a conventional method. The same lateral (165 [Formula: see text]) and axial (80 [Formula: see text]) resolutions at a depth of 5.6 mm were obtained using both the methods, and the proposed method could reduce the beamforming points (i.e., computational complexity) by a factor of the decimation factor (≥4). Images from an excised bovine eye were captured; they showed that the proposed beamformer identified fine anatomical structures such as cornea or iris without compromising the spatial resolution and reduced the computational complexity.

The major issue in orthogonal frequency division multiplexing (OFDM) system is a high peak-to-average power ratio (PAPR) of transmitting signal. Selective mapping (SLM) is the promising technique to reduce PAPR in OFDM system. However, it suffers from high computational complexity. In our proposed method, to achieve low computational complexity, the input data sequences are partitioned into two sub blocks in such a way that the candidate signals are generated by performing circular convolution for the first sub block and by conventional SLM in the second sub block. The candidate signals of modified SLM are obtained by combining two sub block candidate signals. The proposed method reduces PAPR marginally along with reduction in computational complexity. To further reduce PAPR, different phase sequences namely Riemann, New Riemann and chaotic sequences are used in C-SLM. The Matlab simulation shows that, the modified SLM with new Riemann sequence results in high PAPR reduction than other phase sequences. In addition, it provides significant reduction computational complexity compared to C-SLM.