Analysis of moment algorithms for blurred images

One of the main contributions of this paper is to show that contrary to the common belief Tchebichef moments are more sensitive to noise added to the image than Zernike moments. We show this by imposing different types and levels of noise on various images and measuring the error due to the added noise alone after image reconstruction. To calculate the error due to added noise alone, the image reconstruction error is subtracted from the total error, which initially includes both reconstruction and added noise errors. Another contribution of this paper is to present some analysis and compare the reconstruction capability of Tchebichef moments to that of Zernike and Legendre moments in noise free environments independent of the image used. We show this by spectrally analyzing the performance of Tchebichef, Legendre, and Zernike moments using single frequency images. Here the total reconstruction error of an arbitrary image is equal to the integration of the spectral errors, whose transfer functions are calculated using single frequency images, for all frequencies.

This paper proposes an approach combining the set of Krawtchouk moments and HMMs (Hidden Markov Models) for unconstrained offline handwritten Chinese character recognition. The Krawtchouk moments can be effectively used as pattern features in analysis of two-dimensional images. Since the basis set is orthogonal in the discrete domain of the image coordinate space, the implementation of Krawtchouk moments doesn't involve any numerical approximation or coordinate transformation. This property makes Krawtchouk moments superior to conventional, more continuous moments such as Legendre moments and Zernike moments. In the field of character recognition, HMMs architecture has been used widely because of its strong adaptability to written distortion and variability. In this paper, Krawtchouk moments and HMMs are combined to recognize unconstrained offline handwritten Chinese amount in words. Experiments show that the average recognition of Krawtchouk is higher than Zernike and Legendre moments within the HMM framework.

Achieving Premier Invariance to Scale and Rotation for Nandinagari Character Recognition by Comparing Multi Moment Features

In order to improve the recognition rate, this document proposes an automatic system to recognize isolated printed Tifinagh characters by using a fusion of 3 classifiers and a combination of some features extraction methods. The Legendre moments, Zernike moments and Hu moments are used as descriptors in the features extraction phase due to their invariance to translation, rotation and scaling changes. In the classification phase, the neural network, the multiclass SVM (Support Vector Machine) and the nearest neighbour classifiers are combined together. The experimental results of each single features extraction method and each single classification method are compared with our approach to show its robustness.

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.

Aims/ objectives: To demontrate effectiveness of Zernike Moments for Image Classification. Zernike moment(ZM) is an excellent region-based moment which has attracted the attentions of many image processing researchers since its first application to image analysis. Many papers have been published on several works done on ZM but no single paper ever give a detailed information of how the computation of ZM is done from the time the image is captured to the computation of ZM. This work showed how to effectively apply ZM on RGB images. We have demonstrated the effectiveness of Zernike moment in image classification system. A neuro-genetic intelligent system has been built with PNN classifier. The feature extracted viz ZM and Geometric features were further subjected to GA to bring the best combinatorial features for optimal accuracy. The algebraic structure of our novel fitness function enabled the GA to select the best results. The 10-fold CV used enabled the whole system to be unbiased giving a classification accuracy of 90.05%. A demonstration of affine properties of ZM are comprehensively stated and explained. In summary, the ZM enabled the classifier to have improved accuracy of 91% as compared with Geometric features with 89% accuracy.

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.

In this paper, learning-based algorithms for image restoration and blind image restoration are proposed. Such algorithms deviate from the traditional approaches in this area, by utilizing priors that are learned from similar images. Original images and their degraded versions by the known degradation operator (restoration problem) are utilized for designing the VQ codebooks. The codevectors are designed using the blurred images. For each such vector, the high frequency information obtained from the original images is also available. During restoration, the high frequency information of a given degraded image is estimated from its low frequency information based on the codebooks. For the blind restoration problem, a number of codebooks are designed corresponding to various versions of the blurring function. Given a noisy and blurred image, one of the codebooks is chosen based on a similarity measure, therefore providing the identification of the blur. To make the restoration process computationally efficient, the principal component analysis (PCA) and VQ-nearest neighbor approaches are utilized. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms.

Region extraction and labeling is a fundamental process in building computer systems that automatically analyze and interpret images and image sequences of a scene. It involves extracting meaningful regions and their attributes from an image that are of interest in a given domain, e.g., a human face in face recognition and surveillance applications, a vehicle in intelligent highway monitoring, or an industrial tool in automated manufacturing and inspection applications. In this paper, we present a generalized and fast region labeling algorithm that can be applied to numerous image processing tasks: region extraction in binary images, region segmentation from gray scale or color images, region boundary extraction, chain code extraction, run-length coding of images, and image restoration from chain codes. The general applicability of our algorithm stems from its strengths in identifying the fundamental and common computational steps and providing robust and efficient procedures to accomplish these steps without requiring multiple scans of images. Our algorithm is shown to be more effective in terms of space and computational efficiency, in comparison with many existing approaches to region labeling and extraction. Results from our experiments with over 5,000 frames obtained from MPEG-1 video bitstreams demonstrate the good performance of our algorithm in terms of video text segmentation accuracy and computational efficiency.

A neural network model combining an adaptive heteroassociative network and an adaptive autoassociative network with a random Gaussian process is proposed to identify the noncausal blur function and to restore the blurred image at the same time. The noisy blurred images are modeled as continuous associative networks, where the autoassociative part determines the image model coefficients and the heteroassociative part determines the blur function of the system. The estimation and restoration are implemented by using an iterative steepest descent algorithm to minimize the error functions of the networks. Experiment results demonstrate that effective identification and restoration can be performed. >

We have investigated the restoration of electron micrographs exhibiting blurring due to drift and rotation. Blurring due to drift arises in micrographs taken of a specimen which is moving relative to the image plane. A related problem is that of rotational blurring which arises in micrographs of thin sections of helical particles viewed in cross section. The twist of the particle within the finite thickness of the section causes the image to appear rotationally blurred about the helical axis. Restoration algorithms were evaluated by applying them to the restoration of blurred model images degraded by additive Gaussian noise. Model images were also used to investigate how an incorrect estimate of the point spread function describing the blur would effect the restoration. Images were, if necessary, geometrically transformed to a space in which the point spread function of the blur can be considered as linear and space invariant as, under these conditions, the restoration algorithms are greatly simplified. In the case of the rotationally blurred images this procedure was accomplished by transforming the image to polar coordinates. The restoration techniques were successfully applied to blurred micrographs of bacteriophage T4 and crystals of catalase. The quality of the restoration was judged by comparisons of the restored images to undegraded images. Application to micrographs of rotationally blurred cross sections of helical macrofibers of sickle hemoglobin resulted in a reduction in the amount of rotational blurring.

Aim: Image is the most powerful tool to analyze the information. Sometimes the captured image gets affected with blur and noise in the environment, which degrades the quality of the image. Image restoration is a technique in image processing where the degraded image can be restored or recovered to its nearest original image. Materials and Methods: In this research Lucy-Richardson algorithm is used for restoring blurred and noisy images using MATLAB software. And the proposed work is compared with Wiener filter, and the sample size for each group is 30. Results: The performance was compared based on three parameters, Power Signal to Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), Normalized Correlation (NC). High values of PSNR, SSIM and NC indicate the better performance of restoration algorithms. Lucy-Richardson provides a mean PSNR of 10.4086db, mean SSIM of 0.4173%, and NC of 0.7433% and Wiener filter provides a mean PSNR of 6.3979db, SSIM of 0.3016%, NC of 0.3276%. Conclusion: Based on the experimental results and statistical analysis using independent sample T test, image restoration using Lucy-Richardson algorithm significantly performs better than Wiener filter on restoring the degraded image with PSNR (P<0.001) and SSIM (P<0.001).

This study presents an automated quality inspection approach for detecting surface defects in industrial casting parts using image processing and machine learning techniques. A total of ten different feature extraction methods—Histogram of Oriented Gradients (HOG), Local Binary Patterns (LBP), Scale-Invariant Feature Transform (SIFT), Gray Level Co-occurrence Matrix (GLCM), Gabor filters, color histogram, wavelet transform, Hu moments, Zernike moments, and Fourier transform—were applied to 300×300 grayscale images. To evaluate the effect of spatial resolution, features were extracted at five different cell sizes: 25×25, 50×50, 100×100, 150×150, and 300×300. Dimensionality reduction was performed using minimum Redundancy Maximum Relevance (mRMR) and Chi-square (χ²) feature selection techniques. The resulting feature sets were classified with six different algorithms in MATLAB Classification Learner, including Fine Tree, Fine KNN, Wide Neural Network, Bagged Trees, Fine Gaussian SVM, and Binary GLM. Experimental results demonstrated that the highest accuracy rate of 99.7% was achieved with the Wide Neural Network model trained on the complete feature set at a 25×25 cell size. These findings indicate that smaller cell sizes preserve critical surface details and enhance classification performance. The study highlights that the proposed methodology can serve as a highly accurate, efficient, and practical solution for automated defect detection in the casting industry, offering strong potential for real-world industrial applications.

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.

Blind image restoration algorithms for motion blur have been deeply researched in the past years. Although great progress has been made, blurred images containing large blur and rich, small details still cannot be restored perfectly. To deal with these problems, we present a robust image restoration algorithm for motion blur of general image sensors in this paper. Firstly, we propose a self-adaptive structure extraction method based on the total variation (TV) to separate the reliable structures from textures and small details of a blurred image which may damage the kernel estimation and interim latent image restoration. Secondly, we combine the reliable structures with priors of the blur kernel, such as sparsity and continuity, by a two-step method with which noise can be removed during iterations of the estimation to improve the precision of the estimated blur kernel. Finally, we use a MR-based Wiener filter as the non-blind deconvolution algorithm to restore the final latent image. Experimental results demonstrate that our algorithm can restore large blur images with rich, small details effectively.