Haar Wavelets

A new computational method for solving Abel’s integral equation as a singular Volterra integral equation is presented. The method is  based on Haar wavelets approximation. Numerical examples show the validity and applicability of  the method

This issue (DOI: 10.13140/RG.2.2.13132.92807) includes the following articles; P1151705543, author="Tieling Chen", title="Detail Preserving Sorted Difference Filter", P1151738585, author="Vladimir A. Kulyukin", title="GreedyHaarSpiker: An Algorithm for In Situ Detection of Highway Lane Boundaries with 1D Haar Wavelet Spikes", P1151714561, author="Poorva Waingankar and Sangeeta Joshi", title="Video Compression using Efficient Encoding Techniques for Low Bit Rate Applications", P1151733581, author="Ayush Purohit and Shardul Singh Chauhan", title="A Precise Technique for Hand Gesture Recognition", P1151748594, author="D. Boopathy and M. Sundaresan", title="Securing Images on Cloud using Multidimensional Approach", P1151747592, author="M. Anyayahan and M. Balinas and A. La Madrid and M. Laurel and C. Lopez and R. Tolentino", title="Rotational invariant Real Time Text Recognition",

A novel and effective method based on Haar wavelets and Block Pulse Functions (BPFs) is proposed to solve nonlinear Fredholm integro-differential equations of fractional order. The operational matrix of Haar wavelets via BPFs is derived and together with Haar wavelet operational matrix of fractional integration are used to transform the mentioned equation to a system of algebraic equations. Our new method is based on this matrix and the vector forms for representation of Haar wavelets. In addition, an error and convergence analysis of the Haar-approximation is discussed. Since this approach does not need any integration, all calculations would be easily implemented, and it has several advantages in reducing the computational burden. Some examples are included to demonstrate the validity and applicability of the technique.

The objective of this paper is to solve the timefractional Schrödinger and coupled Schrödinger differential equations (TFSE) with appropriate initial conditions by using the Haar wavelet approximation. For the most part, this endeavor is made to enlarge the pertinence of the Haar wavelet method to solve a coupled system of time-fractional partial differential equations. As a general rule, piecewise constant approximation of a function at different resolutions is presentational characteristic of Haar wavelet method through which it converts the differential equation into the Sylvester equation that can be further simplified easily. Study of the TFSE is theoretical and experimental research and it also helps in the development of automation science, physics, and engineering as well. Illustratively, several test problems are discussed to draw an effective conclusion, supported by the graphical and tabulated results of included examples, to reveal the proficiency and adaptability of the method.

Signal & Image Processing : An International Journal is an Open Access peer-reviewed journal intended for researchers from academia and industry, who are active in the multidisciplinary field of signal & image processing. The scope of the journal covers all theoretical and practical aspects of the Digital Signal Processing & Image processing, from basic research to development of application.

This paper deal with the numerical method, based on the operational matrices of the Haar wavelet orthonormal functions approach to approximate solutions to a class of coupled systems of time-fractional order partial differential equations (FPDEs.). By introducing the fractional derivative of the Caputo sense, to avoid the tedious calculations and to promote the study of wavelets to beginners, we use the integration property of this method with the aid of the aforesaid orthogonal matrices which convert the coupled system under some consideration into an easily algebraic system of Lyapunov or Sylvester equation type. The advantage of the present method, including the simple computation, computer-oriented, which requires less space to store, timeefficient, and it can be applied for solving integer (fractional) order partial differential equations. Some specific and illustrating examples have been given; figures are used to show the efficiency, as well as the accuracy of the, achieved approximated results. All numerical calculations in this paper have been carried out with MATLAB.

In this paper, we seek a new method in designing an iris recognition system. In this method, first the Haar wavelet features are extracted from iris images. The advantage of using these features is the high-speed extraction, as well as being unique to each iris. Then the back propagation neural network (BPNN) is used as a classifier. In this system, the BPNN parallel algorithms and their implementation on GPUs have been used by the aid of CUDA in order to speed up the learning process. Finally, the system performance and the speeding outcomes in a way that this algorithm is done in series are presented.

Iris Recognition Systems are ocular- based biometric devices used primarily for security reasons. The complexity and the randomness of the Iris, amongst various other factors, ensure that this biometric system is inarguably an exact and reliable method of identification. The algorithm is responsible for automatic localization and segmentation of boundaries using circular Hough Transform, noise reductions, image enhancement and feature extraction across numerous distinct images present in the database. This paper delves into the various kinds of techniques required to approximate the pupillary and limbic boundaries of the enrolled iris image, captured using a suitable image acquisition device and perform feature extraction on the normalized iris image with the help of Haar Wavelets to encode the input data into a binary string format. These techniques were validated using images from the CASIA database, and various other procedures were also tried and tested.

The performance of Content-Based Image Retrieval (CBIR) system is depends on efficient feature extraction and accurate retrieval of similar images. Content based image retrieval is the task of retrieving the images from the large collection of database on the basis of their own visual content. This paper combines color features using Color Descriptor (CN) and texture features using Gray Level Co-occurrence Matrix (GLCM) to obtain better retrieval efficiency.From large database,using these feature vectors near about similarly matched images are retrieved. It is observed that combination of color features with the texture provides approximately similar results with very less processing time if we compare with individual approach.

The topic of facial recognition has become an intensely investigated field both in the consumer industry as well as the research industry.  Various facial recognition algorithms have been developed mainly making use of eigenfaces as well as principal component analysis and other similar linear algebraic methods.  In this paper, we explore the wavelets approach to this exceedingly difficult and important topic.  In particular, we chose the Haar wavelet due to its inexpensive computational needs, as well as robustness.  Fast computational times were further achieved due to developing our algorithm in MatLab.

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.

In this paper, we seek a new method in designing an iris recognition system. In this method, first the Haar wavelet features are extracted from iris images. The advantage of using these features is the high-speed extraction, as well as being unique to each iris. Then the back propagation neural network (BPNN) is used as a classifier. In this system, the BPNN parallel algorithms and their implementation on GPUs have been used by the aid of CUDA in order to speed up the learning process. Finally, the system performance and the speeding outcomes in a way that this algorithm is done in series are presented.

In this paper, wavelets were used to study the multivariate fractional Brownian motion through the deviations of the random process to find an efficient estimation of Hurst exponent. The results of simulations experiments were shown that the performance of the proposed estimator was efficient. The estimation process was made by taking advantage of the detail coefficients stationarity from the wavelet transform, as the variance of this coefficient showed the power-low behavior. We use two wavelet filters (Haar and db5) to manage minimizing the mean square error of the model.

Analisis wavelet adalah sebuah teknik penjendelaan variabel (variable windowing technique) dan mengijinkan penggunaan interval waktu yang panjang dimana kita menginginkan informasi frekuensi-rendah yang lebih tepat, dan daerah/wila ya h yang lebih pendek dimana kita menginginkan komponen-komponen frekuensi yang lebih tinggi. Paper ini adalah sebuah pemaparan singkat dari transformasi wavelet diskrit (discrete wavelet transform) sebagai salah satu teknik statistika. Teknik ini lebih baik dari pada transformasi fourier. Teknik ini memiliki type hard dan soft. Dengan melakukan perbandingan policy didapat wavelet manual yang memilik i nilai mse (mean square error) terkecil yakni sebesar 2.025 e-19. Kata Kunci: DWT, Threshold, Wavelet 1. PENDAHULUAN Kata wavelet berasal dari bahasa Perancis ondelete yang memiliki arti gelombang kecil. Istilah wavelet dalam pemodelan matematis mengandung arti fungsi dasar yang dapat melakukan rekonstruksi sinyal seperti halnya fungsi sinus dan cosinus yang dapat merekonstruksi sinyal dalam bentuk deret Fourier. Sebagai fungsi pembangun, wavelet mampu merekonstruksi sinyal mulus dan tak mulus termasuk sinyal dengan lompatan, atau titik runcing (Hall dan Patil, 1995). Rekonstruksi sinyal dengan deret Fourier tidak mampu mendekati dengan baik titik-titik dengan sifat tak mulus tersebut (Ogden, 1997). Itulah sedikit keunggula n transformasi wavelet dibandingkan dengan transformasi Fourier. Istilah sinyal sering digunakan dalam ranah keteknikan yang secara matematis mempunyai pengertian sama dengan fungsi dengan domin waktu. Realisasi fungsi dengan domin waktu yang diamati secara diskrit dengan jeda waktu yang sama juga sering disebut runtun waktu. Meskipun pembahasan difokuskan pada fungsi dengan domin waktu, namun pada hakekatnya wavelet dapat digunakan dalam konteks fungsi secara umum.

In the proposed work, classification of diseased and undiseased arecanut have been determined using texture features of Local Binary Pattern (LBP), Haar Wavelets, GLCM and Gabor. This work has been carried out in two stages. In the first stage, LBP have been applied on each color component of HSI and YCbCr color models and histogram of LBP is generated. The statistical method correlation is used to measure the distance between histogram of training set and query sample and obtained a success rate of 92.00%. We have not achieved better results in the first stage. In the second stage, texture features of Haar wavelets, GLCM and Gabor have been used. In this stage, RGB input arecanut image is transformed to HSI and YCbCr color models and texture features are extracted from each color component. Subset of texture features with high degree of discrimination power has been identified empirically based on combination of texture features. The kNN classifier gave a success rate of 100% for d...

This paper presents a new 3D RGB image compression scheme designed for interactive real-time applications. In designing our compression method, we have compromised between two important goals: high compression ratio and fast random access ability, and have tried to minimize the overhead caused during run-time reconstruction. Our compression technique is suitable for applications wherein data are accessed in a somewhat unpredictable fashion, and real-time performance of decompression is necessary. The experimental results on three different kinds of 3D images from medical imaging, image-based rendering, and solid texture mapping suggest that the compression method can be used effectively in developing real-time applications that must handle large volume data, made of color samples taken in three- or higher-dimensional space.

Identification of lithofacies using the depositional energy as a criteria to especially differentiate between coal, shaly-coal, and shale is a very useful attribute. In this study we demonstrate this technique on Natural Gamma Ray logs using Discrete and Continuous Wavelet Transform operations. We also identify potential bed boundaries in the process and characterize them by finding their Hurst parameter using a multiscale operation through wavelet analysis. We then try to correlate the results from two drilled wells and we have found that the Hurst parameter can be used as a very good index for well correlation purposes. The results that we obtain are then compared with interpreted results from other geophysical attributes taken from the boreholes and we find an excellent agreement in the results.

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Appearance-based approaches have the advantage of representing the variability of an object’s
appearance due to illumination change without explicit shape modeling. While a substantial amount of
research has been performed on the representation of object’s diffuse and specular shading, little attention
has been paid to cast shadows which are critical for attaining realism when multiple objects are present in
a scene. We present an appearance-based method for representing shadows and rendering them in a 3D
environment without explicit geometric modeling of shadow-casting object. A cubemap-like illumination
array is constructed, and an object’s shadow under each cubemap light pixel is sampled on a plane. Only
the geometry of the shadow-sampling plane is known relative to the cubemap lighting. The sampled images
of both the object and its cast shadows are represented using the Haar wavelet, and rendered on an
arbitrary 3D background of known geometry. Experiments are carried out to demonstrate the effectiveness
of the presented method.

Edge detection plays a vital role in computer vision and image processing. Edge of the image is one of the most significant features which are mainly used for image analyzing process. An efficient algorithm for extracting the edge features of images using simplified version of Gabor Wavelet is proposed in this paper. Conventional Gabor Wavelet is widely used for edge detection applications. Due do the high computational complexity of conventional Gabor Wavelet, this may not be used for real time application. Simplified Gabor wavelet based approach is highly effective at detecting both the location and orientation of edges. The
results proved that the performance of proposed Simplified version of Gabor wavelet is superior to conventional Gabor Wavelet, other edge detection algorithm and other wavelet based approach. The performance of the proposed method is proved with the help of FOM, PSNR and Average run time.

Image inpainting or restoration is one of the techniques which are being used from medieval times. Wavelets have shown significant performance in the process of image inpainting. But there are many wavelets available which can be used. In this paper we will evaluate the performance of Haar wavelet in image inpainting. Its performance will also be compared with some other wavelets using different cracked images.
Keywords— Haar, Image inpainting, Multiresolution, Texture, Wavelet.