Journal articles: 'Wavelets (Mathematics) Image processing Surfaces'

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JIANG, QINGTANG. "BIORTHOGONAL WAVELETS WITH SIX-FOLD AXIAL SYMMETRY FOR HEXAGONAL DATA AND TRIANGLE SURFACE MULTIRESOLUTION PROCESSING." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 05 (September 2011): 773–812. http://dx.doi.org/10.1142/s0219691311004316.

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This paper discusses the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently, hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for hexagonal data also have high symmetry which is pertinent to the symmetric structure of the hexagonal lattice. The high symmetry of filter banks and wavelets not only leads to simpler algorithms and efficient computations, it also has the potential application for the texture segmentation of hexagonal data. While in the field of computer-aided geometric design (CAGD), when the filter banks are used for surface multiresolution processing, it is required that the corresponding decomposition and reconstruction algorithms for regular vertices have high symmetry, which make it possible to design the corresponding multiresolution algorithms for extraordinary vertices. In this paper we study the construction of six-fold axial symmetric biorthogonal filter banks and the associated wavelets, with both the dyadic and [Formula: see text]-refinements. The constructed filter banks have the desirable symmetry for hexagonal data processing. By associating the outputs (after one-level multiresolution decomposition) appropriately with the nodes of the regular triangular mesh with which the input data is associated (sampled), we represent multiresolution analysis and synthesis algorithms as templates. The six-fold axial symmetric filter banks constructed in this paper result in algorithm templates with desirable symmetry for triangle surface processing.

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de Oliveira, H. M., V. V. Vermehren, and R. J. Cintra. "Multi-dimensional wavelets for scalable image decomposition: Orbital wavelets." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 05 (June 15, 2020): 2050038. http://dx.doi.org/10.1142/s0219691320500381.

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Wavelets are closely related to Schrödinger’s wave functions and the interpretation of Born. Similar to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach allows the increase of the dimension of wavelets through this process. New orbital 2D-wavelets are introduced for the decomposition of still images, showing that it is possible to perform an analysis simultaneously in two distinct scales. An example of such an image analysis is shown.

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Farkov, Yu A., and S. A. Stroganov. "The use of discrete dyadic wavelets in image processing." Russian Mathematics 55, no. 7 (July 2011): 47–55. http://dx.doi.org/10.3103/s1066369x11070073.

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Fryzlewicz, Piotr, and Catherine Timmermans. "SHAH: SHape-Adaptive Haar Wavelets for Image Processing." Journal of Computational and Graphical Statistics 25, no. 3 (July 2, 2016): 879–98. http://dx.doi.org/10.1080/10618600.2015.1048345.

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ZHANG, ZHONG, NARIYA KOMAZAKI, TAKASHI IMAMURA, TETSUO MIYAKE, and HIROSHI TODA. "DIRECTIONAL SELECTION OF TWO-DIMENSIONAL COMPLEX DISCRETE WAVELET TRANSFORM AND ITS APPLICATION TO IMAGE PROCESSING." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 04 (July 2010): 659–76. http://dx.doi.org/10.1142/s0219691310003705.

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In this study, a novel direction selection method using the two-dimensional complex discrete wavelet transform (2D-CDWT) is proposed. In order to achieve arbitrary direction selection, the directional filters are first designed. Calculation procedure of directional selection can be shown as follows: (1) The 16 sub-images are generally generated from the original image by the 2D-CDWT without a down-sampling process and the 12 sub-images that correspond to the high-frequency components are selected. (2) The 12 sub-images are filtered by using the designed directional filter. (3) The down-sampling process is carried out and the resulting images are obtained. Furthermore, this method is applied to the surface analysis of a wafer, and it is confirmed that our method is effective in detecting irregular direction components.

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Zhang, Xi, and Noriaki Fukuda. "Lossy to lossless image coding based on wavelets using a complex allpass filter." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 04 (July 2014): 1460002. http://dx.doi.org/10.1142/s0219691314600029.

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Wavelet-based image coding has been adopted in the international standard JPEG 2000 for its efficiency. It is well-known that the orthogonality and symmetry of wavelets are two important properties for many applications of signal processing and image processing. Both can be simultaneously realized by the wavelet filter banks composed of a complex allpass filter, thus, it is expected to get a better coding performance than the conventional biorthogonal wavelets. This paper proposes an effective implementation of orthonormal symmetric wavelet filter banks composed of a complex allpass filter for lossy to lossless image compression. First, irreversible real-to-real wavelet transforms are realized by implementing a complex allpass filter for lossy image coding. Next, reversible integer-to-integer wavelet transforms are proposed by incorporating the rounding operation into the filtering processing to obtain an invertible complex allpass filter for lossless image coding. Finally, the coding performance of the proposed orthonormal symmetric wavelets is evaluated and compared with the D-9/7 and D-5/3 biorthogonal wavelets. It is shown from the experimental results that the proposed allpass-based orthonormal symmetric wavelets can achieve a better coding performance than the conventional D-9/7 and D-5/3 biorthogonal wavelets both in lossy and lossless coding.

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Low, Yin Fen, and Rosli Besar. "Optimal Wavelet Filters for Medical Image Compression." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 02 (June 2003): 179–97. http://dx.doi.org/10.1142/s0219691303000128.

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Recently, the wavelet transform has emerged as a cutting edge technology, within the field of image compression research. The basis functions of the wavelet transform are known as wavelets. There are a variety of different wavelet functions to suit the needs of different applications. Among the most popular wavelets are Haar, Daubechies, Coiflet and Biorthogonal, etc. The best wavelets (functions) for medical image compression are widely unknown. The purpose of this paper is to examine and compare the difference in impact and quality of a set of wavelet functions (wavelets) to image quality for implementation in a digitized still medical image compression with different modalities. We used two approaches to the measurement of medical image quality: objectively, using peak signal to noise ratio (PSNR) and subjectively, using perceived image quality. Finally, we defined an optimal wavelet filter for each modality of medical image.

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ZENG, LI, RUI MA, JIANYUAN HUANG, and P. R. HUNZIKER. "THE CONSTRUCTION OF 2D ROTATIONALLY INVARIANT WAVELETS AND THEIR APPLICATION IN IMAGE EDGE DETECTION." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 01 (January 2008): 65–82. http://dx.doi.org/10.1142/s0219691308002227.

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Construction of rotationally invariant 2D wavelets is important in image processing, but is difficult. In this paper, the discrete form of a 2D rotationally invariant wavelet is constructed by back-projection from a 1D symmetrical wavelet. Such rotationally invariant 2D wavelets allow effective edge detection in any direction. These wavelets are combined with the 2D directional wavelets for the use in non-maximum suppression edge detection. The resulting binary edges are characterized by finer contours, differential detection characteristics and noise robustness compared to other edge detectors in various test images. In particular, where fine binary edges in noisy images are required, this novel approach compares favorably to the classical methods of Canny and Mallat with detection of more edges thanks to the implicit denoising properties and the full rotational invariance of the method.

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BHATNAGAR, GAURAV, R. JAYAGANTHAN, and BALASUBRAMANIAN RAMAN. "WAVELET ANALYSIS OF SURFACE MORPHOLOGIES OF MAGNETRON SPUTTERED Al-Cu THIN FILMS." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 01 (January 2009): 59–74. http://dx.doi.org/10.1142/s0219691309002775.

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Al - Cu thin films were deposited by DC magnetron sputtering. The films are characterized by atomic force microscopy and its surface morphologies are analyzed by wavelet technique. Multiresolution signal decomposition wavelet technique was employed to extract the surface roughness from the AFM images of Al - Cu thin films. It is observed that the Al - Cu thin films exhibit higher surface roughness value with increasing deposition time. The calculated surface roughness of the thin films, using wavelet technique, is comparable with that of its experimental values.

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Josephine, S., and S. Murugan. "Noise Removal from Brain MRI Images Using Adaptive Bayesian Shrinkage." Journal of Computational and Theoretical Nanoscience 17, no. 4 (April 1, 2020): 1818–25. http://dx.doi.org/10.1166/jctn.2020.8446.

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In MR machine, surface coils, especially phased-arrays are used extensively for acquiring MR images with high spatial resolution. The signal intensities on images acquired using these coils have a non-uniform map due to coil sensitivity profile. Although these smooth intensity variations have little impact on visual diagnosis, they become critical issues when quantitative information is needed from the images. Sometimes, medical images are captured by low signal to noise ratio (SNR). The low SNR makes it difficult to detect anatomical structures because tissue characterization fails on those images. Hence, denoising are essential processes before further processing or analysis will be conducted. They found that the noise in MR image is of Rician distribution. Hence, general filters cannot be used to remove these types of noises. The linear spatial filtering technique blurs the object boundaries and degrades the sharp details. The existing works proved that Wavelet based works eliminates the noise coefficient that called wavelet thresholding. Wavelet thresholding estimates the noise level from high frequency content and estimates the threshold value by comparing the estimated noisy wavelet coefficient with other wavelet coefficients and eliminate the noisy pixel intensity value. Bayesian Shrinkage rule is one of the widely used methods. It uses for Gaussian type of noise, the proposed method introduced some adaptive technique in Bayesian Shrinkage method to remove Rician type of noises from MRI images. The results were verified using quantitative parameters such as Peak Signal to Noise Ratio (PSNR). The proposed Adaptive Bayesian Shrinkage Method (ABSM) outperformed existing methods.

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MAITY, SANTI P., and MALAY K. KUNDU. "PERFORMANCE IMPROVEMENT IN SPREAD SPECTRUM IMAGE WATERMARKING USING WAVELETS." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 01 (January 2011): 1–33. http://dx.doi.org/10.1142/s0219691311003931.

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This paper investigates the scope of wavelets for performance improvement in spread spectrum image watermarking. Performance of a digital image watermarking algorithm, in general, is determined by the visual invisibility of the hidden data (imperceptibility), reliability in the detection of the hidden information after various common and deliberate signal processing operations (robustness) applied on the watermarked signals and the amount of data to be hidden (payload) without affecting the imperceptibility and robustness properties. In this paper, we propose a few spread spectrum (SS) image watermarking schemes using discrete wavelet transform (DWT), biorthogonal DWT and M-band wavelets coupled with various modulation, multiplexing and signaling techniques. The performance of the watermarking methods are also reported along with the relative merits and demerits.

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ZHAN, YINWEI, and HENK J. A. M. HEIJMANS. "NON-SEPARABLE 2D BIORTHOGONAL WAVELETS WITH TWO-ROW FILTERS." International Journal of Wavelets, Multiresolution and Information Processing 03, no. 01 (March 2005): 1–18. http://dx.doi.org/10.1142/s0219691305000713.

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In the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are prefered. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang.2 A characteristic feature of this class of wavelets is that the support of the corresponding filter comprises only two rows. We are concerned with the biorthogonal extension of this kind of wavelets. It turns out that the 2D wavelets in this class are intimately related to some underlying 1D wavelet. We explore this relation in detail, and we explain how the 2D wavelet transforms can be realized by means of a lifting scheme, thus allowing an efficient implementation. We also describe an easy way to construct wavelets with more rows and shorter columns.

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YAN, ZHONGHONG, JIAN PING LI, YONG QIN YANG, and YUAN YAN TANG. "STUDY ON RECURSIVE CONSTRUCTION METHOD OF BIORTHOGONAL WAVELETS FOR SIGNAL PROCESSING." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 02 (June 2004): 197–206. http://dx.doi.org/10.1142/s0219691304000470.

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Wavelet has been applying in signal analyzing, image processing model recognizing, computer sense etc. But among them biorthogonal wavelets with symmetry characteristics (or antisymmetry) in the image compressing, signal examination has more special functions, this paper research a recursive construction method, at the same time, It is valuable to notice that our recursive methods are not the same as the W. Seldens's lifting scheme, the new technique has important mean to adaptive signal processing and more application: such as for QMF•CQF etc. filters. It is very easy to choose the wavelet bases match to questions by dynamically.

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DJEBALI, M., M. MELKEMI, K. MELKEMI, and N. SAPIDIS. "COIFLET BASED METHODS FOR RANGE IMAGE PROCESSING." International Journal of Image and Graphics 07, no. 02 (April 2007): 321–51. http://dx.doi.org/10.1142/s0219467807002672.

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In industry applications, the range images are generally huge points arrays and are additively noised. They usually represent surfaces of 3D objects and are used for reverse engineering process in CAD/CAM domains. To compute the geometrical model of each surface present in the range image, we denoise and sub-sample the raw range data. Denoising allows us to avoid the adverse effects of the noise on the obtained result. Sub-sampling the raw range data leads to a low image processing overheads like those of segmentation process. Based on interpolation properties of particular wavelets named coiflets, we propose a method for smoothing noisy range images. The smoothed image keeps invariant the "topological characteristics" of the represented surfaces. Thereafter, we propose a method for sub-sampling dense range images which leads to the reduction of the amount of raw data by a factor of four. This method eliminates the "redundant" information, thus the obtained result describes the essential details (as the shape of the physical surface) of the initial range image. The smoothing and sub-sampling methods are designed to be easily integrated in any reconstruction algorithm to improve its result and reduce its overhead in spite of its high complexity.

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Herrera-Alcántara, Oscar, and Miguel González-Mendoza. "Inverse formulas of parameterized orthogonal wavelets." Computing 100, no. 7 (January 25, 2018): 715–39. http://dx.doi.org/10.1007/s00607-018-0585-x.

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Abstract We review the parameterization of orthogonal wavelet based filters of length 4, 6, 8, and 10, and present their inverse formulas, which means to determine the parameter values from filter coefficients. Experimental results support the validity of these inverse formulas when parameters are restricted to $$[0, 2\pi )$$ [ 0 , 2 π ) for practical applications, such as image processing where parameters are optimized to maximize the number of negligible wavelet coefficients.

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Geetha, P., and S. Nagarani. "An Efficient Image Segmentation Using Partial Differential Equation for Image Processing Applications." Journal of Medical Imaging and Health Informatics 11, no. 10 (October 1, 2021): 2538–45. http://dx.doi.org/10.1166/jmihi.2021.3840.

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Different processing of the images, such as the image captured, saved and retrieved from another use of the specific image, must be restructured in various ways in the process. More methods such as image restoration, picture segmentation, improvement of the picture etc can be used when processing images. Reconstructed in 3D picture 2D pictures are need to be proper. Including geometric wavelets and geometric analysis the structural work focused upon a variational and a selectable differential equation to test PDE’s which is a convergence of stochastic modelling and analysis of harmonics. This paper focuses primarily on the critical reviews of the image segmentation collection with the PDE application as a mathematical method and introduces the key tool of mathematics and techniques along with the literature-based analysis.

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Nai-Xiang Lian, V. Zagorodnov, and Yap-Peng Tan. "Color image denoising using wavelets and minimum cut analysis." IEEE Signal Processing Letters 12, no. 11 (November 2005): 741–44. http://dx.doi.org/10.1109/lsp.2005.856865.

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KABEER, V., and N. K. NARAYANAN. "WAVELET-BASED ARTIFICIAL LIGHT RECEPTOR MODEL FOR HUMAN FACE RECOGNITION." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 05 (September 2009): 617–27. http://dx.doi.org/10.1142/s0219691309003124.

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This paper presents a novel biologically-inspired and wavelet-based model for extracting features of faces from face images. The biological knowledge about the distribution of light receptors, cones and rods, over the surface of the retina, and the way they are associated with the nerve ends for pattern vision forms the basis for the design of this model. A combination of classical wavelet decomposition and wavelet packet decomposition is used for simulating the functional model of cones and rods in pattern vision. The paper also describes the experiments performed for face recognition using the features extracted on the AT & T face database (formerly, ORL face database) containing 400 face images of 40 different individuals. In the recognition stage, we used the Artificial Neural Network Classifier. A feature vector of size 40 is formed for face images of each person and recognition accuracy is computed using the ANN classifier. Overall recognition accuracy obtained for the AT & T face database is 95.5%.

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FUJINOKI, KENSUKE, and SHUNSUKE ISHIMITSU. "TRIANGULAR BIORTHOGONAL WAVELETS WITH EXTENDED LIFTING." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 04 (July 2013): 1360002. http://dx.doi.org/10.1142/s0219691313600023.

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We present a new family of triangular biorthogonal wavelets that is defined on a triangular lattice by introducing a new operation to generalize two-dimensional lifting, which we call twist. The resulting filters inherit several remarkable features of the early triangular biorthogonal wavelet filters such as the hexagonal symmetry of low-pass filters, symmetrical arrangement of three high-pass filters on the lattice, and that the wavelet decomposition produces uniform energy distributions over three detail components, preserving the isotropy of decomposed images. Additionally, these filters are a biorthogonal set of truly nonseparable two-dimensional wavelet filters that have much larger support, which provides much larger portions of the total energy to three detail components of decomposed images. We show that this plays a crucial role when extracting the edge structure of an image.

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UENO, YOSHITO. "WAVELETS AND FRACTAL IMAGE COMPRESSION BASED ON THEIR SELF-SIMILARITY OF THE SPACE-FREQUENCY PLANE OF IMAGES." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 04 (December 2003): 393–405. http://dx.doi.org/10.1142/s0219691303000256.

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This paper presents a fusion scheme for wavelets and fractal image compression based on the self-similarity of the space-frequency plane of sub-bands after wavelet transformation of images. Various kinds of wavelet transform are examined for the characteristics of their self-similarity and evaluated for the adoption of fractal encoder. The aim of this paper is to reduce the information of the two sets of blocks involved in the fractal image compression by using the self-similarity of images. And also, the new video encoder using the fusion method of wavelets and fractal adopts the similar manner as the motion compensation technique of MPEG encoder. Experimental results show almost the same PSNR and bits rate as conventional fractal image encoder by depending on the sampled images through computer simulations.

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JACQUES, LAURENT, and JEAN-PIERRE ANTOINE. "MULTISELECTIVE PYRAMIDAL DECOMPOSITION OF IMAGES: WAVELETS WITH ADAPTIVE ANGULAR SELECTIVITY." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 05 (September 2007): 785–814. http://dx.doi.org/10.1142/s0219691307002051.

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Many techniques have been devised these last ten years to add an appropriate directionality concept in decompositions of images from the specific transformations of a small set of atomic functions. Let us mention, for instance, works on directional wavelets, steerable filters, dual-tree wavelet transform, curvelets, wave atoms, ridgelet packets, etc. In general, features that are best represented are straight lines or smooth curves as those defining contours of objects (e.g. in curvelets processing) or oriented textures (e.g. wave atoms, ridgelet packets). However, real images present also a set of details less oriented and more isotropic, like corners, spots, texture components, etc. This paper develops an adaptive representation for all these image elements, ranging from highly directional ones to fully isotropic ones. This new tool can indeed be tuned relatively to these image features by decomposing them into a Littlewood–Paley frame of directional wavelets with variable angular selectivity. Within such a decomposition, 2D wavelets inherit some particularities of the biorthogonal circular multiresolution framework in their angular behavior. Our method can therefore be seen as an angular multiselectivity analysis of images. Two applications of the proposed method are given at the end of the paper, namely, in the fields of image denoising and N-term nonlinear approximation.

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Rodrigues, Marco A. M., Eduardo A. B. da Silva, and Paulo S. R. Dini. "Design of High-Performance Wavelets for Image Coding Using a Perceptual Time Domain Criterion." Circuits, Systems and Signal Processing 21, no. 3 (May 2002): 225–42. http://dx.doi.org/10.1007/s00034-004-7041-1.

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KUNDU, MALAY K., and MAUSUMI ACHARYYA. "M-BAND WAVELETS: APPLICATION TO TEXTURE SEGMENTATION FOR REAL LIFE IMAGE ANALYSIS." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 01 (March 2003): 115–49. http://dx.doi.org/10.1142/s0219691303000074.

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This paper describes two examples of real-life applications of texture segmentation using M-band wavelets. In the first part of the paper, an efficient and computationally fast method for segmenting text and graphics part of a document image based on textural cues is presented. It is logical to assume that the graphics part has different textural properties than the non-graphics (text) part. So, this is basically a two-class texture segmentation problem. The second part of the paper describes a segmentation scheme for another real-life data such as remotely sensed image. Different quasi-homogeneous regions in the image can be treated to have different texture properties. Based on this assumption the multi-class texture segmentation scheme is applied for this purpose.

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HEIJMANS, HENK J. A. M., GEMMA PIELLA, and BÉATRICE PESQUET-POPESCU. "ADAPTIVE WAVELETS FOR IMAGE COMPRESSION USING UPDATE LIFTING: QUANTIZATION AND ERROR ANALYSIS." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 01 (March 2006): 41–63. http://dx.doi.org/10.1142/s0219691306001087.

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Classical linear wavelet representations of images have the drawback that they are not optimally suited to represent edge information. To overcome this problem, nonlinear multiresolution decompositions have been designed to take into account the characteristics of the input signal/image. In our previous work20,22,23 we have introduced an adaptive lifting framework, that does not require bookkeeping but has the property that it processes edges and homogeneous image regions in a different fashion. The current paper discusses the effects of quantization in such an adaptive wavelet decomposition. We provide conditions for recovering the original decisions at the synthesis and for relating the reconstruction error to the quantization error. Such an analysis is essential for the application of these adaptive decompositions in image compression.

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BAHRI, MAWARDI, and ECKHARD S. M. HITZER. "CLIFFORD ALGEBRA Cl3,0-VALUED WAVELET TRANSFORMATION, CLIFFORD WAVELET UNCERTAINTY INEQUALITY AND CLIFFORD GABOR WAVELETS." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 06 (November 2007): 997–1019. http://dx.doi.org/10.1142/s0219691307002166.

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In this paper, it is shown how continuous Clifford Cl3,0-valued admissible wavelets can be constructed using the similitude group SIM(3), a subgroup of the affine group of ℝ3. We express the admissibility condition in terms of a Cl3,0 Clifford Fourier transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform of multivector functions. We invent a generalized Clifford wavelet uncertainty principle. For scalar admissibility constant, it sets bounds of accuracy in multivector wavelet signal and image processing. As concrete example, we introduce multivector Clifford Gabor wavelets, and describe important properties such as the Clifford Gabor transform isometry, a reconstruction formula, and an uncertainty principle for Clifford Gabor wavelets.

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Li, Wen-Juan, Jun Wang, Zheng-Hai Huang, Ting Zhang, and Daniel K. Du. "LBP-like feature based on Gabor wavelets for face recognition." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 05 (August 28, 2017): 1750049. http://dx.doi.org/10.1142/s0219691317500497.

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The robust feature extraction method for face representation is an important issue in face recognition. In this paper, we extract a new kind of feature through applying the idea of local binary pattern (LBP) into the resulted sub-images of Gabor transform. The new feature, i.e. Gabor-LBP-Like (GLLBP), together with its extension methods (1) overcome the drawback of losing information after Gabor transform’s down-sampling; (2) are insensitive to noise, compared with the LBP feature extracted from the original face image; and (3) are robust to image variation, especially occlusion and illumination changes when compared with other existing features combined LBP and Gabor transform. To validate the effectiveness of these features, we do experiments on the ORL, FERET, Georgia Tech and LFW facial databases. The numerical results show that GLLBP and its extensions are miraculous features for face recognition.

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CIARLINI, PATRIZIA, GIUSEPPE COSTANZO, and MARIA LAURA LO CASCIO. "WAVELETS AND SPLINES FOR VERTICAL SCRATCH REMOVAL IN OLD MOVIE SEQUENCES." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 03 (September 2006): 433–46. http://dx.doi.org/10.1142/s021969130600135x.

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In old movies, scratches are common damages that mostly result from a mechanical stress during the projection. A method for removing vertical scratches is proposed and suitable to be automatically applied to sequences of images. The method uses a wavelet decomposition of the original digital image, I, in order to separate the high frequency components and to elaborate corrupted data in the regular matrix, A, and in the vertical details matrix, V, only. For A, approximating functions are constructed in suitable spline spaces, which depend on the morphological quality of the image near the scratch. Monochromatic old images and images with simulated scratches have been considered to validate the method.

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LI, LUOQING, and YUAN Y. TANG. "WAVELET-HOUGH TRANSFORM WITH APPLICATIONS IN EDGE AND TARGET DETECTIONS." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 03 (September 2006): 567–87. http://dx.doi.org/10.1142/s0219691306001452.

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In computer vision and image processing, edge detection concerns the localization of significant variations of the grey level image and the identification of the physical phenomena that originated them. It is difficult to design a general edge detection algorithm which performs well in many contexts and captures the requirements of subsequent processing stages. Consequently, over the history of digital image processing, a variety of edge detectors have been devised which differ in their mathematical and algorithmic properties. In this paper, we briefly describe some existing edge detectors. We investigate the wavelet transform with direction which is related to the Canny and Marr–Hildreth's edge detectors. This wavelet transform has a remarkable feature that plays an important role in image processing applications. We discuss its applications to edge and target detections. The direction effect enables the wavelets to analyze the directional features of images. Algorithms and experiments for edge and target detections have been developed based on the theory. And, very promising results have been shown in image processing.

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Song, Yalong, Hong Li, Jianzhong Wang, and Kit Ian Kou. "Multiple one-dimensional embedding clustering scheme for hyperspectral image classification." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 02 (March 2016): 1640004. http://dx.doi.org/10.1142/s021969131640004x.

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In this paper, we present a novel multiple 1D-embedding based clustering (M1DEBC) scheme for hyperspectral image (HSI) classification. This novel clustering scheme is an iteration algorithm of 1D-embedding based regularization, which is first proposed by J. Wang [Semi-supervised learning using ensembles of multiple 1D-embedding-based label boosting, Int. J. Wavelets[Formula: see text] Multiresolut. Inf. Process. 14(2) (2016) 33 pp.; Semi-supervised learning using multiple one-dimensional embedding-based adaptive interpolation, Int. J. Wavelets[Formula: see text] Multiresolut. Inf. Process. 14(2) (2016) 11 pp.]. In the algorithm, at each iteration, we do the following three steps. First, we construct a 1D multi-embedding, which contains [Formula: see text] different versions of 1D embedding. Each of them is realized by an isometric mapping that maps all the pixels in a HSI into a line such that the sum of the distances of adjacent pixels in the original space is minimized. Second, for each 1D embedding, we use the regularization method to find a pre-classifier to give each unlabeled sample a preliminary label. If all of the [Formula: see text] different versions of regularization vote the same preliminary label, then we call it a feasible confident sample. All the feasible confident samples and their corresponding labels constitute the auxiliary set. We randomly select a part of the elements from the auxiliary set to construct the newborn labeled set. Finally, we add the newborn labeled set into the labeled sample set. Thus, the labeled sample set is gradually enlarged in the process of the iteration. The iteration terminates until the updated labeled set reaches a certain size. Our experimental results on real hyperspectral datasets confirm the effectiveness of the proposed scheme.

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Grohs, Philipp, Željko Kereta, and Uwe Wiesmann. "A shearlet-based fast thresholded Landweber algorithm for deconvolution." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 05 (August 24, 2016): 1650032. http://dx.doi.org/10.1142/s0219691316500326.

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Image deconvolution is an important problem, which has seen plenty of progress in the last decades. Due to its ill-posedness, a common approach is to formulate the reconstruction as an optimization problem[Formula: see text] regularized by an additional sparsity-enforcing term. This term is often modeled as an [Formula: see text] norm measured in the domain of a suitable signal transform. The resulting optimization problem can be solved by an iterative approach via Landweber iterations with soft thresholding of the transform coefficients. Previous approaches focused on thresholding in the wavelet-domain. In particular, recent work [C. Vonesch and M. Unser, A fast thresholded Landweber algorithm for wavelet-regularized multidimensional deconvolution, IEEE Trans. Image Process. 17(4) (2008) 539–549.] has shown that the use of Shannon wavelets results in particularly efficient reconstruction algorithms. The present paper extends this approach to Shannon shearlets, which we also introduce in this work. We show that for anisotropic blurring filters, such as the motion blur, the novel shearlet-based approach allows for further a improvement in efficiency. In particular, we observe that for such kernels using shearlets instead of wavelets improves the quality of image restoration and SERG, when compared after the same number of iterations.

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Любимова, Mariya Lyubimova, Князева, and Tatyana Knyazeva. "Processing of tomographic images by means of wavelet analysis." Journal of New Medical Technologies. eJournal 8, no. 1 (November 5, 2014): 1–4. http://dx.doi.org/10.12737/4110.

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The paper is devoted to the problem of processing of tomographic images using wavelet analysis. The features of image processing techniques, indications were analyzed. Wavelets are a signal waveform of limited duration that has an average value of zero. Wavelets are comparable to a sine wave, and they are the basis of Fourier analysis. Wavelet analysis method allows to processing of tomographic images using a large time interval, where more accurate information about the low frequency region and shorter when information is needed on high frequency. The characteristic features of the settings wavelet transforms are described. Their bad choice reduces the reliability of detection of changes in the structure of signals when changing system state. The key stages of the reconstruction tomography images in DICOM format using the method of wavelet analysis were examined; algorithm of noise reduction was investigated. Practical area of application of wavelet analysis doesn´t limited to digital signal processing; it also covers physical experiments, numerical methods and other areas of physics and mathematics. By being able to analyze the non-stationary signals, wavelet analysis has become a powerful alternative Fourier transform in medical applications.

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MATSUYAMA, SAWA, SHIHO MATSUYAMA, and YOSHIFURU SAITO. "DATA HANDLING METHODOLOGY FOR DISCRETE WAVELETS AND ITS APPLICATIONS TO THE DYNAMIC VECTOR FIELDS." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 02 (June 2006): 263–71. http://dx.doi.org/10.1142/s0219691306001221.

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A discrete wavelet transform is one of the effective methodologies for compressing the image data and extracting the major characteristics from various data, but it always requires a number of target data composed of a power of 2. To overcome this difficulty without losing any original data information, we propose here a novel approach based on the Fourier transform. The key idea is simple but effective because it keeps all of the frequency components comprising the target data exactly. The raw data is firstly transformed to the Fourier coefficients by Fourier transform. Then, the inverse Fourier transform makes it possible to the number of data comprising a power of 2. We have applied this interpolation for the wind vector image data, and we have tried to compress the data by the multiresolution analysis by using the three-dimensional discrete wavelet transform. Several examples demonstrate the usefulness of our new method to work out the graphical communication tools.

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EHLER, MARTIN, and KARSTEN KOCH. "THE CONSTRUCTION OF MULTIWAVELET BI-FRAMES AND APPLICATIONS TO VARIATIONAL IMAGE DENOISING." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 03 (May 2010): 431–55. http://dx.doi.org/10.1142/s0219691310003560.

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We remove noise from images by solving a parameter depending variational problem. The choice of the parameter is essential for the success of the approach, and in order to compute a solution, the problem must be discretized. It is commonly known that the parameter choice according to the H-curve criterion performs well in combination with discretizations derived from a dyadic orthonormal wavelet basis. However, the concept of orthonormal wavelet bases is restrictive and bears limitations. In order to have a more flexible tool, we construct new nondyadic wavelet bi-frames by convolving scalar wavelets with wavelet vectors. We discretize the variational problem by these new bi-frames, and we verify that the H-curve method performs well for this much more flexible discretization technique.

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Yang, Hang, Xunbo Li, Bo Huang, Wenjie Yu, and Zhenlin Wang. "A Novel Sensor Deployment Method Based on Image Processing and Wavelet Transform to Optimize the Surface Coverage in WSNs." Chinese Journal of Electronics 25, no. 3 (May 1, 2016): 495–502. http://dx.doi.org/10.1049/cje.2016.05.015.

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FREEDEN, WILLI, and CARSTEN MAYER. "MODELING TANGENTIAL VECTOR FIELDS ON REGULAR SURFACES BY MEANS OF MIE POTENTIALS." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 03 (May 2007): 417–49. http://dx.doi.org/10.1142/s0219691307001835.

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By means of the limit and jump relations of classical potential theory with respect to the vectorial Helmholtz equation, a wavelet approach is established on a regular surface. The multiscale procedure is constructed in such a way that the emerging scalar, vectorial and tensorial potential kernels act as scaling functions. Corresponding wavelets are defined via a canonical refinement equation. A tree algorithm for fast decomposition of a tangential complex-valued vector field given on a regular surface is developed based on numerical integration rules. Some numerical test examples conclude the paper.

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Wakin, Michael. "Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity (Starck, J.-L., et al; 2010) [Book Reviews]." IEEE Signal Processing Magazine 28, no. 5 (September 2011): 144–46. http://dx.doi.org/10.1109/msp.2011.941842.

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Ayache, Antoine, and Céline Esser. "A useful result related with zeros of continuous compactly supported mother wavelets." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 05 (August 28, 2017): 1750044. http://dx.doi.org/10.1142/s0219691317500448.

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In the last two decades, wavelet bases and associated methodologies have become quite important in many domains, such as signal and image processing, harmonic analysis, statistics, and so on. More recently, they also turn out to be quite useful in the probabilistic framework of stochastic processes, in which, among other things, they allow to obtain fine results concerning erratic sample paths behavior. The goal of our paper is to derive a result, related with zeros of continuous compactly supported mother wavelets, which is useful in this probabilistic framework. More precisely, let [Formula: see text] be any arbitrary such wavelet; we show that being given an arbitrary point [Formula: see text] there always exists at least one integer [Formula: see text] such that [Formula: see text].

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ROŞCA, DANIELA. "PIECEWISE CONSTANT WAVELETS ON TRIANGULATIONS OBTAINED BY 1-3 SPLITTING." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 02 (March 2008): 209–22. http://dx.doi.org/10.1142/s0219691308002318.

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We construct piecewise constant wavelets on a bounded planar triangulation, the refinement process consisting of dividing each triangle into three triangles having the same area. Thus, the wavelets depend on two parameters linked by a certain relation. We perform a compression and try to compare different norms of the compression error, when one wavelet coefficient is canceled. Finally, we show how this construction can be moved on to the two-dimensional sphere and sphere-like surfaces, avoiding the distortions around the poles, which occur in other approaches. As numerical example, we perform a compression of some spherical data and calculate some norms of the compression error for different compression rates. The main advantage is the orthogonality and sparsity of the decomposition and reconstruction matrices.

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FLORINDO, JOÃO BATISTA, MÁRIO DE CASTRO, and ODEMIR MARTINEZ BRUNO. "ENHANCING MULTISCALE FRACTAL DESCRIPTORS USING FUNCTIONAL DATA ANALYSIS." International Journal of Bifurcation and Chaos 20, no. 11 (November 2010): 3443–60. http://dx.doi.org/10.1142/s0218127410027805.

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This work presents a novel approach in order to increase the recognition power of Multiscale Fractal Dimension (MFD) techniques, when applied to image classification. The proposal uses Functional Data Analysis (FDA) with the aim of enhancing the MFD technique precision achieving a more representative descriptors vector, capable of recognizing and characterizing more precisely objects in an image. FDA is applied to signatures extracted by using the Bouligand–Minkowsky MFD technique in the generation of a descriptors vector from them. For the evaluation of the obtained improvement, an experiment using two datasets of objects was carried out. A dataset was used of characters shapes (26 characters of the Latin alphabet) carrying different levels of controlled noise and a dataset of fish images contours. A comparison with the use of the well-known methods of Fourier and wavelets descriptors was performed with the aim of verifying the performance of FDA method. The descriptor vectors were submitted to Linear Discriminant Analysis (LDA) classification method and we compared the correctness rate in the classification process among the descriptors methods. The results demonstrate that FDA overcomes the literature methods (Fourier and wavelets) in the processing of information extracted from the MFD signature. In this way, the proposed method can be considered as an interesting choice for pattern recognition and image classification using fractal analysis.

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SASTRY, CHALLA S., and P. C. DAS. "WAVELET BASED MULTILEVEL BACKPROJECTION ALGORITHM FOR PARALLEL AND FAN BEAM SCANNING GEOMETRIES." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 03 (September 2006): 523–45. http://dx.doi.org/10.1142/s0219691306001427.

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In the present work, a new multilevel backprojection procedure for both parallel and fan beam geometries based on 1D MRA wavelet is derived and analyzed. It is based on the characterization property of orthonormal wavelets via their autocorrelation functions. The algorithm does not involve any wavelet-based decomposition in the normal sense, yet it uses a multiresolution formula as a crucial element in a CBP type procedure valid for both the parallel and complex fan beam geometries. The algorithm can be used for wavelet based image analysis.

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Ye, Zhijing, Hong Li, Yalong Song, Jianzhong Wang, and Jon Atli Benediktsson. "A novel semi-supervised learning framework for hyperspectral image classification." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 02 (March 2016): 1640005. http://dx.doi.org/10.1142/s0219691316400051.

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In this paper, we propose a novel semi-supervised learning classification framework using box-based smooth ordering and multiple 1D-embedding-based interpolation (M1DEI) in [J. Wang, Semi-supervised learning using multiple one-dimensional embedding-based adaptive interpolation, Int. J. Wavelets Multiresolut. Inf. Process. 14(2) (2016) 11 pp.] for hyperspectral images. Due to the lack of labeled samples, conventional supervised approaches cannot generally perform efficient enough. On the other hand, obtaining labeled samples for hyperspectral image classification is difficult, expensive and time-consuming, while unlabeled samples are easily available. The proposed method can effectively overcome the lack of labeled samples by introducing new labeled samples from unlabeled samples in a label boosting framework. Furthermore, the proposed method uses spatial information from the pixels in the neighborhood of the current pixel to better catch the features of hyperspectral image. The proposed idea is that, first, we extract the box (cube data) of each pixel from its neighborhood, then apply multiple 1D interpolation to construct the classifier. Experimental results on three hyperspectral data sets demonstrate that the proposed method is efficient, and outperforms recent popular semi-supervised methods in terms of accuracies.

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JEMAI, OLFA, MOURAD ZAIED, CHOKRI BEN AMAR, and MOHAMED ADEL ALIMI. "PYRAMIDAL HYBRID APPROACH: WAVELET NETWORK WITH OLS ALGORITHM-BASED IMAGE CLASSIFICATION." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 01 (January 2011): 111–30. http://dx.doi.org/10.1142/s0219691311003967.

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Taking advantage of both the scaling property of wavelets and the high learning ability of neural networks, wavelet networks have recently emerged as a powerful tool in many applications in the field of signal processing such as data compression, function approximation as well as image recognition and classification. A novel wavelet network-based method for image classification is presented in this paper. The method combines the Orthogonal Least Squares algorithm (OLS) with the Pyramidal Beta Wavelet Network architecture (PBWN). First, the structure of the Pyramidal Beta Wavelet Network is proposed and the OLS method is used to design it by presetting the widths of the hidden units in PBWN. Then, to enhance the performance of the obtained PBWN, a novel learning algorithm based on orthogonal least squares and frames theory is proposed, in which we use OLS to select the hidden nodes. In the simulation part, the proposed method is employed to classify colour images. Comparisons with some typical wavelet networks are presented and discussed. Simulations also show that the PBWN-orthogonal least squares (PBWN-OLS) algorithm, which combines PBWN with the OLS algorithm, results in better performance for colour image classification.

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KIMURA, MOTOAKI, MASAHIRO TAKEI, YOSHIFURU SAITO, and KIYOSHI HORII. "STUDY ON RELATIONSHIP BETWEEN CONDENSED PARTICLES AND STRUCTURE OF CONDENSATION JET USING 2D IMAGE AND DISCRETE WAVELETS MULTIRESOLUTION." International Journal of Wavelets, Multiresolution and Information Processing 04, no. 02 (June 2006): 227–38. http://dx.doi.org/10.1142/s021969130600118x.

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This paper describes the application of discrete wavelet transforms to the analysis of condensation jets in order to clarify the associated fluid and heat transfer phenomena. An experimentally-obtained, two-dimensional image of the condensation particle density around the jet was decomposed into 7 levels of resolution with their respective wavelengths. Based on the known physical characteristics of turbulent flow around the jet, levels 0 and 1 were shown to represent the large-scale components of the condensation particle density and the higher levels represent the small-scale components. From the wavelet-analyzed images, the width of the condensation zone was obtained and this compared well with the width inferred from temperature measurements. Thus, the method was verified and also provided data not available experimentally.

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JEONG, BYEONGSEON, MYUNGJIN CHOI, and HONG OH KIM. "CONSTRUCTION OF SYMMETRIC TIGHT WAVELET FRAMES FROM QUASI-INTERPOLATORY SUBDIVISION MASKS AND THEIR APPLICATIONS." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 01 (January 2008): 97–120. http://dx.doi.org/10.1142/s0219691308002240.

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This paper presents tight wavelet frames with two compactly supported symmetric generators of more than one vanishing moments in the Unitary Extension Principle. We determine all possible free tension parameters of the quasi-interpolatory subdivision masks whose corresponding refinable functions guarantee our wavelet frame. In order to reduce shift variance of the standard discrete wavelet transform, we use the three times oversampling filter bank and eventually obtain a ternary (low, middle, high) frequency scale. In applications to signal/image denoising and erasure recovery, the results demonstrate reduced shift variance and better performance of our wavelet frame than the usual wavelet systems such as Daubechies wavelets.

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PRABAKARAN, S., R. SAHU, and S. VERMA. "A WAVELET APPROACH FOR CLASSIFICATION OF MICROARRAY DATA." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 03 (May 2008): 375–89. http://dx.doi.org/10.1142/s0219691308002409.

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Microarray technologies facilitate the generation of vast amount of bio-signal or genomic signal data. The major challenge in processing these signals is the extraction of the global characteristics of the data due to their huge dimension and the complex relationship among various genes. Statistical methods are used in broad spectrum in this domain. But, various limitations like extensive preprocessing, noise sensitiveness, requirement of critical input parameters and prior knowledge about the microarray dataset emphasise the need for better exploratory techniques. Transform oriented signal processing techniques are successful in many data processing techniques like image and video processing. But, the use of wavelets in analyzing the microarray bio-signals is not sufficiently probed. The aim of this paper is to propose a wavelet power spectrum based technique for dimensionality reduction through gene selection and classification problem of gene microarray data. The proposed method was administered on such datasets and the results are encouraging. The present method is robust to noise since no preprocessing has been applied. Also, it does not require any critical input parameters or any prior knowledge about the data which is required in many existing methods.

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Torbati, Nima, and Ahmad Ayatollahi. "A transformation model based on dual-tree complex wavelet transform for non-rigid registration of 3D MRI images." International Journal of Wavelets, Multiresolution and Information Processing 17, no. 04 (July 2019): 1950025. http://dx.doi.org/10.1142/s0219691319500255.

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Image registration is regarded as an important component of medical procedures. The present study aimed to introduce a new transformation model based on dual-tree complex wavelet transform (DT-CWT). To this aim, parametric registration methods was revised based on the function expansion theory and the gradient descent algorithm was used to introduce a general formulation for transformation models based on spatio-spectral transforms. Then, the performance of the proposed method was evaluated on a public dataset of 3D real magnetic resonance images (MRI) and compared with the transformation model based on wavelets. Finally, the performance of the proposed method was compared with the current state-of-the-art methods (IRTK, SyN and SPM-DARTEL). Based on the experimental results, the proposed method could deliver superior registration performance compared with the previous methods.

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ARIVAZHAGAN, S., T. G. SUBASH KUMAR, and L. GANESAN. "TEXTURE CLASSIFICATION USING CURVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 03 (May 2007): 451–64. http://dx.doi.org/10.1142/s0219691307001847.

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Texture classification has long been an important research topic in image processing. Nowadays classification based on wavelet transform is being very popular. Wavelets are very effective in representing objects with isolated point singularities, but failed to represent line singularities. Recently, ridgelet transform which deal effectively with line singularities in 2D is introduced. But images often contain curves rather than straight lines, so curvelet transform is designed to handle it. It allows representing edges and other singularities along lines in a more efficient way when compared with other transforms. In this paper, the issue of texture classification based on curvelet transform has been analyzed. Features are derived from the sub-bands of the curvelet decomposition and are used for classification for the four different datasets containing 20, 30, 112 and 129 texture images respectively. Experimental results show that this approach allows high degree of success rate in classification to be obtained.

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SHAH, PARUL, S. N. MERCHANT, and U. B. DESAI. "FUSION OF SURVEILLANCE IMAGES IN INFRARED AND VISIBLE BAND USING CURVELET, WAVELET AND WAVELET PACKET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 02 (March 2010): 271–92. http://dx.doi.org/10.1142/s0219691310003444.

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This paper presents two methods for fusion of infrared (IR) and visible surveillance images. The first method combines Curvelet Transform (CT) with Discrete Wavelet Transform (DWT). As wavelets do not represent long edges well while curvelets are challenged with small features, our objective is to combine both to achieve better performance. The second approach uses Discrete Wavelet Packet Transform (DWPT), which provides multiresolution in high frequency band as well and hence helps in handling edges better. The performance of the proposed methods have been extensively tested for a number of multimodal surveillance images and compared with various existing transform domain fusion methods. Experimental results show that evaluation based on entropy, gradient, contrast etc., the criteria normally used, are not enough, as in some cases, these criteria are not consistent with the visual quality. It also demonstrates that the Petrovic and Xydeas image fusion metric is a more appropriate criterion for fusion of IR and visible images, as in all the tested fused images, visual quality agrees with the Petrovic and Xydeas metric evaluation. The analysis shows that there is significant increase in the quality of fused image, both visually and quantitatively. The major achievement of the proposed fusion methods is its reduced artifacts, one of the most desired feature for fusion used in surveillance applications.

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SHANKAR, B. UMA, SAROJ K. MEHER, and ASHISH GHOSH. "NEURO-WAVELET CLASSIFIER FOR MULTISPECTRAL REMOTE SENSING IMAGES." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 04 (July 2007): 589–611. http://dx.doi.org/10.1142/s0219691307001914.

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A neuro-wavelet supervised classifier is proposed for land cover classification of multispectral remote sensing images. Features extracted from the original pixels information using wavelet transform (WT) are fed as input to a feed forward multi-layer neural network (MLP). The WT basically provides the spatial and spectral features of a pixel along with its neighbors and these features are used for improved classification. For testing the performance of the proposed method, we have used two IRS-1A satellite images and one SPOT satellite image. Results are compared with those of the original spectral feature based classifiers and found to be consistently better. Simulation study revealed that Biorthogonal 3.3 (Bior3.3) wavelet in combination with MLP performed better compared to all other wavelets. Results are evaluated visually and quantitatively with two measurements, β index of homogeneity and Davies–Bouldin (DB) index for compactness and separability of classes. We suggested a modified β index in accessing the percentage of accuracy (PAβ) of the classified images also.

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Abramov, A. D., and A. I. Nikonov. "Measurement of Microrelief Parameters Based on the Correlation Method of Image Processing of the Surfaces Under Study." Measurement Techniques 61, no. 11 (February 2019): 1086–90. http://dx.doi.org/10.1007/s11018-019-01553-w.

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Journal articles on the topic 'Wavelets (Mathematics) Image processing Surfaces'

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