Relevant bibliographies by topics / Mellin and scale transform

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Mellin and scale transform'

Author: Grafiati
Published: 11 March 2023

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Journal articles on the topic "Mellin and scale transform"

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Pivarčiová, Elena, Daynier Rolando Delgado Sobrino, Yury Rafailovich Nikitin, Radovan Holubek, and Roman Ružarovský. "Measuring and evaluating the differences of compared images for a correct car silhouette categorization using integral transforms." Measurement Science Review 18, no. 4 (August 1, 2018): 168–74. http://dx.doi.org/10.1515/msr-2018-0024.

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Abstract The present paper focuses on the analysis of the possibilities of using integral transforms for measuring and evaluating the differences of compared images (car silhouettes) with the purpose of a correct car body categorization. Approaches such as the light intensities frequency change, the application of discrete integral transforms without the use of further supplementary information enabling automated data processing using the Fourier-Mellin transforms are used within this work. The calculation of the several metrics was verified through different combinations that implied using and not using the Hamming window and a low-pass filter. The paper introduced a method for measuring and evaluating the differences in the compared images (car silhouettes). The proposed method relies on the fact that the integral transforms have their own transformants in the case of translation, scaling and rotation, in the frequency area. Besides, the Fourier-Mellin transform was to offer image transformation that is resistant to the translation, rotation and scale.
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Xu, Qingwen, Haofei Kuang, Laurent Kneip, and Sören Schwertfeger. "Rethinking the Fourier-Mellin Transform: Multiple Depths in the Camera’s View." Remote Sensing 13, no. 5 (March 5, 2021): 1000. http://dx.doi.org/10.3390/rs13051000.

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Remote sensing and robotics often rely on visual odometry (VO) for localization. Many standard approaches for VO use feature detection. However, these methods will meet challenges if the environments are feature-deprived or highly repetitive. Fourier-Mellin Transform (FMT) is an alternative VO approach that has been shown to show superior performance in these scenarios and is often used in remote sensing. One limitation of FMT is that it requires an environment that is equidistant to the camera, i.e., single-depth. To extend the applications of FMT to multi-depth environments, this paper presents the extended Fourier-Mellin Transform (eFMT), which maintains the advantages of FMT with respect to feature-deprived scenarios. To show the robustness and accuracy of eFMT, we implement an eFMT-based visual odometry framework and test it in toy examples and a large-scale drone dataset. All these experiments are performed on data collected in challenging scenarios, such as, trees, wooden boards and featureless roofs. The results show that eFMT performs better than FMT in the multi-depth settings. Moreover, eFMT also outperforms state-of-the-art VO algorithms, such as ORB-SLAM3, SVO and DSO, in our experiments.
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Wang, Baocheng, Dandan Qu, Qing Tian, and Liping Pang. "Mellin Transform-Based Correction Method for Linear Scale Inconsistency of Intrusion Events Identification in OFPS." Photonic Sensors 8, no. 3 (May 22, 2018): 220–27. http://dx.doi.org/10.1007/s13320-018-0486-9.

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VYAS, VIBHA S., and PRITI P. REGE. "GEOMETRIC TRANSFORM INVARIANT TEXTURE ANALYSIS WITH MODIFIED CHEBYSHEV MOMENTS BASED ALGORITHM." International Journal of Image and Graphics 09, no. 04 (October 2009): 559–74. http://dx.doi.org/10.1142/s0219467809003587.

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Texture based Geometric invariance, which comprises of rotation scale and translation (RST) invariant is finding application in various areas including industrial inspection, estimation of object range and orientation, shape analysis, satellite imaging, and medical diagnosis. Moments based techniques, apart from being computationally simple as compared to other RST invariant texture operators, are also robust in presence of noise. Zernike moments (ZM) based techniques are one of the well-established methods used for texture identification. As ZM are continuous moments, when discretization is done for implementation, errors are introduced. Error, calculated as difference between theoretically computed values and simulated values is proved to be prominent for fine textures. Therefore, a novel approach to detect RST invariant textures present in image is presented in this paper. This approach calculates discrete Chebyshev moments (CM) of log-polar transformed images to achieve rotation and scale invariance. The image is made translation invariant by shifting it to its centroid. The data is collected as samples from Brodatz and Vistex data sets. Zernike moments and its modifications, along with proposed scheme are applied to the same and Performance evaluation apart from RST invariance is noise sensitivity and redundancy. The performance is also compared with circular Mellin Feature extractors.
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Monakov, A. A. "An Algorithm for Estimating the Velocity of a Moving Target Based on Mellin Matched Filter." Journal of the Russian Universities. Radioelectronics 25, no. 3 (June 27, 2022): 22–38. http://dx.doi.org/10.32603/1993-8985-2022-25-3-22-38.

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Introduction. Construction of the radar image of a moving target and estimation of its velocity in synthetic aperture radars (SAR) presents a relevant research problem. The low quality of radar imaging is frequently related to the phenomenon of range cell migration (RCM). Conventional methods for RCM compensation, which are successfully used to obtain radar images of stationary targets, fail to provide the required quality when applied to moving targets. At present, a number of algorithms are used to solve this problem. However, the majority of them employ optimization procedures when searching for estimates of unknown parameters, which fact greatly complicates their implementation. An exception is the LvD algorithm, which implements double keystone transform to construct a radar image without using complex estimate search procedures. Radar images are constructed in the coordinates "longitudinal velocity - lateral velocity", which facilitates estimation of the target velocity components.Aim. Development of an alternative algorithm based on the Mellin matched filter (MMF) for estimating the velocity and constructing the radar image of a moving target in a side-looking SAR.Materials and methods. The derived algorithm is based on the invariance of the integral Mellin transform to the signal scale and uses the MMF to estimate the target velocity components.Results. An algorithm for constructing the radar image of a moving target based on the MMF was synthesized. An analysis of the LvD algorithm showed its capacity for selecting the optimum scale factor when implementing a second KT. The conducted computer simulation of the MMF and LvD algorithms showed their equal accuracy. Under the same simulation scenarios, both algorithms yield effective estimates of the velocity components of a moving target when the signal-to-noise ratio is greater than -10 dB.Conclusion. The proposed algorithm for constructing a radar image can be used in SAR systems designed for detection and velocity estimation of a moving target.
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Chen, Hui-Chi. "Improved performance of scale-invariant pattern recognition using a combined Mellin radial harmonic function and wavelet transform." Optical Engineering 46, no. 10 (October 1, 2007): 107204. http://dx.doi.org/10.1117/1.2799534.

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Monjur, Mehjabin Sultana, Shih Tseng, Renu Tripathi, and M. S. Shahriar. "Incorporation of polar Mellin transform in a hybrid optoelectronic correlator for scale and rotation invariant target recognition." Journal of the Optical Society of America A 31, no. 6 (May 16, 2014): 1259. http://dx.doi.org/10.1364/josaa.31.001259.

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Lizzi, Fedele, Mattia Manfredonia, and Flavio Mercati. "Localizability in κ-Minkowski spacetime." International Journal of Geometric Methods in Modern Physics 17, supp01 (June 23, 2020): 2040010. http://dx.doi.org/10.1142/s0219887820400101.

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Using the methods of ordinary quantum mechanics, we study [Formula: see text]-Minkowski space as a quantum space described by noncommuting self-adjoint operators, following and enlarging T. Poulain and J.-C. Wallet, “[Formula: see text]-Poincaré invariant orientable field theories with at 1-loop: Scale-invariant couplings, preprint (2018), arXiv:1808.00350 [hep-th]. We see how the role of Fourier transforms is played in this case by Mellin transforms. We briefly discuss the role of transformations and observers.
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Padovese, L. R., N. Martin, and F. Millioz. "Time—frequency and time-scale analysis of Barkhausen noise signals." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 223, no. 5 (April 30, 2009): 577–88. http://dx.doi.org/10.1243/09544100jaero436.

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Carrying out information about the microstructure and stress behaviour of ferromagnetic steels, magnetic Barkhausen noise (MBN) has been used as a basis for effective non-destructive testing methods, opening new areas in industrial applications. One of the factors that determines the quality and reliability of the MBN analysis is the way information is extracted from the signal. Commonly, simple scalar parameters are used to characterize the information content, such as amplitude maxima and signal root mean square. This paper presents a new approach based on the time—frequency analysis. The experimental test case relates the use of MBN signals to characterize hardness gradients in a AISI4140 steel. To that purpose different time—frequency (TFR) and time-scale (TSR) representations such as the spectrogram, the Wigner-Ville distribution, the Capongram, the ARgram obtained from an AutoRegressive model, the scalogram, and the Mellingram obtained from a Mellin transform are assessed. It is shown that, due to nonstationary characteristics of the MBN, TFRs can provide a rich and new panorama of these signals. Extraction techniques of some time—frequency parameters are used to allow a diagnostic process. Comparison with results obtained by the classical method highlights the improvement on the diagnosis provided by the method proposed.
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Sasiela, Richard J., and John D. Shelton. "Transverse spectral filtering and Mellin transform techniques applied to the effect of outer scale on tilt and tilt anisoplanatism." Journal of the Optical Society of America A 10, no. 4 (April 1, 1993): 646. http://dx.doi.org/10.1364/josaa.10.000646.

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Dissertations / Theses on the topic "Mellin and scale transform"

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Pratt, John Graham le Maistre. "Application of the Fourier-Mellin transform to translation-, rotation- and scale-invariant plant leaf identification." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=33440.

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The Fourier-Mellin transform was implemented on a digital computer and applied towards the recognition and differentiation of images of plant leaves regardless of translation, rotation or scale. Translated, rotated and scaled leaf images from seven species of plants were compared: avocado ( Persea americana), trembling aspen (Populus tremuloides), lamb's-quarter (Chenopodium album), linden (Tilla americana), silver maple (Acer saccharinum), plantain (Plantago major) and sumac leaflets (Rhus typhina ). The rate of recognition was high among translated and rotated leaf images for all plant species. The rates of recognition and differentiation were poor, however, among scaled leaf images and between leaves of different species. Improvements to increase the effectiveness of the algorithm are suggested.
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Hutchison, Luke Alexander Daysh. "Fast Registration of Tabular Document Images Using the Fourier-Mellin Transform." BYU ScholarsArchive, 2004. https://scholarsarchive.byu.edu/etd/4.

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Image registration, the process of finding the transformation that best maps one image to another, is an important tool in document image processing. Having properly-aligned microfilm images can help in manual and automated content extraction, zoning, and batch compression of images. An image registration algorithm is presented that quickly identifies the global affine transformation (rotation, scale, translation and/or shear) that maps one tabular document image to another, using the Fourier-Mellin Transform. Each component of the affine transform is recovered independantly from the others, dramatically reducing the parameter space of the problem, and improving upon standard Fourier-Mellin Image Registration (FMIR), which only directly separates translation from the other components. FMIR is also extended to handle shear, as well as different scale factors for each document axis. This registration method deals with all transform components in a uniform way, by working in the frequency domain. Registration is limited to foreground pixels (the document form and printed text) through the introduction of a novel, locally adaptive foreground-background segmentation algorithm, based on the median filter. The background removal algorithm is also demonstrated as a useful tool to remove ambient signal noise during correlation. Common problems with FMIR are eliminated by background removal, meaning that apodization (tapering down to zero at the edge of the image) is not needed for accurate recovery of the rotation parameter, allowing the entire image to be used for registration. An effective new optimization to the median filter is presented. Rotation and scale parameter detection is less susceptible to problems arising from the non-commutativity of rotation and "tiling" (periodicity) than for standard FMIR, because only the regions of the frequency domain directly corresponding to tabular features are used in registration. An original method is also presented for automatically obtaining blank document templates from a set of registered document images, by computing the "pointwise median" of a set of registered documents. Finally, registration is demonstrated as an effective tool for predictive image compression. The presented registration algorithm is reliable and robust, and handles a wider range of transformation types than most document image registration systems (which typically only perform deskewing).
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Erturk, Alp. "Rotation, Scale And Translation Invariant Automatic Target Recognition Using Template Matching For Satellite Imagery." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/3/12611434/index.pdf.

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In this thesis, rotation, scale and translation (RST) invariant automatic target recognition (ATR) for satellite imagery is presented. Template matching is used to realize the target recognition. However, unlike most of the studies of template matching in the literature, RST invariance is required in our problem, since most of the time we will have only a small number of templates of each target, while the targets to be recognized in the scenes will have various orientations, scaling and translations. RST invariance is studied in detail and implemented with some of the competing methods in the literature, such as Fourier-Mellin transform and bipectrum combined with log-polar mapping. Phase correlation and normalized cross-correlation are used as similarity metrics. Encountered drawbacks were overcome with additional operations and modifications of the algorithms. ATR using reconstruction of the target image with respect to the template, based on bispectrum, log-polar mapping and phase correlation outperformed the other methods and successful recognition was realized for various target types, especially for targets on relatively simpler backgrounds, i.e. containing little or no other objects.
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Cheung, Yun Kuen. "Analysis of weighted digital sums by mellin transform /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?MATH%202009%20CHEUNG.

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Spratt, W. J. "A classical and distributed theory of Mellin multiplier transforms." Thesis, University of Strathclyde, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371980.

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Hutchison, Luke A. D. "Fast registration of tabular document images using the Fourier-Mellin Transform /." Diss., CLICK HERE for online access, 2003. http://contentdm.lib.byu.edu/ETD/image/etd404.pdf.

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Balčiūnas, Aidas. "Mellin transforms of Dirichlet L-functions." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20141209_112534-52265.

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In the thesis moromorphic continuation of modified Mellin transforms of Dirichlet L-functions to the whole complex plane have been obtained.
Disertacijoje gauta modifikuotosios Melino transformacijos L- funkcijai meromorfinis pratęsimas į visą kompleksinę plokštumą.
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Serretta, Hyram. "Investigation of ship target recognition using neural networks in conjunction with the Fourier Mellin transform." Master's thesis, University of Cape Town, 1998. http://hdl.handle.net/11427/22040.

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The purpose of this dissertation is to investigate the feasibility of using neural networks in conjunction with the Fourier Modified Direct Mellin Transform (FMDMT) for the recognition of ship targets. The FMDMT is a modification of the Direct Mellin Transform for digital implementations, and is applied to the magnitudes of the Discrete Fourier Transforms (DFT) of range profiles of ships. Necessity for the use of the FMDMT is corroborated by the fact that features can be extracted from the range profiles of targets, regardless of target aspect angle. Variation in aspect angle results in variation of the independent variable. Feature extraction is made possible by the scale invariant properties of the Mellin Transform. Substantial emphasis was placed on preprocessing techniques applied in the implementation of the FMDMT on simulated range profiles and in particular, real ship profiles. The FMDMT was thus examined extensively and utilised as it was developed and demonstrated in [20]. At the completion of this examination, the recognition procedures and methods were applied on simulated data with the aid of a radar simulator developed and adapted for this dissertation. Results of the recognition of simulated ship targets were scrutinized closely and recorded. Employment of this procedure afforded the ability to compare the recognition results for real ship data with those of simulated ship data at a later stage. Acquisition of a large database of ship profiles was made successful by a ship target data capture plan implemented at the Institute for Maritime Technology (IMT) in Simon's Town. The database included the radar range profile data for the SAS Protea and the Outeniqua, which carried out several successful full circular manoeuvres in the line of sight of the search radar utilised (Raytheon). The relevant ships performed these circular manoeuvres in order that the acquired data incorporate radar range profiles of the relevant ships at most aspect angles from 0 degrees to 360 degrees. Extensive and thorough testing of the performance of the FMDMT would thus be possible since every possible aspect angle would be scrutinized. Preprocessing of data and recognition of targets was implemented in exactly the same manner and order as was the case with the simulated ship data. Extensive examination of the FMDMT revealed that the MDMT should only be applied to one side of a real and even Fourier Transform of a ship target. Literature on the FMDMT had failed to elaborate on this point. Comparison of the recognition results for real and simulated data, indicates a great similarity in success, thus validating the methods and procedures described theoretically and adopted practically for preprocessing of the radar range profiles and recognition of the targets. In order to demonstrate the feasibility of ship target recognition using the procedures and methods incorporated in the dissertation, real ship data for an entire range of different ships should be acquired in the same manner as indicated above. Bibliography: pages 117-118.
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Nazaikinskii, Vladimir, Bert-Wolfgang Schulze, Boris Sternin, and Victor Shatalov. "Quantization of symplectic transformations on manifolds with conical singularities." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2508/.

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The structure of symplectic (canonical) transformations on manifolds with conical singularities is established. The operators associated with these transformations are defined in the weight spaces and their properties investigated.
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Tunaitytė, Ingrida. "Rymano dzeta funkcijos Melino transformacija kritinėje tiesėje." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20100903_125540-17250.

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Books on the topic "Mellin and scale transform"

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Fikioris, George. Mellin-Transform Method for Integral Evaluation. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01697-4.

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Lukkarinen, Mari. The Mellin transform of the square of Riemann's zeta-function and Atkinson's formula. Helsinki: Suomalainen Tiedeakatemia, 2005.

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Szmydt, Zofia. The Mellin transformation and Fuchsian type partial differential equations. Dordrecht: Kluwer Academic Publishers, 1992.

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Loeser, Franc̦ois. Faisceaux pervers, transformation de Mellin et déterminants. [Paris, France]: Société mathématique de France, 1996.

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Convolution and equidistribution: Sato-Tate theorems for finite-field Mellin transforms. Princeton: Princeton University Press, 2012.

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Sasiela, Richard J. Electromagnetic wave propagation in turbulence: Evaluation and application of Mellin transforms. 2nd ed. Bellingham, WA: SPIE Press, 2007.

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Sasiela, Richard J. Electromagnetic wave propagation in turbulence: Evaluation and application of Mellin transforms. 2nd ed. Bellingham, Wash: SPIE, 2007.

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Sasiela, Richard J. Electromagnetic wave propagation in turbulence: Evaluation and application of Mellin transforms. Berlin: Springer-Verlag, 1994.

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Liang-Gee, Chen, ed. VLSI design of wavelet transform: Analysis, architecture and design examples. London: Imperial College Press, 2007.

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Devinder, Gupta, and National Institute of Standards and Technology (U.S.), eds. Polystyrene films for calibrating the wavelength scale of infrared spectrophotometers - SRM 1921. Gaithersburg, MD: U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1995.

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Book chapters on the topic "Mellin and scale transform"

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Adam, Sébastien, Jean Marc Ogier, Claude Cariou, Rémy Mullot, Joël Gardes, and Jacques Labiche. "Character Recognition, Orientation, and Scale Estimation Thanks to the Fourier Mellin Transform." In Advances in Pattern Recognition, 472–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-44522-6_49.

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Davies, Brian. "The Mellin Transform." In Texts in Applied Mathematics, 195–210. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4684-9283-5_12.

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Ramaré, Olivier. "The Mellin Transform." In Excursions in Multiplicative Number Theory, 203–15. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-73169-4_20.

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Nicolas, Jean-Marie, and Jean-Luc Bernatets. "Attenuation Correction Using Mellin Transform." In Acoustical Imaging, 459–69. Boston, MA: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4613-2523-9_42.

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Crowdy, Darren. "Geometry-Fitted Fourier-Mellin Transform Pairs." In Springer Proceedings in Mathematics & Statistics, 37–53. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41945-9_2.

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Fikioris, George. "Mellin Transforms and the Gamma Function." In Mellin-Transform Method for Integral Evaluation, 5–16. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01697-4_2.

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Jorgenson, Jay, and Serge Lang. "Convolutions, Spherical Functions and the Mellin Transform." In Springer Monographs in Mathematics, 131–75. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4684-9302-3_4.

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Gourrame, Khadija, Hassan Douzi, Rachid Harba, Riad Rabia, Frederic Ros, and Mehamed ElHajji. "Image Watermarking Based on Fourier-Mellin Transform." In Lecture Notes in Computer Science, 348–56. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-51935-3_37.

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Fikioris, George. "The Mellin-Transform Method of Evaluating Integrals." In Mellin-Transform Method for Integral Evaluation, 21–24. Cham: Springer International Publishing, 2007. http://dx.doi.org/10.1007/978-3-031-01697-4_4.

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Jahan, Akbari. "Mellin Transform of Bose–Einstein Integral Functions." In Advances in Intelligent Systems and Computing, 121–28. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-5952-2_11.

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Conference papers on the topic "Mellin and scale transform"

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Sheng, Yunlong, and Henri H. Arsenault. "Scale invariance of the Mellin transform filters." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.thtt3.

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The Mellin radial harmonic filters recently reported are based on the radial Mellin transform of objects in a polar coordinate system. The filters provide scale-invariant pattern recognition by matching the angular information of the object. Phase-only Mellin filters coded similarly in the Fourier plane were also reported. But both filters have only approximative scale invariance. In their definition, a small radius r=0. The r0 remains constant for objects with different sizes, that leads to scale dependence. We show that strict scale invariance can be achieved only when the object function is constant for 0 0. We also consider the behavior of the Mellin filters as a function of the position of the polar coordinate origin. We found that the proper centers for the Mellin filters are usually located outside the object.
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Erbach, Peter S., and Don A. Gregory. "Scale invariant optical Mellin-wavelet joint transform correlation." In Aerospace/Defense Sensing and Controls, edited by David P. Casasent and Tien-Hsin Chao. SPIE, 1996. http://dx.doi.org/10.1117/12.235673.

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Mazumdar, Amartya, and Anindya S. Dhar. "VLSI implementation of discrete Mellin transform for real time scale analysis of images." In TENCON 2009 - 2009 IEEE Region 10 Conference. IEEE, 2009. http://dx.doi.org/10.1109/tencon.2009.5396057.

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McMillen, John D., and O. R. Mitchell. "The Orthonormal Fourier-Mellin Transform For Precision Scale Detection And Range Data Acquisition." In Robotics and IECON '87 Conferences, edited by David P. Casasent and Ernest L. Hall. SPIE, 1988. http://dx.doi.org/10.1117/12.942716.

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Francis, Christina Raichel, Vrinda V. Nair, and Salini Radhika. "A scale invariant technique for detection of voice disorders using Modified Mellin Transform." In 2016 International Conference on Emerging Technological Trends (ICETT). IEEE, 2016. http://dx.doi.org/10.1109/icett.2016.7873650.

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Sheng, Yunlong, and Henri H. Arsenault. "Shift invariant Fourier-Mellin features for pattern recognition." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.fp6.

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The scale-invariant and rotation-invariant Fourier-Mellin transform depends on the position of the object. This limits its field of use. We propose filters of the form rs–2 exp(jmθ) with complex-valued s = v + jw. The filter contains no object information. The correlation function of the filter with an input object at every point (x', y') in the output plane is the Fourier-Mellin transform of the object developed about the origin (x', y') of a polar coordinate system. The shift-invariant features are then extracted: these are the distances between the correlation maxima from the filters with different orders s and m and the intensities of those maxima. The logpolar coordinate transform normally used for the optical Fourier-Mellin transform is not required. The method is invariant under changes of position, scale, orientation, rotation, and intensity. It also allows input containing multiple objects simultaneously. The invariant features can be used for image classification or as inputs to neural networks for invariant associative and adaptive pattern recognition.
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Sheng, Yulong. "Orthogonal invariant Fourier-Mellin moments." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.thl1.

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Conventional image moment invariants suffer from information redundancy and are sensitive to noise. We propose new orthogonal image moments based on the function set {Q n (r)exp(jmθ)}, where (r,θ) are polar coordinates and the polynomial Q n (r) is obtained by orthogonalizing the powers {r0,r1,r2,…, r n }. The moments are rotation invariant because of the circular Fourier expansion. The scale invariance is obtained by normalizing separately the power terms r n . This behavior is similar to that of the Zernike moments, but the Zernike circle polynomials are obtained by orthogonalizing the powers {r |m |,r |m |+2,r |m |+4,…}. The new moments are based on the separable circular-Fourier and radial-Mellin transform with the power n of the r n completely independent on the m. That allows much lower order n than that used in the Zernike moment and the pseudo-Zernike moments. Thus, the new moments would be less sensitive to noise. The orthogonal Fourier-Mellin moments may be expressed and calculated in terms of the complex moments. Only the definition of the complex moments should be modified to allow real valued moment orders.
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Erturk, Alp, A. Aydin Alatan, and Tolga Ciloglu. "Rotation, scale and translation invariant automatic target recognition based on Fourier-Mellin transform and bispectrum for satellite imagery." In 2010 IEEE 18th Signal Processing and Communications Applications Conference (SIU). IEEE, 2010. http://dx.doi.org/10.1109/siu.2010.5652019.

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Mohan, N. L., K. G. Reddy, and S. V. Seshagiri‐Rao. "Use of scale and shift invariances of the Mellin‐Fourier transforms in seismics." In SEG Technical Program Expanded Abstracts 1991. Society of Exploration Geophysicists, 1991. http://dx.doi.org/10.1190/1.1889103.

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Sheng, Y., and H. H. Arsenault. "Invariant recognition using circular Fourier radial-mellin descriptors." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/oam.1985.the3.

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An invariant moment method is used to achieve image recognition and classification that is invariant under changes of position, rotation, contrast, and scale. The generalized image descriptors are calculated from circular Fourier radial Mellin transforms, which are radial moments of circular harmonic functions. The radial moments are redundant, and only one or a few orders need be used. The selection of the harmonic order depends on the geometrical properties of the image. The normalization procedure used to obtain scale and contrast invariance yields a weighting effect on the invariant features. Multiclass pattern recognition invariance under changes of position, orientation, scale, and contrast was achieved on some letters using the nearest neighbor rule. Experimental results are shown, including using the classification of images degraded by high levels of noise.
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Reports on the topic "Mellin and scale transform"

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Chaney, Ronald. Complexity as a Scale-Space for the Medial Axis Transform. Fort Belvoir, VA: Defense Technical Information Center, January 1993. http://dx.doi.org/10.21236/ada279817.

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Lei, Lydia. Three dimensional shape retrieval using scale invariant feature transform and spatial restrictions. Gaithersburg, MD: National Institute of Standards and Technology, 2009. http://dx.doi.org/10.6028/nist.ir.7625.

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Collier, Wiehrs L. VLSI (Very Large Scale Integrated Circuits) Implementation of a Quantized Sinusoid Filter Algorithm and Its Use to Compute the Discrete Fourier Transform. Fort Belvoir, VA: Defense Technical Information Center, March 1986. http://dx.doi.org/10.21236/ada168605.

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Hovakimyan, Naira, Hunmin Kim, Wenbin Wan, and Chuyuan Tao. Safe Operation of Connected Vehicles in Complex and Unforeseen Environments. Illinois Center for Transportation, August 2022. http://dx.doi.org/10.36501/0197-9191/22-016.

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Autonomous vehicles (AVs) have a great potential to transform the way we live and work, significantly reducing traffic accidents and harmful emissions on the one hand and enhancing travel efficiency and fuel economy on the other. Nevertheless, the safe and efficient control of AVs is still challenging because AVs operate in dynamic environments with unforeseen challenges. This project aimed to advance the state-of-the-art by designing a proactive/reactive adaptation and learning architecture for connected vehicles, unifying techniques in spatiotemporal data fusion, machine learning, and robust adaptive control. By leveraging data shared over a cloud network available to all entities, vehicles proactively adapted to new environments on the proactive level, thus coping with large-scale environmental changes. On the reactive level, control-barrier-function-based robust adaptive control with machine learning improved the performance around nominal models, providing performance and control certificates. The proposed research shaped a robust foundation for autonomous driving on cloud-connected highways of the future.
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Herbert, George. How Can Middle-income Countries Improve Their Skills Systems Post- COVID-19? Institute of Development Studies (IDS), February 2021. http://dx.doi.org/10.19088/k4d.2021.082.

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Vocational training systems in middle-income countries are going to face multiple challenges in the post-COVID era, notably, challenges related to (1) automation; (2) the transition to a green economy, and (3) demographic pressures. Of these, automation - linked to the burgeoning ‘fourth industrial revolution’ that is set to transform the global economy - represents the most serious challenge and is the only one of the three challenges discussed in any depth in this paper. Whilst estimates of the likely scale of automation in the coming years and decades vary widely, it appears likely that waves of automation will lead to a dramatic decline in many kinds of jobs that largely involve routine, repetitive tasks. These trends pre-date COVID-19, but the disruption caused by the pandemic provides an opportunity to prepare for these challenges by implementing vocational training system reforms as part of the Build Back Better agenda. Reforms to vocational training systems will be crucial to ensuring middle-income countries respond appropriately to accelerating labour market changes. However, they should only form a limited part of that response and need to be integrated with a wide range of other policy measures. Vocational training reform will need to occur in the context of major reforms to basic education in order to ensure that all workers are equipped with the cross-cutting cognitive and socio-emotional skills they will require to perform hard-to-automate tasks and to be able to learn and adapt rapidly in a changing economy. Middle-income countries will also likely need to progressively expand social protection schemes in order to provide a safety net for workers that struggle to adapt to changing labour market requirements.
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Yao, Yixin, Mingyuan Fan, Arnaud Heckmann, and Corazon Posadas. Transformative Solutions and Green Finance in the People’s Republic of China and Mongolia. Asian Development Bank Institute, November 2022. http://dx.doi.org/10.56506/xfvh2542.

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Asia has experienced widespread transformation and growth, accompanied by increased demographic pressure, greater intensification of agricultural production, industrialization, and urbanization. This economic growth has been very resource- and carbon-intensive, while climate change has triggered or exacerbated behaviors and defense mechanisms that have come at the expense of the natural environment. Therefore, we examine and compare three Asian Development Bank (ADB) projects in two member countries of the Central Asia Regional Economic Cooperation: one in the People’s Republic of China (PRC) and two in Mongolia that relate to sustainable green development and use innovative financial mechanisms, and behavior-changing nudges. We provide comparative analyses and aim to demonstrate effective, innovative, and sustainable green finance and green transformation approaches in these two countries to address these pressures. The ADB–PRC loan for the Anhui Huangshan Xin’an River Ecological Protection and Green Development project aims to help Huangshan municipality reduce water pollution in the Xin’an River Basin, which is part of the Yangtze River Economic Belt. The project is piloting innovative green financing mechanisms to reduce rural pollution and complement the ongoing interprovincial eco-compensation scheme while supporting green agroecological businesses through two interventions: the Green Investment Fund and the Green Incentive Mechanism. In Mongolia, ADB and the Government of Mongolia have developed two large-scale transformative projects using integrated design and innovative green financing mechanisms to leverage private sector investment: (i) Aimags and Soums Green Regional Development Investment Program, which aims to promote green urban–rural linkages, green agribusiness development, natural capital, rangeland regeneration, and soil carbon sequestration through the (ii) Ulaanbaatar Green Affordable Housing and Resilient Urban Renewal Project, which aims to transform Ulaanbaatar’s vulnerable and substandard peri-urban areas into low-carbon, resilient eco-districts that provide access to green affordable housing.
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