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Quantization (physics) - Wikipedia, the free encyclopedia The first method to be developed for quantization of field theories was canonical quantization. Canonical quantization of a field theory is analogous to the construction of quantum mechanics from classical mechanics. One also speaks of field quantization, as in the "quantization of the electromagnetic field", where one refers to photons as field "quanta" (for instance as light quanta). en.wikipedia.org /wiki/Quantization_(physics)

Quantization (image processing) - Wikipedia, the free encyclopedia A common quantization algorithm is the Octree-based algorithm, as described in the MSDN article on ASP.NET color quantization. Although more frequent in the past, nowadays color quantization with pallets of lower than 256 colours is mainly used in GIF and PNG images. Quantization techniques generally compress by compressing a range of values to a single quantum value. en.wikipedia.org /wiki/Quantization_(image_processing)

Quantization Efficiency for Eight or more Sampling Levels The quantization thresholds are shown by the vertical lines, and the zero level for signal input coincides with the central threshold, rather than with the center of a level as in Fig. For consideration of such a scheme it is necessary to know the quantization efficiency factors for the larger numbers of levels, that is, the fractions by which the signal-to-noise ratio at the correlator output is degraded by the quantization. Quantization thresholds for nine-level representation of the signal are indicated by the vertical lines. www.cv.nrao.edu /alma/almaweb/www/memos/html-memos/alma220/memo220.html

Variable Quantization In video, nonlinear quantization of the scene brightness is obtained as a side effect of the gamma correction of the source that compensates for the nonlinear "gamma" characteristic of a CRT display. Variable quantization is the main technique for controlling instantaneous bit rate in order to match average bit rate to a constant channel bit rate and to prevent buffer overflow or underflow. Nonuniform quantization can also be applied to individual coefficients of a transformed signal. www.bretl.com /mpeghtml/varquant.HTM

Quantization Quantization refers to the process of approximating the continuous set of values in the image data with a finite (preferably small) set of values. In scalar quantization, each input symbol is treated separately in producing the output, while in vector quantization the input symbols are clubbed together in groups called vectors, and processed to give the output. The input to a quantizer is the original data, and the output is always one among a finite number of levels. www.debugmode.com /imagecmp/quantize.htm

Quantization - Encyclopedia.WorldSearch In physics, quantization is either the taking of discrete rather than continuous values for some physical quantities; or the procedure to construct a quantum theory from its classical limit. In signal processing, quantization is the process of approximating a continuous signal by a set of discrete symbols or integer values. Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously. encyclopedia.worldsearch.com /quantisation.htm

Gamasutra - Features - "Image Compression with Vector Quantization" [04.16.01] Strictly speaking, quantization is the procedure of approximating continuous with discrete values; in practice, the input values to the quantization procedure are often also discrete, but with a much finer resolution than that of the output values. You can do vector quantization (VQ) too, replacing vectors from a continuous (or dense discrete) input set with vectors from a much sparser set (note that here by vector we mean an ordered set of N numbers, not just the special case of points in 3D space). By quantizing each component of the vector for itself, we gain nothing over standard scalar quantization; however, if we quantize the entire vectors, replacing them with vectors from a carefully chosen sparse nonuniform set and storing just indices into that set, we can get a much more compact representation of the image. www.gamasutra.com /features/20010416/ivanov_01.htm

Saratov State University :: Online Contester Quantization transforms each measured value x to some other value l(x) selected from the predefined set L of levels. Your task is given measures and levels sets to choose quantized value for each measure in such a way, that the deviation of quantization is minimal possible. Usually to perform the quantization the closest to the value level of the levels set is chosen. acm.sgu.ru /problem.php?contest=0&problem=205

Tips & Techniques: The Quantization Factor Sometimes you are better off avoiding quantization and fixing the rhythmic errors by either manually editing the notes one by one, or by recording a new track or portion of a track. This variation is sometimes listed as the “quantization percentage” or “quantization amount.” When you quantize notes to the nearest eighth-note at 100 percent, every note will move to its closest eighth-note position in the measure. Quantization is a mixed blessing: it can correct rhythmic inaccuracies but can also strip music of expression. www.metmagazine.com /mag/quantization_factor

Quantization - Wikipedia, the free encyclopedia Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously. This is a disambiguation page, a list of pages that otherwise might share the same title. en.wikipedia.org /wiki/Quantization

oleg-msc.html Quantization is the process of representing an image with a small number of well selected colours. The algorithm takes into account previously allocated colours in the shared colour map, thus the quantization accuracy may be improved. A new colour quantization approach is presented--the local K-means algorithm. www.cs.ualberta.ca /~graphics/alumni/thesis-abstracts/oleg-msc.html

On the Quantization of the Red-Shifted Light from Distant Galaxies Large-scale redshift quantization needed to be confirmed by analyzing redshifts of an entirely different class of objects. There is no reason why the quantization should not apply to larger collections of galaxies, so redshift differentials within small groups were collected and analyzed. Several ways can be conceived to explain this quantization. www.ldolphin.org /tifftshift.html

spie ms 1.9 The method treats each DCT coefficient as an approximation to the local response of a visual "channel." For a given quantization matrix, the DCT quantization errors are adjusted by contrast sensitivity, light adaptation, and contrast masking, and are pooled non-linearly over the blocks of the image. The estimation of the quantization matrix requires a maximum of ten (and probably many fewer) iterations, each of which consists of a modest number of simple operations on each DCT pixel. With this model we may estimate the quantization matrix for a particular image that yields minimum bit rate for a given total perceptual error, or minimum perceptual error for a given bit rate. vision.arc.nasa.gov /publications/spie93abw/spie93abw.html.d/spie93.html

lossy.html So in many cases the 8-bit quantization produced a smaller file after the lossless step, and the 8-bit quantized signals always had a smaller mean squared error than their 6-bit counterparts. Lossy compression (quantization) is feasible because of the abilities of the human auditory system. Tan quantization gives preference to the louder parts of the signal. www.owlnet.rice.edu /~elec301/Projects01/bytes_dust/info/lossy.html

High-Pass Quantization for Mesh Encoding Since high-frequency errors modify the appearance of the surface, they are highly noticeable, and commonly, this form of quantization must be done conservatively to preserve the precision of the coordinates. We show that the high-frequency quantization errors in the delta-coordinates are transformed into low-frequency errors when the quantized delta-coordinates are transformed back into standard Cartesian coordinates. In this paper we present a new quantization method for the geometry of 3D meshes, which enables aggressive quantization without significant loss of visual quality. www.cs.tau.ac.il /~sorkine/ProjectPages/Highpass

Rigidity of K-Theory under Deformation Quantization, by Jonathan Rosenberg Quantization, at least in some formulations, involves replacing some algebra of observables by a (more non-commutative) deformed algebra. From this we derive that the algebraic K-theory with finite coefficients of a deformation quantization of the functions on a compact symplectic manifold, forgetting the topology, recovers the topological K-theory of the manifold. In view of the fundamental role played by K-theory in non-commutative geometry and topology, it is of interest to ask to what extent K-theory remains "rigid" under this process. www.math.uiuc.edu /K-theory/0136

Definition: quantization quantization: A process in which the continuous range of values of an analog signal is sampled and divided into nonoverlapping (but not necessarily equal) subranges, and a discrete, unique value is assigned to each subrange. Note: An application of quantization is its use in pulse-code modulation. If the sampled signal value falls within a given subrange, the sample is assigned the corresponding discrete value for purposes of modulation and transmission. www.atis.org /tg2k/_quantization.html

Optimizing Color Quantization for ASP.NET Images (ASP.NET Technical Articles) The results of the quantization are displayed alongside the original image and one that has been quantized in GDI+ (which appears very grainy). The first is to iterate over the source, the second is to quantize the pixels and produce the resulting image and color palette. The results of the quantization process are shown below. msdn.microsoft.com /library/en-us/dnaspp/html/colorquant.asp?frame=true

Extension of Two-Stage Vector Quantization-Lattice Vector Quantization First, according to high resolution quantization theory, generalized vector quantization-lattice vector quantization (G-VQ-LVQ) is formulated in order to release the constraint of the spherical boundary for the second-stage lattice vector quantization (LVQ), which would provide possibilities of improving this kind of two-stage unstructured/structured quantizer by using more efficient LVQ. P. Zador, "Asymptotic quantization error of continuous signals and the quantization dimension," IEEE Trans. M. Eyuboglu and G. Forney Jr., "Lattice and trellis quantization with lattice- and trellis-bounded codebooks-high-rate theory for memoryless sources," IEEE Trans. www.comsoc.org /comm/private/1997/dec/1538_45comm12-pan.html

A zero-mode quantization of the Skyrmion In the semi-classical approach to the Skyrme model, nuclei are approximated by quantum mechanical states on a finite-dimensional space of field configurations; in zero-mode quantization this space is generated by rotations and isorotations. Here, simulated annealing is used to find the axially symmetric Skyrme configuration which extremizes the zero-mode quantized energy for the nucleon. www.maths.tcd.ie /report_series/abstracts/tcdm0508.html

Single-pass constant- and variable-bit-rate MPEG-2 video compression Picture quantization scalers are computed as in (23) and the macroblock-level rate-control strategy of Section 2 is used to maintain the picture targets. Therefore, a quantization scaler, larger than the values normally assigned by the CBR encoder, is assigned to pictures in soft segments. This information is then used to compute a set of optimized quantization parameters which closely match the source distribution of the video data and would provide a better compressed stream during a second-pass encoding. www.research.ibm.com /journal/rd/434/mohsenian.html

SurfWax: News, Reviews and Articles On Quantization This is the "reverse" of quantization: the coefficients are multiplied by the same scaling factor that was used in the quantizer... The demonstration of space quantization, carried out in Frankfurt, Germany, in 1922 by Otto Stern and Walther Gerlach, ranks among the dozen or so canonical experiments that ushered in the heroic age of quantum physics. The oversampling also positions the quantization noise and harmonics way up in the frequency spectrum, where they can easily be lopped off by a capacitor filter. news.surfwax.com /telecom/files/Quantization.html

Quantization Except for quantization, these steps have a clearly defined inversion, so that in the definition of the quantization matrix the key criterion is the quality difference between the original and the encoded/decoded image. [Jain89]), quantization describes a step of eliminating or reducing the relevance of coefficients that carry little information (a different, analogous quantization is found in the thresholding of coefficients in principal component analysis).   In its original meaning, quantization is the step of passing from a continuous to a discrete variable, like in analogue-to-digital signal conversion. ikpe1101.ikp.kfa-juelich.de /briefbook_data_analysis/node227.html

Vector Quantization Vector quantization (VQ) is a lossy data compression method based on the principle of block coding. Gersho and R. Gray, Vector Quantization and Signal Compression. In the earlier days, the design of a vector quantizer (VQ) is considered to be a challenging problem due to the need for multi-dimensional integration. www.data-compression.com /vq.html

Nearly Optimal Vector Quantization via Linear Programming These methods lead to the first known polynomial-time full-search vector quantization codebook design algorithm and tree pruning algorithm with provable worst-case performance guarantees. We present new vector quantization algorithms based on the theory developed by the authors. The new approach is to formulate a vector quantization problem as a 0-1 integer linear program. www.cs.duke.edu /~jsv/Papers/catalog/node75.html

Amplitude Quantization We define a quantization interval to be the range of values assigned to the same integer. To find the power in the quantization error, we note that no matter into which quantization interval the signal's value falls, the error will have the same characteristics. The plotted temperatures were quantized to the nearest degree. cnx.rice.edu /content/m0051/latest

Journal of Lie Theory , Vol. 8, No. 2, pp. 401-414, 1998 The quantization of cohomology phenomenon surfaced during the recent classification of finite-dimensional Lie algebras of first and zero order operators in two complex variables; this classification revealed that quantization holds for all two-dimensional homogeneous spaces. The present article presents the first known counter-examples to quantization of cohomology; it is shown that quantization can fail even if ${\scriptstyle\gal}$ is semi-simple, and even if the homogeneous space in question is compact. A explanation for the quantization phenomenon is given in the case of semi-simple ${\scriptstyle\gal}$. www.emis.de /journals/JLT/vol.8_no.2/15.html

[76] What is Vector Quantization? A VQ-based codec that is based on the Predictive Residual Vector Quantization is in ftp://mozart.eng.buffalo.edu/pub/prvq_codec/ VQ software is also available in ftp://isdl.ee.washington.edu/pub/VQ/ For a book on Vector Quantization, see the reference (Gersho and Gray) given in item 7 of this FAQ. Some vector quantization software for data analysis that is available in the ftp://cochlea.hut.fi/pub/ directory. A short introduction to Vector Quantization, written by Alex Zatsman : In Scalar Quantization one represents the values by fixed subset of representative values. www.faqs.org /faqs/compression-faq/part2/section-7.html

Quantization Research Demo A first version of an elaborated quantization demo allows you to explore the experimental data and results obtained. At the bottom of the demo the various experimental conditions are indicated, the ternary plot (time clumping map) shows the responses for the different stimuli. www.nici.kun.nl /mmm/quantization-demo/index.html

Modeling Shape and Topology of Low-Resolution Density Maps of Biological Macromolecules -- De-Alarcón et al. 83 (2): 619 -- Biophysical Journal The algorithm also calculates the average quantization error for each pseudo-atom, which is simply the average distance from TABLE 2 Shape stability with different initializations of vector quantization (2) A natural way for quantizing a given data space is to partition the space into groups (or clusters) in such a way that all www.biophysj.org /cgi/content/full/83/2/619

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