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Topic: Quantization

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	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.
		The input to a quantizer is the original data, and the output is always one among a finite number of levels.
		The quantization error (x - x') is used as a measure of the optimality of the quantizer and dequantizer.
	www.debugmode.com /imagecmp/quantize.htm (404 words)

	ImpulseAdventure - JPEG Quality and Quantization Tables for Digital Cameras, Photoshop
		Note that the quantization tables generated from a save within Photoshop CS are concatenated together into a single quantization table of length 132 instead of the 2 x 67 that we see in other software programs and the digital camera itself.
		The only case in which you can mathematically figure out the quantization tables from the quality setting is in programs such as Irfanview and other IJG-based JPEG encoders, where the quantization table is scaled by the quality setting (according to the function shown in the comment posted on 2006-03-07).
		Given that the quantization table coefficients are up to the encoder to specify, one should be able to select a set based off of the JPEG Annex's suggested matrix.
	www.impulseadventure.com /photo/jpeg-quantization.html (0 words)

	PlanetMath: Quantization
		Quantization is the process of obtaining a quantum system from a classical system.
		It should be emphasized the result of quantization is not unique; in fact, methods of quantization usually possess inherent ambiguities, in the sense that, while performing quantization, one usually must make choices at certain points of the process.
		This is version 1 of Quantization, born on 2005-12-25.
	planetmath.org /encyclopedia/Quantisation.html (366 words)

	Tips & Techniques: The Quantization Factor
		Quantization is a mixed blessing: it can correct rhythmic inaccuracies but can also strip music of expression.
		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.
		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.
	metmagazine.com /mag/quantization_factor (881 words)

	Quantization (physics) (Site not responding. Last check: )
		Quantization is the taking of discrete rather than continuous values for some physical quantities.
		In physics, quantization refers to the formulation of a classical theory in the formalism of quantum physics.
		quantization is a special formalism of quantum theory suited to deal with variable number of particles.
	www.serebella.com /encyclopedia/article-Quantization_(physics).html (1278 words)

	Variable Quantization (Site not responding. Last check: )
		By coarsely quantizing the less significant coefficients in a transform (less significant meaning less noticeable either because the the energy is low and/or because it is less visible/audible), the bit rate can be greatly reduced.
		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.
		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.
	www.bretl.com /mpeghtml/varquant.HTM (302 words)

	IM v6 Examples -- Color Quantization
		There color quantization is used to reduce the number of colors in a randomized image using various colorspaces.
		Secondly, as quantization is trying to pick colors that are close to the maximum number of existing color pixels in an image, this is best achieved by NOT matching a 'pure' primary or secondary color as these are the always at the extremes of the color space being used.
		This quantization color space is thus recommended when reducing the number of colors for an image you plan to save to a format with boolean or no transparency, such as GIF or XPM image formats.
	www.imagemagick.org /Usage/quantize (12178 words)

	Quantization Schemes
		In the example of the curve given in the figure, this quantization scheme gives rise to the pattern with curve points shown in magenta.
		The same idea as above is applied in this quantization scheme except that each mesh node is considered to be the center of a cricle of radius T/2 as shown in the figure below.
		It can be readily seen that the square quantization does not give any diagonal segments (assuming that the line drawing never passes through the intersection of two mesh lines), whereas they do occur in circular and grid-intersect quantizations.
	cgm.cs.mcgill.ca /~athens/cs644/Projects/2004/JunaedSattar-RafaAbsar/quan.html (429 words)

	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 (1448 words)

	JYH: Quantization in Estimation and Control
		Hodel treat the measurement quantizer as a deterministic and memoryless nonlinearity pheneomena, which lends the problem to Lyapunov-like analysis.
		The sawtooth-shaped error functions of the quantizer are not invertible at boundaries of the quantization level, but these points are a set of measure zero.
		Instead, the quantizer model is simply embedded in the observer structure, so that the estimator output is quantized in the same way that the plant output is quantized.
	www.eng.auburn.edu /~jhung/jyh_quantize.html (833 words)

	Quantization (Site not responding. Last check: )
		The process of converting a sampled sound into a digital value is termed quantization.
		In simple terms, quantization can be viewed as converting real (continuous sound), values into integer (discrete sound) values.
		Decreasing the quantization to 8-bits, to save 50% of the required storage, decreases the S/N ratio to about 50 dB, approximately the same quality as AM radio.
	ei.cs.vt.edu /~netinfo/notes/chap1/digitalsound/quantization.html (232 words)

	net.sourceforge.jiu.color.quantization (JIU API documentation)
		Performs the popularity color quantization algorithm that maps an image to the colors occurring most frequently in the input image.
		A color quantizer that maps to a palette which is equidistantly distributed in the RGB color cube.
		Quantization is usually done to reduce the amount of data necessary to represent the image.
	schmidt.devlib.org /jiu/doc/api/net/sourceforge/jiu/color/quantization/package-summary.html (261 words)

	Quantization in Comp.DSP
		I am digitizing the sampled signal be using a uniform quantizer, so the step (q) between two consective quantization levels is fixed and is "q = Vin/2^N" where 'q' is the quantization step,...
		In chapter three, the PDF of quantization error is not a gaussian.
		Randy, This was related to SNR from 16-bit quantization, and useful dynamic range limited by the quantization.
	www.dsprelated.com /comp.dsp/keyword/Quantization.php (940 words)

	4200 - Conversion Principles - Quantization
		Quantization is the process of assigning a discreet amplitude value to each discreet pulse.
		The quantizer's accuracy is defined by the size of Q. The size of Q is defined by the number of intervals available.
		Quantization error is correlated to the signal, and manifests as distortion.
	www.mtsu.edu /~djbrown/4200_Site/Conversion_Quantization.html (991 words)

	High-Pass Quantization for Mesh Encoding
		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.
		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.
	cg.cs.tu-berlin.de /~sorkine/ProjectPages/Highpass (338 words)

	Signal Quantization and Compression Overview
		Quantization is a nonlinear and irreversible operation that maps a given amplitude x(n) at time t=nT into a value x
		Nonetheless, in a linear quantization scheme, we assign as many reconstruction levels for larger amplitudes as for smaller amplitudes, which are more probable to occur.
		This scheme is equivalent to applying non-uniform quantization to the original signal, where smaller quantization levels are used for smaller values and larger quantization levels are used for larger values.
	www.ee.ucla.edu /~dsplab/sqc/over.html (719 words)

	Effects of Noise on Sampler Quantization Errors
		To investigate the generation of harmonics by quantization errors the test signal is a 20 Hz sine wave intentionally centered on one of the FFT spectrum channels to eliminate any windowing sidelobes that would obscure the sine wave's harmonics.
		All of the harmonics are definitely produced by A/D quantization because the strength of the harmonics relative to the fundamental decreases with increasing fundamental amplitude.
		An rms noise amplitude of one quantization interval corresponds to a -8 dB on the horizontal axis.
	www.cv.nrao.edu /~rfisher/SamplerErr/harmonics.html (1863 words)

	Embedded.com - Managing quantization errors in digital motor control systems (Site not responding. Last check: )
		The most critical area where quantization effects are felt is in the numerical representation of the algorithm.
		A practical way to analyze quantization errors is to study the actual digital controller using both simulation and experimental analysis.
		To compare the quantization impact among three data formats, the estimated speed responses and corresponding d- and q-axis reference currents were monitored.
	www.embedded.com /showArticle.jhtml?articleID=193302779 (1027 words)

	Reducing ADC Quantization Noise
		Because the quantization noise is highly correlated with the input sinewave—the quantization noise has the same time period as the input sinewave—spectral averaging will also raise the noise harmonic levels.
		These are both highly desirable characters for quantization noise; the first guarantees that the output of the quantizer is, on average, equal to the input; the second guarantees that there will be no "noise modulation." Noise modulation occurs when the power of the quantization noise depends on, or is modulated by, the signal.
		Wannamaker gives sufficient (but not necessary) conditions on the character of this "filtered dither" that will guarantee the resulting quantization noise power is independent of the signal, and shows that the resulting dither noise spectrum will be similar in shape to the quantization noise spectrum with the addition of a constant (in frequency) noise power.
	www.mwrf.com /Articles/Index.cfm?ArticleID=10586 (1934 words)

	NeuQuant: Neural Image Quantization
		The NeuQuant Neural-Net image quantization algorithm (© Anthony Dekker 1994) is a replacement for the common Median Cut algorithm.
		The C code for the algorithm and the matching '.h' include file are both available.
		Tiny distortions in these highlights introduced by quantization are not noticeable, although examination of the enlargements in the test images shows that NeuQuant does nevertheless minimise these distortions (compared with the other methods).
	members.ozemail.com.au /~dekker/NEUQUANT.HTML (0 words)

	Vector Quantization
		Vector quantization (VQ) is a lossy data compression method based on the principle of block coding.
		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.
		Gersho and R. Gray, Vector Quantization and Signal Compression.
	www.data-compression.com /vq.html (721 words)

	Image Processing Fundamentals - Quantization Noise
		Quantization noise is inherent in the amplitude quantization process and occurs in the analog-to-digital converter, ADC.
		The noise is additive and independent of the signal when the number of levels L >= 16.
		Quantization noise can usually be ignored as the total SNR of a complete system is typically dominated by the smallest SNR.
	www.ph.tn.tudelft.nl /Courses/FIP/noframes/fip-Quantiza.html (129 words)

	Copenhagen Interpretation of Quantum Mechanics (Stanford Encyclopedia of Philosophy)
		Planck's empirical discovery of the quantization of action requires a revision of the foundation for the use of classical concepts, because they are not all applicable at the same time.
		In experimental cases where the quantization of action plays a significant role, the application of a classical concept does not refer to independent properties of the object; rather the ascription of either kinematic or dynamic properties to the object as it exists independently of a specific experimental interaction is ill-defined.
		The quantization of action demands a limitation of the use of classical concepts so that these concepts apply only to a phenomenon, which Bohr understood as the macroscopic manifestation of a measurement on the object, i.e.
	plato.stanford.edu /entries/qm-copenhagen (4409 words)

	Definition of Quantization (image processing)
		Quantization, involved in image processing, is the process seeking to reduce the number of colors required to represent an image.
		Although more frequent in the past, currently color quantization is only used in 8-bit (256 color) images, as GIF images and some PNG images.
		An usual quantization algorithm is the Octree-based algorithm, as described in the MSDN (http://msdn.microsoft.com) article on ASP.NET color quantization
	www.wordiq.com /definition/Quantization_%28image_processing%29 (181 words)

	Quantization
		Where sampling is the process of taking a sample at regular time intervals, quantization is the process of assigning an amplitude value to that sample.
		Computers use bits to store such data and the higher the number of bits used to represent a value, the more precise the sampled amplitude will be.
		Since the original signal is continuous and can have infinite possible values, quantization error will be introduced in the approximation.
	www.cs.sfu.ca /~tamaras/digitalAudio/Quantization.html (168 words)

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