Just as in the case of scalar quantization, we can interpret vq as the cascade of two operations. Vq concerns the mapping in a multidimensional space from a possibly continuousamplitude source ensemble to a discrete ensemble. Recall that a pdf f x satis es the following properties. Vector quantities are important in the study of motion. Difference between scalar and vector quantity with. Because quantization is a manytofew mapping, it is an inherently nonlinear and irreversible process i.
The area of vector quantization is an active one, and new techniques that use vector quantization are continually being developed. Lecture 6 scalar and vector quantization wenhsiao peng, ph. Ee5585 data compression march 8, 20 lecture scalar. We know that time passes and physical objects have mass. A vector has more than one number associated with it. So, take a look at the article provided to you, for better understanding. The length of the vector represents its magnitude and the arrow head indicates. This learning technique uses the class information to reposition the voronoi vectors slightly, so as to improve the quality of the classifier decision regions. These two quantities, the speed and direction of the car, a magnitude and a direction together form a vector we call velocity. For eachblock, find the nearest codeword in the codebook and output its index. Some examples of vector quantities include force, velocity, acceleration, displacement, and momentum. Additional quantization levels are used for outer part of pdf. The mean of vectors of each cluster replaces the centroid first.
These quantities are often described as being a scalar or a vector quantity. Vector quantization is presented as a process of redundancy removal that makes effective use of four interrelated properties of vector parameters. Vector quantization is a lossy compression technique used in speech and image coding. Jul 05, 2017 java project tutorial make login and register form step by step using netbeans and mysql database duration. In contrast, scalar quantization can utilize effectively only linear dependency and pdf shape. In this paper, we have proposed a novel quantization, namely, meanremoved product quantization for largescale image retrieval, which can be combined with any pqbased algorithm.
For each index, output the codeword with that index into the destination image. Perceptual vector quantization has been enabled by default in daala for some time now. Quantization is the process of mapping a continuous or discrete scalar or vector. Learning vector quantization lvq, different from vector quantization vq and kohonen selforganizing maps ksom, basically is a competitive network which uses supervised learning. What is the difference between a scalar and vector. Scalar and vector quantization national chiao tung university chunjen tsai 11062014. Relativistic quantum field theory i quantization of the f r e scalar ield february 14, 2008 alan guth alan guth massachusetts institute o f t echnology 8. Scalars may or may not have units associated with them. With scalar quantization, a sift feature is quantized to a descriptive and discriminative bit vector, of which the first tens of bits are taken out as code word. And weight has uniform p d f between 40 and 240 pounds. We learn a scalar quantizer for the unbalanced means of the dataset vector and employ pq or opq on the balanced residuals subsequently. Reduce distinct output values to a much smaller set map an input value vector to an approximated value vector. It has a magnitude, called speed, as well as a direction, like north or southwest or 10 degrees west of north.
Lecture 6 scalar and vector quantization mmse scalar quantizer high rate approximation mmse scalar quantizer of various sources. Learning vector quantization lvq learning vector quantization lvq is a supervised version of vector quantization that can be used when we have labelled input data. An estimation model will be used in order to obtain the compression rate. If there are much fewer reference vectors than data vectors, it is much cheaper to store. The basic concepts are illustrated by means of simple examples and. The disttance of each vector from these centroids is found and each vector is associated with a cluster. If you continue browsing the site, you agree to the use of cookies on this website. The scalar components of the vector are individually quantized in. It is the only quantization method since the removal of all scalar quantization code.
One important application is vector quantization, a technique used in the compression of speech and images 15. Vector quantization can reduce the number of reconstruction levels when distortion is held constant, while scalar quantization cannot. This function is for training a codebook for vector quantization. It has various uses in signal and image compression and in classification. Ee5585 data compression march 8, 20 lecture instructor. Vector quantization an overview sciencedirect topics. Difference between scalar and vector vector addition and subtraction solved questions mathematics and science were invented by humans to understand and describe the world around us.
Celp coding uses the vq method to compress data, such as an excitation signal, lpcs, and codebook gain. Introduction to vectors and scalars vectors and scalars. In vector quantization, a vector is selected from a finite list of possible vectors to represent an input vector of samples. Both these are examples of scalar quantizationthe input and. Purpose and scope the main purpose of this paper is to present the reader with information that can be used in making a realistic assessment of the benefits and costs of vector quantization relative to scalar quantization, especially in speech coding applications. We divide the sequence into blocks of 2 samples each, and employ a pdfoptimized vector. Vector quantization in speech coding labrosa about. Our initial approach to both scalar and vector quantization will be to minimize meansquared distortion subject to a constraint on the size of the quantization alphabet. Lvq systems can be applied to multiclass classification problems in a natural way. Lecture 6 scalar and vector quantization introduction. Show full abstract and nonuniform scalar quantization, and then vector quantization. For a source with arbitrary pdf, when the rate is high. Mathematics and science were invented by humans to understand and describe the world around us. Achieved with uniform quantizer and more quantization levels.
For example, things like time, mass, weight, force, and electric charge, are physical quantities with which we are all familiar. Samples taken from a signal are blocked a preliminary version of this paper appeared in the proc. The quantization of a massless conformally coupled scalar. Scalar quantization strategies build a codebook with a training set, then always encode and decode with that fixed codebook. It works by dividing a large set of points vectors into groups having approximately the same number of points. In this chapter, we begin our study of quantization, one of the simplest and. A lot of mathematical quantities are used in physics to explain the concepts clearly. You can have more that two numbers associated with a vector.
It will only consist of the computation of the minimum number of bits required to code the codebook without. Quantization outline overview of source coding systems scalar quantization vector quantization ratedistortion characterization of lossy coding. Massachusetts institute of technology physics department 8. Many notions introduced for scalar quantization extend in a straightforward way to vector quantization. May 30, 2019 difference between vector quantization and scalar quantization 1. Gamasutra image compression with vector quantization. A scalar quantity is a one dimensional measurement of a quantity, like temperature, or mass. Assuming that you know the pdf of the samples to be quantized. Furthermore, a novel soft quantization strategy is applied in scalar quantization to. Convert each index value into quantized output value. The purpose of vector quantization is to compress vectorial data. An analysis raja balasubramanian, member, zeee, charles a. A vector quantizer maps kdimensional vectors in the vector space rk into a finite set of vectors y yi. Scalar quantization for large scale image search wengang zhou1, yijuan lu2, houqiang li3.
A vector can be conveniently represented by a straight line with an arrow head. The code below shows how the quantiz function uses partition and codebook to map a real vector, samp, to a new vector, quantized, whose entries are either 1, 0. A vector quantity has a direction and a magnitude, while a scalar has only a magnitude. Changing the quantization dimension from one for scalar to multi for vec. Our quantizer is independent of collections of images. It works by encoding values from a multidimensional vector space into a finite set of values from a discrete subspace of lower dimension. For the canonical quantization we must use the real. Scalar and vector quantization foundation of video. Scalars and vectors scalar quantities physical quantities that require only a number and a unit for their.
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. There are two types of quantization scalar quantization and vector quantization. The journals that report work in this area include ieee transactions on information theory, ieee transactions on communications, ieee transactions on signal processing, and ieee transactions on image processing, among others. Vector quantization, also called block quantization or pattern matching quantization is often used in lossy data compression.
The scalar quantization will use maxs tables and the vector quantization will use the lbg algorithm 3. Both these are examples of scalar quantizationthe input and output values are scalars, or single numbers. Vector quantization vq is a kind of signal compression method. Adaptive quantization we can adapt the quantizer to the statistics of the input mean, variance, pdf forward adaptive encoderside analysis divide input source in blocks analyze block statistics set quantization scheme send the scheme to the decoder via side channel backward adaptive decoderside analysis adaptation based on quantizer. A key issue in lvq is the choice of an appropriate measure of distance or similarity for training and classification. Nov 17, 2011 scalar quantization, typically denoted as y qx is the process of using quantization function q to map a scalar input value x to scalar output value y.
V vn v magnitude of v n unit vector whose magnitude is one and whose direction coincides with that of v unit vector can be formed by dividing any vector, such as the geometric position vector, by its length or magnitude. Scalar quantization an overview sciencedirect topics. The magnitude of the vector a is written as a or a. For a quantizer q with quantization cells b 1, b 2 and reconstruction points a 1, a 2, one may introduce the quadratic distortion measure. Lecture 6 scalar and vector quantization introduction quantization lossy compression method reduce distinct output values to a much smaller set map an input value vector to an approximated value vector approaches scalar quant. Scalars and vectors scalars and vectors a scalar is a number which expresses quantity. Artem mosesov scalar quantization basics being a subset of vector quantization, scalar quantization deals with quantizing a string of symbols random variables by addressing one symbol at a time as opposed to the entire string of symbols. In scalar quantization, a scalar value is selected from a finite list of possible values to represent a sample. Basic concept of quantization quantization is the process of representing a large, possibly infinite, set of values with a smaller set example. For a layperson, the two terms, are same, but in the world of physics, there is a huge difference between scalar and vector quantity. Such a source is modeled as a realvalued random variable, thus fully characterized by a probability density function pdf f x. Scalar quantization, typically denoted as y qx is the process of using quantization function q to map a scalar input value x to scalar output value y. Vector quantization can lower the average distortion with the number of reconstruction levels held constant, while scalar quantization cannot. What is the difference between scalar and vector quantization.
See the bibliography on the selforganizing map som and learning vector quantization lvq. We will look at scalar quantization and continue with vector quantization in the. D multimedia architecture and processing laboratory mapl department of computer science, national chiao tung university. It is the lossy version of a singlesymbol method shannon also proved that for lossy we can achieve the theoretical bound on compression rd curve via blocking taken to the limit this blocking idea motivates vector quantization. Vector quantization vq is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. The data set is split to two clusters, first, and the mean of each cluster is found centroids.
A few examples of these include force, speed, velocity and work. The mathematical quantities explaining the motion of a body are bifurcated into two groups, i. Allebach, fellow, zeee abstruct we propose an efficient vector quantization vq technique that we call sequential scalar quantization ssq. Meanremoved product quantization for largescale image. We may define it as a process of classifying the patterns where each output unit represents a class. Our initial approach to both scalar and vector quantization will be to minimize meansquared. A note on learning vector quantization 221 where px is the probability distribution of the input patterns and ws are the reference or codebook vectors and sx is defined by iix wsox i i ix will for alit. The general idea is to nd a good set of reference vectors and then replace each data vector simply by the index of its best reference vector.
Quantization has applications in the areas of signal processing, speech processing and image processing. Build a codebook for each image and transmit the codebook with the image. Finish the distance moved scalar thethe displacementdisplacement vectorvector the displacement vector start 2. Jan 05, 2018 the mathematical quantities explaining the motion of a body are bifurcated into two groups, i. Lecture 6 scalar and vector quantization introduction quantization lossy compression method reduce distinct output values to a much smaller set map an input valuevector to an approximated valuevector approaches scalar quant. All the code can be found in the daala git repository, in the pvq. Vector quantization vq is a critical step in representing signals in digital form for computer processing. Recall that a pdf fx satisfies the following properties.
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