A vector quantizer maps kdimensional vectors in the vector space rk into a finite set of vectors y yi. What is the difference between scalar and vector quantization. In addition to that each element matha\in amath gets assigned a unique element mathfa\in bmath. In this chapter we shall use the ideas of the plane to develop a new mathematical concept, vector. 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. Scalar quantization how is scalar quantization abbreviated.
We will look at scalar quantization and continue with vector quantization in the. Vector quantization can lower the average distortion with the number of reconstruction levels held constant, while scalar quantization cannot. We discuss uniform quantizers but also a pdf optimized nonuniform quantizer also refered to as the max loyd quantizer. The main difference between scalar and vector quantity is associated with the direction, i.
Scalars and vectors scalars and vectors a scalar is a number which expresses quantity. Quantization of the scalar, electromagnetic and dirac fields. Quantization has applications in the areas of signal processing, speech processing and image processing. Scalars and vectors physics video scalar vs vector quantities explained, examples. Ee368b image and video compression quantization no.
A comparison of scalar and vector quantization of wavelet. On the other hand, multidimensional quantities are explained by. It will only consist of the computation of the minimum number of bits required to code the codebook without. A key issue in lvq is the choice of an appropriate measure of distance or similarity for training and classification. Quantization is the process of mapping a continuous or discrete scalar or vector, produced by a source, into a set of digital symbols that can be transmitted or stored using a nite number of bits. Lecture 6 scalar and vector quantization introduction. Vectors and scalars questions practice khan academy. Vq can achieve significant coding gains over scalar quantization, but at a price. 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. In the remainder of the paper, we discuss the representation used by aq, the lookup tablebased computation of scalar products and distances, the encoding algorithms for. As against this, vector quantity changes with the change in their magnitude, direction or both.
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. Scalars and vectors are differentiated depending on their definition. These quantities are often described as being a scalar or a vector quantity. Additive quantization for extreme vector compression. In 2d the vector can be expressed in terms of its components aa xy, and unit vectors ooij, 22 oo cos sin tan x y x y y xy x a a i a j a a a a a a a a a a. Lecture 6 scalar and vector quantization mmse scalar quantizer high rate approximation mmse scalar quantizer of various sources. The mathematics of the field quantization will remain.
Scalar and vector quantization national chiao tung university chunjen tsai 11062014. 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. The mathematics of the field quantization will remain unchanged with. Lecture 6 scalar and vector quantization introduction midrise vs.
Scalar quantity changes only when there is a change in their magnitude. We know that time passes and physical objects have mass. Midtread for symmetric distributions wenhsiao peng, ph. These two quantities, the speed and direction of the car, a magnitude and a direction together form a vector we call velocity. It can get very confusing when the terms are used interchangeably. This learning technique uses the class information to reposition the voronoi vectors slightly, so as to improve the quality of the classifier decision regions. Achieved with uniform quantizer and more quantization levels. Ee5585 data compression march 8, 20 lecture instructor. Mar 12, 2020 scalar quantization and vector quantization ppt, data compression notes edurev is made by best teachers of. Quantization outline overview of source coding systems scalar quantization vector quantization ratedistortion characterization of lossy coding. There are two types of quantization scalar quantization and vector quantization.
Build a codebook for each image and transmit the codebook with the image. In contrast, scalar quantization can utilize effectively only linear dependency and pdf shape. Introduction to vectors and scalars vectors and scalars. Samples taken from a signal are blocked a preliminary version of this paper appeared in the proc. Vector quantization, also called block quantization or pattern matching quantization is often used in lossy data compression. Changing the quantization dimension from one for scalar to multi for vec.
One important application is vector quantization, a technique used in the compression of speech and images 15. Such errors create a wideband noise called as quantization noise. Quantization of the scalar, electromagnetic and dirac. We will also talk about the principle of compounding based on which nonuniform quantizers implemented utilizing a uniform quantizer. With vector quantization, an index no longer represents a scalar value, but an entire vector. Overview of different variations of vector quantization schemes. Difference between scalar and vector quantity with. Lvq systems can be applied to multiclass classification problems in a natural way. Scalar quantization strategies build a codebook with a training set, then always encode and decode with that fixed codebook. The equation of motion in each field will contain a gravitational covariant derivative that will produce new energymomentum dispersion relation. 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. Quantization is the process of mapping a continuous or discrete scalar or vector. Scalar and vector measurements a simple tutorial answering. 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.
Jan 05, 2018 the following points are noteworthy, so far as the difference between scalar and vector quantity is concernedthe scalar quantity is described as the quantity that has only one characteristic, i. Scalar quantization an overview sciencedirect topics. Java project tutorial make login and register form step by step using netbeans and mysql database duration. 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. A scalar quantity is defined as the physical quantity that has only magnitude, for example, mass and electric charge. Reduce distinct output values to a much smaller set map an input value vector to an approximated value vector. Lecture 6 scalar and vector quantization introduction midright vs. Traditionally, discrete hidden markov models dhmm use vector quantized speech feature vectors.
Real scalar field, em field and dirac field can be quantized in gravity. May 05, 2015 this makes dealing with vector quantities a little more complicated than scalars. A scalar pdf optimized scalar quantizer, with two levels, y0 0. A\to bmath has two sets mathamath and mathbmath as domain and codomain. It is a type of quantization error, which usually occurs in analog audio signal, while quantizing it to digital. Note that the definition of a regular vector quantizer is consistent with the scalar case and. If you have studied physics, you have encountered this concept in that part of physics concerned with forces and equilibrium. The magnitude of the vector a is written as a or a. 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. Scalar and vector quantization foundation of video. For each index, output the codeword with that index into the destination image. In the case of continuous sources with values in r or rn quantization must necessarily. The vector quantity is a physical quantity which needs both magnitude and direction to define it. Vector quantization can reduce the number of reconstruction levels when distortion is held constant, while scalar quantization cannot.
For example, things like time, mass, weight, force, and electric charge, are physical quantities with which we are all familiar. Lecture 6 scalar and vector quantization nctu mapl. On the slide we list some of the physical quantities discussed in the beginners guide to aeronautics and group them into either vector or scalar quantities. Midtread quantizers midrise uniform quantizer even l 0 is a decision boundary midtread uniform quantizer odd l 0 is a reconstruction level better for small l in videoimage coding midrise vs. Perceptual vector quantization for video coding jeanmarc valin and timothy b. What is the difference between scalar function and vector. Midtread quantizers midright uniform quantizer even l 0 is a decision boundary midtread uniform quantizer odd l 0 is a reconstruction level better for small l in videoimage coding midright vs. For the canonical quantization we must use the real. A lot of mathematical quantities are used in physics to explain the concepts clearly. Ee5585 data compression march 8, 20 lecture scalar. Pdf scalar quantization of features in discrete hidden.
Scalar quantization and vector quantization ppt, data. Jan 18, 2010 scalar and vector measurements a simple tutorial answering. Scalars may or may not have units associated with them. A scalar pdfoptimized scalar quantizer, with two levels, y0 0. Jul 05, 2017 java project tutorial make login and register form step by step using netbeans and mysql database duration. This document is highly rated by students and has been viewed 875 times. We have proposed to incorporate vector quantization into hashing to address the issues of nonadaptive projection space partition and limited distance range of the previous sbq and mbd methods scalar quantization, which sig. A lowerspace vector requires less storage space, so the data is compressed. Basic concept of quantization quantization is the process of representing a large, possibly infinite, set of values with a smaller set example.
Scalars and vectors physics video scalar vs vector quantities explained, examples duration. An estimation model will be used in order to obtain the compression rate. Example of scalar and vector quantization source sequence x. Displacement, velocity, acceleration, electric field. On the other hand, multidimensional quantities are explained by vector quantity. Binary encoding and quantization yao wang tandon school of engineering, new york university yao wang, 2017 el6123. For example, in music, the signals keep changing continuously, where a regularity is not found in errors. Because quantization is a manytofew mapping, it is an inherently nonlinear and irreversible process i. 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. By definition, speed is the scalar magnitude of a velocity vector. For eachblock, find the nearest codeword in the codebook and output its index.
Additional quantization levels are used for outer part of pdf. In this firs segment we will discuss scalar quantization. The dispersion relation in each case preserves the old energy accompanied with a perturbed term. The scalar quantization will use maxs tables and the vector quantization will use the lbg algorithm 3. Reduce distinct output values to a smaller set map an input value vector to an approximated value vector. See the bibliography on the selforganizing map som and learning vector quantization lvq. We summarize the main contributions of this paper as follows. Recall that a pdf fx satisfies the following properties. Weight is a force which is a vector and has a magnitude and direction. 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.
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