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# Vector quantization

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### Vector quantization

1. 1. EFFICIENT CODEBOOK DESIGNFOR IMAGE COMPRESSIONUSING VECTOR QUANTIZATION
2. 2. CONTENTS• Introduction• Compression techniques• Types of lossless data compression• Types of lossy data compression• Vector quantization• LBG algorithm
3. 3. INTRODUCTION• Data compression is a process of encoding data so that it takes lesser storage space and lesser transmission time than the data which is not compressed.• Data compression is the art or science of representing information in a compact form.• Compression is possible because most real world data is very redundant.
4. 4. COMPRESSION TECHNIQUES• Mainly there are two types of compression techniques.1) Lossless Compression: – Lossless compression techniques involve no loss of information. If the data have been losslessly compressed, the original data can be recovered exactly from the compressed data.2) Lossy Compression: – Lossy compression techniques involve some loss of information, and data that have been compressed using lossy techniques generally cannot be recovered exactly.
5. 5. TYPES OF LOSLESS DATA COMPRESSION• Dictionary coders – Zip (file formats)• Entropy coding – Huffman coding ( simple entropy coding)• Run-length coding
6. 6. TYPES OF LOSSY DATA COMPRESSION• Scalar Quantization: – The most common type of quantization is scalar quantization. Scalar quantization, typically denoted as y =Q(x) is the process of using quantization function Q( ) to map a scalar input value x to scalar output value y.• Vector Quantization:– A vector quantizer maps k-dimensional vectors in the vector space Rk into a finite set of vectors Y = {yi: i = 1, 2, ..., N}. Each vector yi is called a code vector or a codeword. and the set of all the codewords is called a codebook.
7. 7. VECTOR QUANTIZATION• The amount of compression will be described in terms of the rate, which will be measured in bits per sample. Suppose we have a codebook of size k, and the input vector is of dimension L. We need to use [log 2 k] bits to specify which of the code-vectors was selected. The rate for an L- dimensional vector quantizer with a codebook of size K is [log 2 k]/L .
8. 8. VECOR QUANTIZATION Source output Encoder Decoder Reconstruction Find closest TableGroup Unblock code-vector lookupintovectors 5
9. 9. VECTOR QUANTIZATION ENCODING• VQ was first proposed by Gray in 1984.• First, construct codebook which is composed of codevector.• For one vector being encoding, find the nearest vector in codebook. (determined by Euclidean distance)• Replace the vector by the index in codebook.• When decoding, find the vector corresponding by the index in codebook.
10. 10. LBG ALGORITHM• Proposed by Linde, Buzo, Gray• The basic idea is to divide a group of vector. To find a most representative vector from one group. Then gather the vectors to form a codebook.
11. 11. LBG ALGORITHM1. Divide image into blocks. Then we can view one block as k-dimension vector. Ex: block: 4x4 , consider 512x512 image, which can be divided into (512x512)/(4x4)=16384 blocks. Each block can be viewed 16 dimension vector.2. Arbitrarily choose initial codebook.3. Set these initial codebook as centroids. Other vectors are grouped. Vectors are in the same group when they have the same nearest centroid.4. Again, to find new centroids for every group. Get a new codebooks. Repeat 2,3 steps until the centroids of every group converge.
12. 12. APPLICATION OF VECTORQUANTIZATION Vector quantization technique is efficiently used in various areas of biometric modalities like finger print pattern recognition ,face recognition by generating codebooks of desired size.