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We can then generate binary codeword for each symbol in the alphabet, wherein the code length of a symbol increases with its decreasing probability in a logarithmic fashion. This is called a variable-length coding. Huffman coding [2] is a familiar example of variable-length coding. It is also called entropy coding because the average code length of a large sequence approaches the entropy of the source. Then one possible set of codes for the symbols is shown in the table below. These are variable-length codes, and we see that no code is a prefix to other codes.

Hence, these codes are also known as prefix codes. Observe that the most likely symbol a2 has the least code length and the least probable symbols a1 and a3 have the largest code length. We also find that the average number of bits per symbol is 1. We will discuss source entropy in detail in Chapter 5. One drawback of Huffman coding is that the entire codebook must be available at the decoder. Depending on the number of codewords, the amount of side information about the codebook to be transmitted may be very large and the coding efficiency may be reduced.

Arithmetic coding does not require the transmission of codebook and so achieves a higher compression than Huffman coding would. For compressing textual information, there is an efficient scheme known as Lempel—Ziv LZ coding [3] method. As we are concerned only with image and video compression here, we will not discuss LZ method further.

With this short description of the various compression methods for still image and video, we can now look at the plethora of compression schemes in a tree diagram as illustrated in Figure 1. It should be pointed out that lossless compression is always included as part of a lossy compression even though it is not explicitly shown in the figure. It is used to losslessly encode the various quantized pixels or transform coefficients that take place in the compression chain. If for instance images and video are compressed using a proprietary algorithm, then decompression at the user end is not feasible unless the same proprietary algorithm is used, thereby encouraging monopolization.

Waveletdomain coding Moving frame coding A taxonomy of image and video compression methods. This will eventually open up growth potential for the technology and will benefit the consumers as the prices will go down. This has motivated people to form organizations across nations to develop solutions to interoperability.

### Still Image and Video Compression with MATLAB

MPEG [5] denotes a family of standards used to compress audio-visual information. Since its inception MPEG standard has been extended to several versions. MPEG-1 was meant for video compression at about 1. MPEG-7 is more on standardization of description of multimedia information rather than compression. It is intended for enabling efficient search of multimedia contents and is aptly called multimedia content description interface.

MPEG aims at enabling the use of multimedia sources across many different networks and devices used by different communities in a transparent manner. This is to be accomplished by defining the entire multimedia framework as digital items. It describes image sampling and quantization schemes followed by various color coordinates used in the representation of color images and various video formats.

Unitary transforms, especially the DCT, are important compression vehicles, and so in Chapter 3, we will define the unitary transforms and discuss their properties. We will then describe image transforms such as KLT and DCT and illustrate their merits and demerits by way of examples.

## Still Image and Video Compression with MATLAB

In Chapter 4, 2D DWT will be defined along with methods of its computation as it finds extensive use in image and video compression. Chapter 5 starts with a brief description of information theory and source entropy and then describes lossless coding methods such as Huffman coding and arithmetic coding with some examples. It also shows examples of constructing Huffman codes for a specific image source. We will then develop the idea of predictive coding and give detailed descriptions of DPCM in Chapter 6 followed by transform domain coding procedures for still image compression in Chapter 7.

Chapter 8 deals with image compression in the wavelet domain as well as JPEG standard.

1. Macroeconomic Foundations of Macroeconomics (Routledge Frontiers of Political Economy).
2. Very High Angular Resolution Imaging: Proceedings of the 158th Symposium of the International Astronomical Union, held at the Women’s College, University of Sydney, Australia, 11–15 January 1993.
3. Quantum Dots (NanoScience and Technology).
4. Still Image and Video Compression with MATLAB by K. S. Thyagarajan - joycerreromri.ga.
5. All I Need Is Money: How To Finance Your Invention;
6. Pleasure Horse (The Saddle Club, Book 51).

Video coding principles will be discussed in Chapter 9. Various motion estimation techniques will be described in Chapter 9 with several examples. Therefore, some form of data compression must be applied to the visual data before transmission or storage. In this chapter, we have introduced terminologies of lossy and lossless methods of compressing still images and video. The existing lossy compression schemes are DPCM, transform coding, and wavelet-based coding. Although DPCM is very simple to implement, it does not yield high compression that is required for most image sources.

It also suffers from distortions that are objectionable in applications such as HDTV. More recently 2D DWT has gained importance in video compression because of its ability to achieve high compression with good quality and because of the availability of a wide variety of wavelets. The examples given in this chapter show how each one of these techniques introduces artifacts at high compression ratios. In order to reconstruct images from compressed data without incurring any loss whatsoever, we mentioned two techniques, namely, Huffman and arithmetic coding.

Even though lossless coding achieves only about compression, it is necessary where no loss is tolerable, as in medical image compression. It is also used in all lossy compression systems to represent quantized pixel values or coefficient values for storage or transmission and also to gain additional compression. Theory, IT 2 , —, IRE, 40, —, Ziv and A. Theory, IT 5 , —, The sensors are made from semiconductors and may be of charge-coupled devices or complementary metal oxide semiconductor devices.

The photo detector elements in the arrays are built with a certain size that determines the image resolution achievable with that particular camera. To capture color images, a digital camera must have either a prism assembly or a color filter array CFA.

## ISBN 13: 9780470484166

The prism assembly splits the incoming light three-ways, and optical filters are used to separate split light into red, green, and blue spectral components. Each color component excites a photo sensor array to capture the corresponding image. All three-component images are of the same size. The three photo sensor arrays have to be aligned perfectly so that the three images are registered.

Cameras with prism assembly are a bit bulky and are used typically in scientific and or high-end applications. Consumer cameras use a single chip and a CFA to capture color images without using a prism assembly. The most commonly used CFA is the Bayer filter array.

The CFA is overlaid on the sensor array during chip fabrication and uses alternating color filters, one filter per pixel. This arrangement produces three-component images with a full spatial resolution for the green component and half resolution for each of the red and blue components. The advantage, of course, is the small and compact size of the camera. The disadvantage is that the resulting image has reduced spatial and color resolutions. Whether a camera is three chip or single chip, one should be able to determine analytically how the spatial resolution is related to the image pixel size.

In the following section, we will develop the necessary mathematical equations to describe the processes of sampling a continuous image and reconstructing it from its samples. Even though practical images are of finite size, we assume here that the extent of the image is infinite to be more general. In order to acquire a digital image from f x, y , a it must be discretized or sampled in the spatial coordinates and b the sample values must be quantized and represented in digital form, see Figure 2.

The process of discretizing f x, y in the two spatial coordinates is called sampling and the process of representing the sample values in digital form is known as analog-todigital conversion. Let us first study the sampling process. Since the spacing is constant the resulting sampling process is known as uniform sampling.

Further, equation 2. In an ideal image sampling, the sample width approaches zero. The sampling indicated by equation 2. Figure 2. Equation 2.

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This is done easily if we use the Fourier transform. Because the sampled image is the product of the continuous image and the sampling function as in equation 2. Since the Fourier transform of the sampled image is continuous, it is possible to recover the original continuous image from the sampled image by filtering the sampled image by a suitable linear filter.

We can state formally the sampling process with constraints on the sample spacing in the following theorem.

## Approaches to create a video in matlab - Stack Overflow

Sampling Theorem for Lowpass Image A lowpass continuous image f x, y having maximum frequencies as given in equation 2. From equation 2. Thus, the continuous image is recovered from the sampled image exactly by linear filtering when the sampling is ideal and the sampling rates satisfy the Nyquist criterion as given in equation 2.

What happens to the reconstructed image if the sampling rates are less than the Nyquist frequencies? Fx S and Fy S samples per unit distance. If the sampling rates are below the Nyquist rates, namely, Fx S and Fy S , then the continuous image cannot be recovered exactly from its samples by filtering and so the reconstructed image suffers from a distortion known as aliasing distortion.

This can be inferred from Figure 2. It is seen from Figure 2. When the sampling rates are greater than the corresponding Nyquist rates, the replicas do not overlap and there is no aliasing distortion as shown in Figure 2.