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The luma component, which is the BW equivalent is a weighted sum of the R, G, and B components, and the chroma corresponds to the color differences with luma being absent. Specifically, luma is obtained from the gamma-corrected R, G, and. As can be seen from equation. In both cases, when all three components have unity values, the luma attains a value of 1, which corresponds to white. Similarly, when all three components are equal to zero, the luma value is also zero and corresponds to black. The chroma components are obtained from the gamma-corrected red, green, and blue components by subtracting out the luma from blue and red components.

The standard also specifies reversible color transformation, which is described in equation. In order to accommodate underflow and overflow that may occur during digital processing such as filtering some foot room and headroom are allowed in the video compression standards. In such cases, the color difference components in digital representation are denoted Cb and Cr. More precisely, for 8-bit color images an offset of 16 is added to the luma component, which is scaled by 9 so that black level corresponds to 16 and white level to Luma values above 35 are clipped to 35 and values below 16 are clipped to The chroma components are represented in offset binary form by adding 18 to 11 0.

Analysis of Image Compression Methods using DCT and Wavelet Transform in Matlab

A complete scan of the image is called a frame. InSDTV, each frame consists of 55 lines and the video is captured at the rate of 30 fps actually, at 9. The video is interlaced to mean that each frame consists of two fields called the first field and second field. The image is scanned twice successively to capture the two fields giving a field rate of 60 per second Each field is made up of 6.

In Europe, Asia, and Australia, the field rate is 50 Hz and each field is made up of In practice, a digital video is obtained as follows: A spatio-temporal image is converted into a one-dimensional time-domain signal by scanning the analog video in a raster scan order. In a TV camera, an electron beam scans an electrically charged plate on to which an image is focused, thereby generating a time-domain signal. Corresponding to an interlaced video, each field consists of alternating lines.

In order to accommodate the return of the electron beam to the left of the screen as well as to the top of the screen, horizontal and vertical synchronizing pulses are introduced into the time-domain video signal. The time-domain signal is sampled at the appropriate rate satisfying the Nyquist rate, each sample is then converted to an 8-bit or higher digital value and recorded as an array of numbers, thus yielding digital video. For more information on temporal sampling and digital conversion, readers are referred to [8]. In progressive scanning, a frame of image is scanned sequentially from left-to-right and top-to-bottom.

The two systems, namely, the interlaced and progressive scanning, are denoted by the number of lines followed by the letter i or p followed by the frame rate.

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Note that there are active lines in a frame. Similarly, 65i50 refers to the PAL system. A color video consists of luma and chroma components. Because the human visual system has a higher sensitivity to luminance than to chrominance, the chroma components are lowpass filtered and subsampled. In digital encoding of color video, the components used are Y, Cb, and Cr.

The chroma components Cb and Cr are lowpass filtered and subsampled. This gives rise to three different subsampling formats as described below.

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The term is used to indicate that for every four Y pixels, there are four Cb pixels and four Cr pixels. This scheme is typically used in video editing or digital mastering. Thus, for every four Y pixels, there are two Cb pixels and two Cr pixels. This reduces the raw data of a color image to Thus, for every four Y pixels, there is one Cb pixel and one Cr pixel.

These sampling rates are dictated by the Nyquist sampling rates. When the sampling rates are below the Nyquist rates, aliasing distortions occur. We have demonstrated the effect of undersampling in Example. Practical sampling techniques use pulse of finite spatial extent as opposed to the ideal impulse sampling. The result is the smearing of the image as shown in Example.. Even though most image acquisition devices are based on sampling using rectangular grids, image sampling using nonrectangular grids are of importance, especially in machine vision and biomedical imaging.

We have described, in particular, the linear transformation for hexagonal sampling grid and illustrated it by a couple of examples in this chapter. Image quantization follows the sampling process. It approximates the value of an analog sample and represents it in a binary number.

Learn How to Build and Analysis MATLAB Code Compress JPEG images-Using Gauss Trans. DCT

An optimal quantizer is one that minimizes the MSE between the input analog image and the output digital image and is called the Lloyd Max quantizer. Such an optimal quantizer is obtained by solving the transcental equations. An iterative procedure for solving the transcental equations called the Lloyd algorithm has been described, and the corresponding MATLAB code has been listed. Both uniform and nonuniform quantizer designs have been explained using Examples. One effect of quantizing an image coarsely is the contouring, which occurs when pixels in a neighborhood all have nearly the same value.

We showed that dithering is one way of mitigating the contouring effect and demonstrated how the dithered quantizer improves the image quality at 4 bpp Figure. In this chapter, we have also described briefly the color coordinates used in image compression as well as the interlaced and progressive scanning used in NTSC and PAL systems.

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All the examples are accompanied by the respective MATLAB code that generates all the images and various other numerical outputs. Mersereau, The processing of hexagonally sampled two dimensional signals, Proc. IEEE, , Theory, IT-8, 17 , Theory, 7 1, Gersho and R. Netravali and B. For an analog image with amplitude in the range V, design a uniform quantizer with 56 output levels by specifying the decision boundaries and output levels. Calculate the mean square error for the quantizer Show that a Laplacian random variable with unit variance can be generated from a uniformly distributed random variable U by using the transformation 1 ln U.

We have also seen that captured images can be manipulated in the spatial or pixel domain for the purpose of visual enhancement. However, certain image processing operations are more intuitive and efficient if we process the image in a different domain. For instance, digital filters are easy to design and interpret if we adopt the Fourier transform domain. Another interesting aspect of using a frequency domain representation of an image stems from the fact that it is much more efficient to decorrelate an image in the frequency domain than in the spatial domain.

This will prove to be very useful in image and video compression.

Again, it is more efficient to capture certain features of an image in the frequency domain for pattern classification and identification purposes than in the pixel domain. This is so because of the reduction of dimensions in the frequency domain and the resulting reduction in the computational load. It must be pointed out that Fourier or frequency domain is not the only alternative domain to represent images.

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In fact, any orthogonal coordinates will be suitable to represent an image. The type of domain to choose deps on the inted application. Moreover, the transformation that we choose must be linear and invertible so that we can recover the image from the transform domain. It should also be orthogonal so that one can manipulate the transformed image indepently along the different dimensions.

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With that in mind, we will study orthogonal and unitary transforms and explore their theoretical limits on achievable compression as well as their implementation issues. These basis images may be indepent of the image being transformed as in DCT, or may be computed from the image itself as in KLT. Unitary transforms have very useful properties, especially from the standpoint of image compression and we will concentrate on such transforms.

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In the following, we will describe both one-dimensional 1D and two-dimensional D unitary transforms. A is called the kernel matrix and its elements may be real or complex. The elements of y are called the transform coefficients, and the vector y is known as the transformed vector. However, a unitary transform need not be orthogonal.

The following example illustrates this statement. Example 3. We can think of the basis vectors as the discrete-time sinusoids at different frequencies and the set of transform coefficients as the unique spectral signature of the sequence when the transform is sinusoidal. In terms of W N, equation 3. One such fast algorithm is the most familiar fast Fourier transform FFT [1, ]. There are two implementations of the FFT algorithm called decimation in time and decimation in frequency, both of which use the divide and conquer rule.

Let us look at the decimation in time algorithm.