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Figure 43 An Analog Signal Sampled at Various Frequencies
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There is no requirement that the Y component be sampled at higher frequencies than the Cb and Cr components It is possible to create a JPEG file with the Cb or Cr component having a higher sampling frequency than the Y component What makes sampling frequencies confusing when programming with graphics files is that generally the data you are dealing with has already been digitized Instead of converting analog data to digital, in JPEG programming sampling is generally used to reduce the amount of data from one or more components In most applications, what you are really doing with sampling frequencies is shrinking and stretching component values across multiple pixels When an image is compressed using JPEG, each component is assigned a horizontal and vertical sampling frequency that can range from 1 to 4 The higher the sampling frequency, the more data used for the component The number of samples for a component is relative to the maximum sampling frequency in each dimension for the image Say, for example, that Y has a horizontal sampling frequency of 4, Cb 2, and Cr 1 This means that in the horizontal direction there are 2 Y component values for every Cb value and 4 for every Cr value If, for each component, the vertical sampling frequency were the same as the horizontal sampling frequency, each Y component value would be mapped to a single pixel, each Cb component to 4 pixels, and each Cr component to 16 pixels Figure 44 illustrates such a sampling The process of reducing the number of data points a component contributes is called down-sampling An encoder can implement down sampling by encoding only every second, third, or fourth pixel or by taking an average value The reverse process of stretching down-sampled pixels is called up-sampling The simplest method for implementing down sampling is to repeat a data value across multiple pixels Sometimes filtering processes are used to reduce blocking effects
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Figure 44 Component Sampling Frequencies
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Y: H=4, V=4 Cb: H=2, V=2 Cr: H=1, V=1
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Introduction to JPEG Note that it is entirely possible to create an image where the Y component is down-sampled when an image is compressed This is not normally done except for experimentation since it tends to produce images that contain flaws when decompressed Another sampling trap is that the JPEG standard does not forbid combinations of sampling frequencies that result in the need to sample fractions of pixels Suppose the Y component has a vertical sampling frequency of 3, the Cb component a sampling frequency of 2 This means that each data value for the Cb component in the vertical direction represents 1 pixels Most JPEG applications do not permit this kind of fractional sampling
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JPEG Operation Figure 45 shows the steps of JPEG encoding The following are brief descriptions of the steps Sampling The first stage in JPEG encoding is sampling In this phase pixel data is converted from the RGB to the YCbCr colorspace and down sampling is performed Discrete Cosine Transform JPEG images are compressed in 8 8 pixel blocks called data units The discrete cosine transform (DCT) converts the data unit values into a sum of cosine functions Quantization The quantization phase of JPEG compression gets rid of discrete cosine transform coefficients that are not essential for recreating a close approximation of the original Quanitization is the main process that makes JPEG a lossy compression scheme Huffman Coding The Huffman code phase encodes the quantized DCT coefficients while eliminating runs of zero values In the JPEG standard this phase is referred to as entropy coding because the JPEG standard allows arithmetic coding to be used in place of Huffman coding
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Figure 45 JPEG Encoding Overview
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Interleaved and Noninterleaved Scans
Interleaved and Noninterleaved Scans Earlier in this chapter we said that a scan could contain data for one or more components A scan with one component is referred to as noninterleaved In a noninterleaved scan, the data units are encoded one row at a time, top to bottom, left to right If a scan has data from more than one component, it is known as interleaved Interleaved scans are encoded as groups of data units known as minimum coded units, or MCUs A component's vertical sampling frequency specifics the number of data unit rows it contributes to an MCU, and its horizontal frequency gives the number of columns (In a noninterleaved scan an MCU is always I data unit) Within an MCU the data units for each component are encoded from top to bottom, left to right Components are not interleaved within an MCU Figure 46 shows how the data units would be encoded in an MCU in an image with three components and with horizontal and vertical sampling frequencies of 4 2, 2 4, and 1 1 Each tiny square represents a single pixel The thick rectangles show how sampling groups the pixels into data units The numbers show the order in which each data unit is encoded within the MCU The maximum horizontal and vertical sampling frequency values are both 4, so each MCU will represent a 32 32 (8 4 by 8 4) block of pixels The sampling frequencies for each component specify the relationship of the component to the MCU The first component has a horizontal sampling frequency of 4, so it contributes 4 columns of data units The vertical sampling frequency is 2, so the component contributes 2 rows of data units Scans are always encoded with complete MCUs If the image height or width is not a multiple of the MCU size, extra pixel values are inserted into the image data so that the compressed data always contains complete MCUs The JPEG