# - Acharya T.

ISBN 0-471-48422-9

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Detailed discussion of the principles behind the Trellis-coded quantization algorithm is out of scope for this book. For Trellis Coding algorithm and the particular version of TCQ used in JPEG2000 Part 2, the reader is referred to [10, 11] and Annex D of the Part 2 standard [2].

PART 2: EXTENSIONS 255

10.2.4 Visual Masking

The visual masking extension provides improvement of image quality over areas like texture regions with low-intensity range in an image, and robustness against variations of image complexity for a given fixed bit rate. As shown in Figure 10.1, a “point-wise extended nonlinearity” module is inserted between the forward wavelet transformation and quantization modules at the encoder, and a “masking compensation” module is added after the dequantization, prior to the inverse wavelet transformation.

Encoder -► - Decoder

Fig. 10.1 Visual masking extension.

The quality improvement of visual masking (point-wise extended nonlinearity) is achieved in two steps. The first step, self-contrast masking, applies a point-wise power function to the original wavelet coefficients Xi with a normalized unit DC gain. That is,

j/i = sign(xi)\xi\a

where a £ [0,1] is a real number. A typical value of a is 0.7 as suggested in Part 2, Annex E. The second step, neighborhood masking, normalizes y* by a neighborhood weighting factor Wi, which is a function of the magnitudes of the neighboring pixels, that is,

z=Vi_ = sign(xi)\xi\a

1 Wi Wi '

As described in Part 2, Annex E, the following weighting function for extended nonlinearity is adopted in the standard,

Wi = 1 + (a Y \xk\0)/\<t>i\

k neighborhood

where \(pi\ denotes the size of the neighborhood, a is a constant with value of (10000/2hlt-dept/l_1)^, bit-depth is the bit depth of the image component, x^ is the quantized neighboring coefficients, and f3 also assumes a value between 0 and 1. The size of the neighborhood and the parameter (3 are used to control the degree of neighborhood masking. A new marker segment VMS (Visual MaSking) is used to embed these control parameters for all tile-components in the code-stream. The presence of the VMS marker segment is signaled in the compressed file via the third bit of the capability Rsiz parameter (Rsiz3 = 1) of the SIZ marker segment.

256

BEYOND PART 1 OF JPEG2000 STANDARD

The inverse extended nonlinearity, masking compensation, is done based on the following equation,

Xi = sign(zi)[\zi\(l + (a ^ l*fc|/3)/l0il)]1/“

neighborhood

where Zi is the dequantized wavelet coefficients.

10.2.5 Arbitrary Wavelet Decomposition

Instead of symmetrical dyadic wavelet subband decomposition, that is, filtering and downsampling by a factor of two in both horizontal and vertical directions as described in Part 1 of the standard, an extension is defined in Annex F of JPEG2000 Part 2 standard that allows arbitrary (more general, not necessarily dyadic) wavelet subband decomposition. Various wavelet subbands can be obtained through combination of vertical and/or horizontal filtering and decimation. As described in Part 1, the orientation of each subband is denoted by a two-letter code, where the first letter indicates horizontal filtering and the second letter indicates vertical filtering. There are three possible letters, H, L, and X, that can be used to denote a subband in this extended mode of arbitrary decomposition. The letter H (or L) implies that high-pass (or low-pass) filtering followed by a downsampling of factor two was applied. The letter X indicates no vertical or horizontal filtering and decimation was applied. Figure 10.2 shows an example of extended 3-level wavelet decompositions. For example, the 2XH subband was obtained at the second level of decomposition by a high-pass filtering in the vertical direction (column-wise) with downsampling, and no horizontal filtering and decimation was applied.

3LX ! 3HX -----am— 2XH 1HL

1LH 1HH

Fig. 10.2 Extended 3-level wavelet subband decompositions.

The key purpose for this extension is to provide the capability of fine tuning the compression performance by providing control over the decorrelation

PART 2: EXTENSIONS 257

process. Two new marker segments, DFS (down-sampling factor styles) and ADS (arbitrary decomposition styles), along with two extended marker segments (COD and COC) are introduced in the Part 2 standard for the need of arbitrary decomposition. The application of this extension is signaled in the compressed file via the fifth bit of the capability Rsiz parameter (Rsiz$ = 1) in the SIZ marker segment.

10.2.6 Arbitrary Wavelet Transformation

As discussed in Chapter 6, Part 1 of JPEG2000 specified only two filters for discrete wavelet transform: the (9, 7) filter pair for irreversible transform and the (5, 3) filter pair for reversible transform. Extensions in Part 2 of the standard also allow employment of the user-defined arbitrary wavelet filters. In order to specify all the parameters for arbitrary wavelet filter kernels, a new marker segment, ATK (arbitrary transformation kernels), is introduced to carry information such as

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