QccWAVWaveletDWT2DInt.3

NAME

QccWAVWaveletDWT2DInt, QccWAVWaveletInverseDWT2DInt - integer-valued separable 2D discrete wavelet transform and inverse transform for a 2D signal

int QccWAVWaveletDWT2DInt(QccMatrixInt matrix, int num_rows, int num_cols, int origin_row, int origin_col, int subsample_pattern_row, int subsample_pattern_col, int num_scales, const QccWAVWavelet *wavelet);
int QccWAVWaveletInverseDWT2DInt(QccMatrixInt matrix, int num_rows, int num_cols, int origin_row, int origin_col, int subsample_pattern_row, int subsample_pattern_col, int num_scales, const QccWAVWavelet *wavelet);

DESCRIPTION

QccWAVWaveletDWT2DInt() performs an integer-valued separable 2D discrete wavelet transform (DWT) of a two-dimensional signal, matrix, which is represented as a matrix of num_rows rows and num_cols columns. origin_row and origin_col indicates the row and column indices, respectively, of the upper-left corner of the image. Usually, one assumes that the upper-left corner of the image is indexed as (0, 0) - in this case, both origin_row and origin_col would be zero. num_scales gives the number of scales, or levels, of the decomposition. QccWAVWaveletDWT2DInt() implements a dyadic, or octave, decomposition of matrix; that is, the low-low subband (baseband) is recursively decomposed into a lowpass and three highpass bands for each level of decomposition, each of which being one quarter the size of the baseband that was decomposed. The output of the DWT is returned in matrix, overwriting the original input matrix. The output subbands reside in matrix with the baseband in the upper-left corner, with highpass subbands successively "nested" from the upper-left corner to lower-right corner. QccWAVWaveletDWT2DInt() calls QccWAVWaveletAnalysis2DInt(3) for each level of decomposition, using the baseband subband for the current level of decomposition as input. As a result, the transform recursively decomposes the upper-left corner of the input matrix. wavelet must indicate an integer-valued lifting scheme (see QccWAVLiftingSchemeInteger(3) ).

QccWAVWaveletInverseDWT2DInt() performs the corresponding separable 2DInt inverse DWT of matrix which is assumed to have been produced by QccWAVWaveletDWT2DInt(). num_scales gives the number of levels of decomposition that exist in matrix. QccWAVWaveletInverseDWT2DInt() calls QccWAVWaveletSynthesis2DInt(3) for each level of synthesis.

subsample_pattern_row and subsample_pattern_col indicate the even- or odd-phase subsampling to be used at each level of row and column decomposition. In most applications, even subsampling at all levels is desired, in which case both subsample_pattern_row and subsample_pattern_col should be set to zero. In more general settings, when some mixture of even- and odd-phase subsampling is desired, subsample_pattern_row and subsample_pattern_col can be integers between 0 and (2 ^ num_levels) - 1. In these integers, the jth bit (where j = 1 is the least-significant bit) indicates whether the jth level of decomposition employs even or odd subsampling (0 = even, 1 = odd). For example, if subsample_pattern_row is 5, then the first and third row decompositions use odd-phase subsampling, while all others use even subsampling.

Use QccWAVSubbandPyramidIntDWT(3) and QccWAVSubbandPyramidIntInverseDWT(3) to perform a 2D separable DWT or inverse DWT on a QccWAVSubbandPyramidInt data structure (which is the recommended way to do it, since the QccWAVSubbandPyramidInt structure stores the number of levels of decomposition along with the transform coefficients).

INTEGER-TO-INTEGER WAVELET TRANSFORMS

Transforms generally provide perfect reconstruction in that the inverse transform will perfectly invert transform coefficients into an exact representation of the original signal. However, when implemented in floating-point arithmetic, the potential for loss arises due to the limits of finite precision in both the forward and inverse transforms. On the other hand, transforms that map integer-valued signals into integer-valued transforms coefficients can guarantee perfect reconstruction, provided an inverse transform can be found. For this reason, lifting schemes, in which inverse transforms are trivial, are favored for the implementation of integer-valued wavelet transforms. Typically, the general approach proposed by Calderbank et al. is followed wherein rounding of floating-point values to integers is performed at each prediction and update step in a lifting scheme. Integer versions of several popular biorthogonal wavelets were created in this manner by Calderbank et al., as well as by Xiong et al.

In traditional floating-point lifting, the prediction and update steps are generally followed by a single application of scaling by a constant in order to produce the usual unitary normalization. This scaling step is somewhat problematic for integer-valued lifting since the scaling constant is usually not an integer. In applications wherein unitary scaling is not required (e.g., in some applications that process each subband completely independently), the scaling step is simply dropped in order to implement an integer-valued version of the transform. Alternatively, one can append three additional lifting steps to implement the scaling; these additional lifting steps can then be rendered integer-valued via appropriate rounding (e.g., Xiong et al.) making the transforms approximately normalized. This latter approach of scaling via additional lifting steps is employed in the integer-valued lifting schemes implemented in QccPack.

RETURN VALUES

These routines return 0 on success and 1 on error.

AUTHOR

Table of Contents

NAME
SYNOPSIS
DESCRIPTION
INTEGER-TO-INTEGER WAVELET TRANSFORMS
RETURN VALUES
SEE ALSO
AUTHOR

NAME

SYNOPSIS

DESCRIPTION

INTEGER-TO-INTEGER WAVELET TRANSFORMS

RETURN VALUES

SEE ALSO

AUTHOR