Quantization what if sampled value falls on midpoint
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Step-by-step explanation:
Compression
StéphaneMallat , in A Wavelet Tour of Signal Processing (Third Edition), 2009
Weighted Quantization and Regions of Interest
Visual distortions introduced by quantization errors of wavelet coefficients depend on the scale 2j. Errors at large scales are more visible than at fine scales [481]. This can be taken into account by quantizing the wavelet coefficients with intervals that depend on the scale 2j. For bit/pixel, wj = 2−j is appropriate for the three finest scales. The distortion in (10.34) shows that choosing such weights is equivalent to minimizing a weighted mean-square error.
Such a weighted quantization is implemented like in (10.35) by quantizing weighted wavelet coefficients fB[m]/wj with a uniform quantizer. The weights are inverted during the decoding process. JPEG-2000 supports a general weighting scheme that codes weighted coefficients w[m]fB[m] where w[m] can be designed to emphasize some region of interest Ω ⊂ [0, 1]2 in the image. The weights are set to w[m] = w > 1 for the wavelet coefficients where the support of intersects Ω. As a result, the wavelet coefficients inside Ω are given a higher priority during the coding stage, and the region Ω is coded first within the compressed stream. This provides a mechanism to more precisely code regions of interest in images—for example, a face in a crowd.
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