The quantization is an adaptive non-uniform

scalar quantization. For each biometric sample, the enrolling procedure produces a quantizing template which related with the feature vector of the biometric sample.

A residual is calculated at each node as before, but is divided by the square root of the corresponding residual variance estimate prior to the scalar quantization operation.

It has been shown [12] that for encoding memoryless sources with R bits per sample using a reproduction alphabet with [2.sup.R+1] symbols, TCQ requires only 4 multiplies, 2N + 4 adds, N compares, and 4 rate-(R - 1) scalar quantizations per data sample, where N is the number of states in the encoding trellis.

Neuhoff, "Low resolution

scalar quantization for Gaussian and Laplacian sources with absolute and squared distortion measures," Technical Report, 2006.

Take a 2-bit scalar quantization for example, there are 5 quantization interval and 4 quantization results, i.e., the quantization order is 4.

Then, for the proposed QF scheme, the complexity of the scalar quantization is thus analyzed here.

Besides, after nonuniform

scalar quantization and being scrambled by the couple chaotic systems, the low frequency wavelet coefficients of 7 MSBs of the stego-image are converted into binary sequence as fragile watermark to be embedded into the stego-image by an improved LSB steganographic scheme.

Neuhoff, "Asymptotic MSE distortion of mismatched uniform

scalar quantization", IEEE Trans.

Optimization of robust and switched nonuniform scalar quantization model is analyzed in [3], for the case when the power of an input signal varies in a wide range.

This paper is organized as follows: A general analysis of non-uniform scalar quantization and A-law companding is given in Section 2.

Adaptive

scalar quantization without side information // IEEE Transactions on Image Processing, 1997.--Vol.